The attitude dynamics and orbit dynamics of large rigid space structures are coupled with each other under gravity gradient, which may affect the stability of the large rigid space structures. In this paper, the gravity gradient stability of a large rigid space structure is studied under both small and large disturbances. Based on the rigid body dynamics and orbit dynamics, an accurate dynamic model without any linearization of the large rigid space structure is established via the natural coordinate formulation (NCF), which is able to describe the large overall motions of the structures. By using the generalized-α algorithm, the gravity gradient stability of the large rigid space structure is simulated and analyzed via various examples, including the influence of large disturbance angles, the positions at the stabilization and unstabilization regions. Finally, the relationship between spinning stability and gravity gradient stability is also investigated via a large spinning space structure.

The awareness of the vulnerability of existing structures under both seismic and energy viewpoints highlight the need to develop integrated retrofit solutions combining the structural and thermal performances. In this perspective, the study explores the efficacy of the Resisto 5.9 Tube system, a seismic coat that improves the seismic behaviour of masonry and reinforced concrete (RC) structures, also enhancing their energy performances, thanks to the thermal coat integrated in the basic steel system. The research involves the application of a design procedure specifically developed for this retrofit system from the seismic perspective. Once all the system elements are designed, non-linear static analyses are performed with a Finite Element software comparing the building’s seismic performances before and after the application of Resisto 5.9 Tube. The results demonstrate a significant increase in seismic safety coefficient, proving that this intervention type can be useful to obtain the seismic upgrading of existing RC buildings.

Motivated by the PEACOC project on metal recovery from solid wastes, an innovative magnetic density separation (MDS) process has been developed for granular material sorting. It has intrinsic advantages over the existing industrialized MDS by eliminating fluid turbulence and particle jamming problems. The new MDS applies an inclined planar magnet and a horizontal basin containing a static magnetic fluid as the separation medium. A particle sliding phenomenon is identified as a feature of the process which could help the separation. The MDS successfully sorted shredded PCBAs to concentrate valuable metals and sorted shredded wires to reduce metallic contaminants in the plastic fractions. A pilot scale facility is introduced to show the design to achieve continuous production and to reduce the consumption of ferrofluid.

Branching patterns are ubiquitous in nature, consequently over the years many researchers have tried to characterize the complexity of their structures. Due to their hierarchical nature and resemblance to fractal trees, they are often thought to have fractal properties, however their non-homogeneity (i.e., lack of strict self-similarity) is often ignored. In this paper we review and examine the use of the box-counting and sandbox methods to estimate the fractal dimensions of branching structures. We highlight the fact that these methods rely on an assumption of self-similarity that is not present in branching structures due to their non-homogeneous nature. Looking at the local slopes of the log-log plots used by these methods reveals the problems caused by the non-homogeneity. Finally, we examine the role of the canopies (endpoints or limit points) of branching structures in the estimation of their fractal dimensions.

Fractal array antennas are multiband arrays having ultra wide band and space filling facility. But Side lobe levels and large number of antenna elements are the major designing challenges of these arrays. In this paper, design and analysis of octagonal fractal array antenna is investigated with Morse-Thue fractal density tapering technique (MTFDT). Due to the proposed technique, a remarkable improvement has observed in Side lobe levels and thinning of the elements can also be attained at the various iterations of octagonal fractal array antenna. These arrays are analyzed and simulated by MATLAB-15 programming.

The effectiveness of a hybrid technique for identifying seismic damage in planar, multistory, steel X or V-braced frames is demonstrated here through an example of a six-story frame. This proposed technique, referred to as “M and P”, combines the instrumental Monitoring (M) with Pushover analysis (P). According to the methodology, the diagram of stepping eigenfrequencies of the frame in the inelastic region is initially plotted against seismic roof displacement. The fundamental natural frequency detected via the monitoring process is then utilized in this key diagram to reveal the inelastic roof displacement that corresponds to the damage state of the steel braced frame. This displacement is subsequently used as the target in the pushover analysis, facilitating the identification of seismic damage in the existing steel braced frame. Finally, the damage image is correlated with the damage stiffness matrix of the frame at the same inelastic roof displacement. The investigation results indicate that combining instrumental monitoring with pushover analysis enables accurate identification of seismic damage potential in existing steel braced frames.

Various peptides or non-structural amino acids are recognized by their specific target proteins and perform biological role in various pathways in vivo. Understanding the interactions between target protein and peptides (or non-structural amino acids) provides key information on the molecular interactions, which can be potentially translated to the development of novel drugs. However, it is experimentally challenging to determine the crystal structure of protein-peptide complexes. To obtain structural information on substrate recognition of peptide-recognizing enzyme, X-ray crystallographic studies were performed using triglycine (Gly-Gly-Gly) as main-chain of peptide. The crystal structure of Parengyodontium album Proteinase K in complex with triglcyine was determined at 1.4 Å resolution. Two different bound conformations of triglycine were observed at the substrate recognition site. The triglycine backbone forms stable interactions with β5-α4 and α5-β6 loops of main-chain. One of the triglycine-binding conformations was identical with the binding mode of a peptide-based inhibitor from a previously reported crystal structure of Proteinase K. Triglycine has potential application X-ray crystallography to identify substrate recognition sites in peptide binding enzymes.

In this work, we'll present the power spectra density, auto-correlation function, dentrended fluctuation analysis and multifractal spectrum are performed to the daily light curves of Blazars monitored by Fermi LAT. Some signs of power law are found.

The paper continues the study of efficient algorithms for the computation of zeta functions over the complex plane. We aim to apply the modifications of algorithms to the investigation of underlying fractal structures associated with the Riemann zeta function. We discuss the computational complexity and numerical aspects of the implemented algorithms based on series with binomial-like coefficients.

Carotid atherosclerotic lesions are a major cause of cerebrovascular disease (CVD). Identification and quantification of carotid plaques are important for categorizing the vulnerability of plaques for rupture and assessing the impact of treatments. The irregularity of plaque surface is associated with previous plaque rupture and plays an important role in the risk of stroke. Thus, the aim of this study is to develop and validate novel vulnerability biomarkers from three-dimensional ultrasound (3DUS) images by analyzing the surface morphological characterization of carotid plaque using fractal geometry features. 3D box-counting and 3D blanket are the two types of 3D fractal dimension that were employed to describe the smoothness of plaques. This fractal dimension analysis tool was used to evaluate the effect of atorvastatin using 3DUS carotid images, which were acquired from 6 patients treated with atorvastatin with 80 mg daily and 5 patients with placebo. The Student's T Test results showed that those two fractal features were effective for detecting the statin-related changes in carotid atherosclerosis with p<0.0068 and p<0.015 respectively, suggesting that 3D fractal dimension measurements can be used effectively to analyze the surface characteristics of carotid plaques, especially for evaluating the impact of the treatment.

Western countries are experiencing an increasing aging population, resulting in heightened disability and mobility issues. This trend is expected to escalate in the coming decades. Therefore, ensuring adequate accessibility in collective residential housing –where individuals spend much of their daily lives– is of paramount importance. This paper presents a case study focused on the accessibility of building entrances in collective residential housing in Southeast Spain, specifically in the Region of Murcia. In this region, 9.8% of the population has disabilities, and 15.75% were over 64 years old in 2020. The study began by compiling the relevant national and regional accessibility regulations for existing buildings. Subsequently, extensive fieldwork was conducted, analyzing 150 collective residential housing buildings. Based on this analysis, a set of recommendations to enhance accessibility was formulated for buildings not complying with the regulations. The results are presented and discussed in detail. The most frequent recommendation was the construction of accessible ramps, identified as the primary solution in over 40% of cases, either alone or in conjunction with other measures. In 54% of the cases, multiple interventions were necessary to achieve effective accessibility adaptation. The findings of this study could inform the development of public policies aimed at improving accessibility conditions in urban areas.

Serial femtosecond crystallography (SFX) using an X-ray free-electron laser (XFEL) enables determination of room-temperature structures without causing radiation damage. Using an optical pump-probe or mix-and-injection, SFX enables the intermediate state visualization of a molecular reaction. In SFX experiments, serial and stable microcrystal delivery to the X-ray interaction point is vital for reasonable data collection and efficient beam time. The Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL) facility established SFX instruments at a nanocrystallography and coherent imaging (NCI) experimental station. Various sample delivery methods, including injection, fixed-target scanning, and hybrid methods, have been developed and applied to collect XFEL diffraction data. Herein, we review the currently available sample delivery methods for SFX at the NCI experimental station at the PAL-XFEL. This article will help PAL-XFEL users access the SFX system for their experiments.

The age-related loss of muscle mass and strength is referred to as “sarcopenia”. The combined effect of sarcopenia and osteoporosis is a devastating threat to the old adult, accounting for reduced mobility, risk for falls and subsequent fractures. In previous studies, we observed a high degree of inter-individual variability of paraspinal muscle fatty infiltration, one most relevant index of muscle wasting. This aspect solicited us to develop a computerized method to quantitatively characterize muscle fatty infiltration in aging and diseases. Magnetic resonance images of paraspinal muscles from 58 women of different age (age range 23-85 years) and physio-pathological status (healthy young, pre-menopause, post-menopause, and os-teoporosis), were used to set up the method. It is based on fractal analysis of lean muscle area (contractile muscle) to estimate muscle fatty infiltration. In particular, lacunarity was computed by parameter β from our hyperbola model function, used to fit the GBA (gliding box algorithm) curvilinear plot. Succolarity was estimated by parameter µ, for the four main directions, through an algorithm implemented on purpose. Results show that fractal lacunarity, by quantifying muscle fatty infiltration, can discriminate be-tween osteoporosis and healthy aging while succolarity can separate the other three groups showing similar lacunarity. Therefore, fractal features of contractile muscle, by measuring fatty infiltration, can represent good indices of sarcopenia in aging and disease.

Advanced Finite Element (FE) modeling and simulations were performed on vehicular crashes into a Three-bar Metal Bridge Rail (TMBR). The FE models of a sedan, a pickup truck, and a TMBR section were adopted in the crash simulations subject to Manual for Assessing Safety Hardware (MASH) Test Level 2 (TL-2) and Test Level 3 (TL-3) requirements. The test vehicle models were first validated using full-scale physical crash tests conducted on a two-bar metal bridge using a sedan and a pickup truck with similar overall physical properties and sizes to their respective vehicles used in the simulations. The validated vehicular models were then used to evaluate the crash performance of the TMBR using MASH Evaluation Criteria for structural adequacy, occupant risk, and post-impact trajectory. The TMBR met all MASH TL-2 requirements but failed to meet the MASH TL-3 Criteria H and N requirements when impacted by the sedan. The TMBR was also evaluated under in-service conditions (behind a 1.52-m wide sidewalk) and impacted by the sedan under MASH TL-3 conditions. The simulation results showed that the TMBR behind a sidewalk met all safety requirements except for the occupant impact velocity in the longitudinal direction, which exceeded the MASH limit by 3.93%.

Entropy as a mathematical concept is the first of its own kind, and second to none. Barely one or two papers in literature have investigated fractal dimensions of very basic entropies, such as Shannon, Tsallis, and Rényi entropic expressions. This was a thoughtful inspiration to delve into a step forward towards a unified information- theoretic fractal theory. The storytelling of this current paper starts by introducing my third entropy formula, namely Ismail’s entropy, , as a novel generalization to Shannonian entropy with a visionary link to both long- and short-range interactions, (LRIs), (SRIs) respectively. Clearly, this would generate a fourfold unification with statistical mechanics as well as contemporary physics. Hence, this adds more credibility and weight for this study. The fractal dimension of , is identified in this paper. As an essential part of this work, it was influential to spotlight the importance of fractal geometry to space industry as well as education, which is crucial to develop our societies. Thus, some potential fractal applications to CubeSat Technologies and Education are highlighted. So, will the deep search for more ground-breaking research has come to an end. Certainly, not. This was another inspiration to propose new open problems to widen research gates to the scientific community for more research pathways. Consequently, the paper ends with closing remarks combined with some challenging open problems and the next phase of research.

In this paper, we make research on fractal characteristics of the superposition of fractal surfaces in the view of fractal dimension. We give the upper bound of the lower and upper Box dimension of the graph of the sum of two bivariate continuous functions and calculate the exact values of them under some particular conditions. Further, it has been proved that the superposition of two continuous surfaces cannot keep the fractal dimensions invariable unless both of them are two-dimensional. A concrete example of numerical experiment has been provided to verify our theoretical results. This study can be applied to the fractal analysis of metal fracture surfaces or computer image surfaces.

The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non extensive statistics have been formulated along the last several years, in particular a fractal structure in thermodynamics functions was recently proposed as a possible origin for non extensive statistics in physical systems. In the present work we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that evidenced the connections between those fluctuations and Tsallis statistics. Finally, the fractal scale invariance is discussed in terms of the Callan-Symanzik Equation.

Porous hierarchical structure has been widely used in engineering for its high specific strength and stiffness, improved corrosion-resistance and multifunctionality. The design of multi-scale topology optimization for such structures has been a hot topic during the past two decades. In this paper, a new hybrid MMC-density topology optimization method of cellular structures with quasi-periodic microstructures is proposed. The so-called ‘quasi-periodic’ means the microstructures in different macro points have similar topology but with different parameters. The key idea is to describe the microstructural topology using MMC and describe the micro layout using the variable density. Sensitivities of the structural compliance with respect to the two types of design variables are derived and gradient optimization method is applied to update the design variables. The presented numerical examples show that the quasi-periodic cellular structures have better performance than single-scale structures and periodic cellular structures. Numerical examples demonstrate the effectiveness of the proposed approach.

Substrate binding proteins (SBP) bind to specific ligands in the periplasmic region and bind to membrane proteins to participate in transport or signal transduction. Typical SBPs consist of two α/β domains and recognize the substrate by hinge motion between two domains. Conversely, short length Rhodothermus marinus SBP (named as RmSBP) exists around the methyl-accepting chemotaxis protein. We previously determined the crystal structure of RmSBP consisting of a single α/β domain, but the substrate recognition mechanism is still unclear. To better understand the short length RmSBP, we performed comparative structure analysis, computational substrate docking, and X-ray crystallographic study. RmSBP shares a high level of similarity in α/β domain with other SBP proteins, but it has a distinct topology in the C-term region. The substrate binding model suggested that conformational change in the peripheral region of RmSBP was required to recognize the substrate. We determined the crystal structures of RmSBP at pH 5.5, 6.0, and 7.5. RmSBP showed structural flexibility of the β1-α2 loop, β5-β6 loop, and extended C-term domain based on the electron density map and temperature B-factor analysis. These results provide information that will further the understanding of the function of the short length SBP.

The fractal dimension of is identified in this paper. More importantly, the undertaken research has shown how affects the Koch snowflake . The study has demonstrated the existence of negative values of (Koch snowflake), which connects to a considerable number of extremely intriguing mathematical and physical research areas. The information-theoretic impact on the Sierpiniski Gasket dimension , which corresponds to , was treated in a more fundamental way. Notably, the credibility of this current study adds to the existing kThe fractal dimension of is identified in this paper. More importantly, the undertaken research has shown how affects the Koch snowflake . The study has demonstrated the existence of negative values of (Koch snowflake), which connects to a considerable number of extremely intriguing mathematical and physical research areas. The information-theoretic impact on the Sierpiniski Gasket dimension , which corresponds to , was treated in a more fundamental way. Notably, the credibility of this current study adds to the existing knowledge for the information- theoretic fractal dimensions. On another applicative note, this paper offers some potential applications of fractal dimension to smart cities. The investigation of the threshold theorems for and in terms of the triad is part of the next study phase. Additionally, investigating the newly obtained 's corresponding arbitrary Sierpinski Gasket for the first time.applicative note, this paper offers some potential applications of fractal dimension to smart cities. The investigation of the threshold theorems for and in terms of the triad is part of the next study phase. Additionally, investigating the newly obtained 's corresponding arbitrary Sierpinski Gasket for the first time.

Acoustic emission monitoring (AEM) has emerged as an effective technique for detecting wire-breaks resulting from, e.g., stress corrosion cracking, and its application on prestressed concrete bridges is increasing. The success of this monitoring measure depends crucially on a carefully designed sensor layout. For this the attenuation of elastic waves within the structure’s material is determined ideally in-situ through object-related measurements with a reproducible signal source, typically a rebound-hammer. This assumes that the attenuation coefficients derived from rebound-hammer tests are comparable to those from wire-breaks, thus allowing their results to be directly applied to wire-break detection without further adjustments. This study challenges this assumption by analysing attenuation behaviour through an extensive dataset. Employing time-domain and frequency analysis, the research generates attenuation profiles from laboratory experiments and in-situ measurements across various girders and bridge structures, extracting the slope and standard deviation of the residuals. While generally validating this approach, the findings highlight differences in attenuation behaviour from among wire-break signals and rebound-hammer impulses, whereby the latter potentially underestimates the relevant attenuation of wire-breaks by approximately 20 %. Consequently, a transfer factor is proposed to adjust object-related measurement results for wire-break scenarios, including a variance of 1.0 dB/m to cover a 95 % confidence interval for sample scattering. Moreover, the anisotropic attenuation behaviour across different structures was studied, showing that transverse attenuation consistently exceeds the longitudinal, significantly influenced by structural features such as voids. In prefabricated concrete bridges with in-situ-cast concrete slabs, transverse signal transmission remains unhindered across multiple elements. Finally, the results provide a valuable reference for the design of sensor layouts in bridge monitoring, particularly benefiting scenarios where direct in-situ experiences are lacking.

Pore structure characterization and fractal analysis have great significance for understanding and evaluating tight limestone reservoirs. In this work, the pore structure of tight limestone is characterized combined with low-temperature nitrogen adsorption (LTNA) and low-field nuclear magnetic resonance (NMR), and the fractal dimension of tight limestone pore structure is discussed based on LTNA and NMR data. The results indicate that the pores of tight limestone have H3 and H4 types, the pore size distribution (PSD) of H3 type is a wave distribution ranging from 2 to 10 nm, and the PSD of H4 type is a unimodal distribution ranging from 2 to 10 nm. The transverse relaxation time (T2) spectrum of tight limestone shows single peak (DF), double peak (SF) and three peak (TF), and the T2 spectrums for micropores, mesopores and macropores range from 0.1 to 10 ms, from 10 to 100 ms, and greater than 100 ms, respectively. The LTNA fractal dimension of tight limestone (DL) ranges between 2.4446 and 2.7688, with an average of 2.5729, and the NMR fractal dimensions of micropores (DNMR1), mesopores (DNMR2) and macropores (DNMR3) are distributed between 0.3744 to 1.1293, 2.4263 to 2.9395 and 2.6582 to 2.9989, respectively. Moreover, there is no correlation between fractal dimension and permeability and porosity, a negative correlation between DL and average pore radius, a positive correlation between DL and specific surface area, and a positive correlation between DNMR2 and DNMR3 and micropore content, while DNMR2 and DNMR3 are negatively correlated with the content of mesopores and macropores.

Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, represented by a set of physical equations such as the Navier-Stokes equations, energy balances and hydrological cycle among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal dimensions, which are non-integer values that represent the complexity of variables like the precipitation. However, observed precipitation is measured as an aggregate variable over time, thus physical analysis of the observed fluxes is very limited. Therefore, this review aims to go through the different approaches used in the identification and analysis of the complexity of the observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for classification of climatic features, including monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy and time scaling in intensity-duration-frequency curves.

The Fractal Analysis of Medical Images is an investigation field in those that numerous results of important value have been obtained. This work describes the basic foundations of the Fractal Analysis and its application has more than enough medical images, leaning on in five scientific investigations.

The global incidence of cutaneous squamous cell carcinoma (cSCC), a prevalent and aggressive skin cancer, has risen significantly, posing a substantial public health challenge. This study investigates the tumor microenvironment (TME) of cSCC by focusing on the spatial distribution patterns of immune and vascular markers (CD31, CD20, CD4, and CD8) using fractal dimension (FD) analysis. Our analysis encompassed 141 cases, including 100 invasive cSCC and 41 specimens with pre-invasive lesions exclusively, and the rest being peripheral pre-invasive lesions from the invasive cSCC class. The FD values for each marker were computed and compared between pre-invasive and invasive lesion classes. The results revealed significant differences in FD values between the two classes for CD20 and CD31 markers, suggesting distinct alterations in B cell distribution and angiogenic activity during cSCC progression. However, CD4 and CD8 markers did not exhibit significant changes individually. Still, the CD4/CD8 ratio showed a significant difference, indicating a potential shift in the immune landscape as lesions progress from pre-invasive to invasive stages. These findings underscore the complexity and heterogeneity of the TME in cSCC and highlight the potential of FD analysis as a quantitative tool for characterizing tumor progression. Further research is needed to elucidate the implications of these differences in the clinical management of cSCC.

Fiber-reinforced mycelium (FRM) composites offer an innovative and sustainable approach to construction materials for architectural structures. Mycelium, the root structure of fungi, can be combined with various natural fibers (NF) to create a strong and lightweight material with environmental benefits. Incorporating NF like hemp, jute, or bamboo into the mycelium matrix enhances mechanical properties. This combination results in a composite that boasts enhanced strength, flexibility, and durability. Natural FRM composites offer sustainability through the utilization of agricultural waste, reducing the carbon footprint compared to conventional construction materials. Additionally, the lightweight yet strong nature of the resulting material makes it versatile for various construction applications, while its inherent insulation properties contribute to improved energy efficiency in buildings. Developing and adopting natural FRM composites showcase a promising step towards sustainable and eco-friendly construction materials. Ongoing research and collaboration between scientists, engineers, and the construction industry will likely lead to further improvements and expanded applications. This article provides a comprehensive analysis of the current research and applications of natural FRM composite for innovative and sustainable construction materials. Additionally, the paper reviews the mechanical properties and potential impacts of these natural FRM composites in the context of sustainable architectural construction practices. Recently, the relevance of mycelium-based materials has extended beyond their original fields of microbiology and mycology to architecture.

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

In this article, we first present and discuss eighteenth-century descriptions of minerals that contributed decisively to the development of crystallography. Remarkably, these old crystallographic descriptions included morphologies with symmetries incompatible with an internal periodic order of atoms, which, however, have been recognised to be characteristics of quasicrystals. Moreover, we also review a number of studies of minerals with aperiodic crystal structures, including recently reported natural quasicrystals of extra-terrestrial origin. Finally, we discuss the current investigations addressing the search for new quasicrystalline minerals in nature.

We develop a quantitative microscopic theory of decaying Turbulence by studying the dimensional reduction of the Navier-Stokes loop equation for the velocity circulation. We have found an infinite dimensional manifold of solutions of the Navier-Stokes loop equation\cite{M93, M23PR} for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This family of solutions corresponds to a fractal curve in complex space $\mathbb C^d$, described by an algebraic equation between consecutive positions plus a nonlinear periodicity condition. We derive the constrained SDE for the evolution of the fractal curve at a fixed moment of physical time as a function of an auxiliary stochastic time. We expect this stochastic process to cover our fixed manifold of the solutions of the decaying Turbulence. The energy density of the fluid decays as $\mathcal E_0/t$, where $\mathcal E_0$ is an initial dissipation rate. Presumably, we have found a new phase of extreme Turbulence yet to be observed in real or numerical experiments.

Abstract: A new method for constructing exact solutions of the General Relativity equations for a dusty matter with fractal property is proposed. This method allows to find the solution of the GR-equations in terms of matter velocities : the connection coefficients and the Ricci tensor of space-time are expressed in terms of matter velocities; the metric tensor and the matter density are found as functions of velocity from the GR-equations. The connection coefficients and the Ricci tensor are invariant with respect to the discrete scaling transformation of velocity , where is constant. Therefore, the found solution can be used to simulate the fractal properties of the cosmic web in terms of matter velocities. This solution includes isotropic and anisotropic distributions of matter density. In an isotropic case, there is a class of exact solutions including both the well-known Friedmann’s solution and a solution with a periodic distribution of the matter density in space. This last solution may be used to simulate the quasi-periodic distribution of matter in the cosmic web. It is possible that, the cosmic web and its fractal properties are the space-time primary properties. These properties are described with a deformation tensor of the space-time.

This study investigates the utilization of innovative green composites made from hemp shiv, a waste by-product of hemp cultivation, with the aim of promoting sustainability within the construction industry. The manufacturing method involve the application of pressure in a mold to create the samples. These materials were produced using an environmentally friendly binder consisting of colophony, arabic gum and corn starch, moreover white glue and bioepoxy are also used to compare with the green resins. Three different binder compositions for the specimens. The samples underwent mechanical testing through tensile and bending assessments, and their performance was compared to that of non-green binders to validate the effectiveness of the manufacturing processes. The study revealed that decreasing the moisture content during the curing process is crucial for improving the mechanical properties. The best results were achieved when using arabic gum as a binder, yielding a tensile strength of 2.16 MPa and a bending strength of 5.25 MPa, with a composition of 62.5% hemp shiv and a manufacturing process involving a pressure of 5 MPa.

When describing the tribological behaviour of technical surfaces, the need for full length scale microtopographic characterization often arises. The self-affine of surfaces and the characterization of self-affine by a fractal dimension and its implantation into tribological models are commonly used. The goal of our present work was to determine the frequency range of fractal behaviour of surfaces by analysing the microtopographic measurements of a brake plunger. We also wanted to know if the bifractal and multifractal behaviour can be detected in real machine parts. As a result, we developed a new methodology for determining the fractal range boundaries to separate the nano- and micro-roughness. In order to reach our goals, we used atomic force microscope (AFM) and stylus instrument to provide measurements in wide frequency range (19 nm - 3 mm). As a result of the power spectral density (PSD) based fractal evaluation, it was found that the examined surface could not be characterized by a single fractal dimension and that we developed a methodology for stopping the margin of validity of each fractal dimension, and we also developed a methodology for determining the limits of validity of certain fractal dimensions.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

The dynamic behaviour of a machine tool (MT) directly influences the machining performances. The adoption of lightweight structures may reduce the effects of undesired vibrations and increasing the workpiece quality. This paper aims to present and compare a set of hybrid materials that may be excellent candidate to fabricate the MT moving parts. The selected materials have high dynamic characteristics and capacity to damp mechanical vibrations. In this way, starting by the kinematic model of a milling machine that highlights the main critical factors, this study paper evaluates a number of prototypes made of Al Foam sandwiches (AFS), Al Corrugated sandwiches (ACS) and materials reinforced by carbon fibres (CFRP). A set of prototypes has been fabricated, represented the Z-axis ram of a commercial milling machine. The static and dynamical properties have been evaluated by using both FE simulations and experimental tests. The obtained results show that the proposed structures may be a valid alternative to the conventional materials of MT moving parts, increasing machining performances. In particular, the AFS prototype highlighted a damping coefficient that is 20 times greater than a conventional ram (e.g. steel). The CFRP structure is able to satisfy the machining requirements with a reduced weight of 48.5%, while the ACS prototype showed a good trade-off between stiffness and damping.

Theoretical studies on the generation of nondiffracting and nondispersive light pulses and their experimental implementation are one of the renowned problems within electromagnetics. Current technologies enable creation of short-duration pulses of a few cycles with high power and fluency. An application of these techniques to the field of nondiffracting and nondispersive pulses requires a proper mathematical description of highly focused vector pulses. In this work, we study vector optical bullets in a dielectric medium with different polarization structures: linear, azimuthal, and radial. We report the differences caused by the vector model compared to the scalar model. We analyze effects caused by superluminal, subluminal, or even negative group velocity on properties of vector optical bullets inside a dielectric material.

The construction industry has a notable negative impact on the environment; thus, the promotion of the use of timber structures is an alternative to mitigate its effects. The research develops an artificial intelligence-based decision approach in the calculation of timber structures focused on the enhancement of the sustainability of roof structures. Based on the optimization carried out through genetic algorithms and the framework established in Eurocode 5, a general set of equations has been proposed for a laminated timber roof structure. The tool, which determines the most suitable roof structure for each strength class of laminated timber, allows for the determination of the dimensions of beams and purlins and their respective separations in order to minimize wood consumption. The ultimate goal is to offer multiple solutions regarding strength classes and structural designs in order to foster informed sustainable choices that promote efficient use of resources in construction.

In this work we present a novel steganography algorithm, based on Fractal Transform domain, combined with the principles of Cryptography. The proposed method uses a private key, which will indicate which segment of the image will be taken and encoded with the Fractal Transform, to then insert the secret bits in the transformed coefficients, thus generating the stego image.

The main purpose of this study is the determination of the optimal data acquisition and processing parameters of electric and seismic tomographic techniques, for the investigation of complex geological environments. Two different study areas, in central-east Peloponnese and SW Attica were selected, where a detailed geological mapping and surface geophysical survey were carried out. The applied geophysical survey included the application of electrical resistivity tomography (ERT) and seismic refraction tomography (SRT). The geoelectrical measurements were acquired with different arrays and electrode configurations. Moreover, various types of seismic sources were used at seventeen shot locations along the seismic arrays. For the processing of geoelectrical data, clustered datasets were created increasing the depth of investigation and the discriminatory capability. The seismic data processing included: (a) creation of synthetic models and seismic records to determine the effectiveness and capabilities of the technique, (b) spectral analysis of the seismic records to determine the optimal seismic source type and (c) inversion of the field data to create representative subsurface velocity models. The results of the two techniques successfully delineated the complex subsurface structure that characterizes these two geological environments. The application of the ERT combined with the SRT, are the two dominant, high-resolution techniques for the elucidation of complex subsurface structures.

In steel structures, oblique thin steel plates serve as panel zones in structures spanning large spaces (e.g., warehouses and gymnasiums). Considerable research has been conducted on the shear buckling of panels due to seismic loads acting on a structure. Conversely, under snow or wind loads, the panel zone may experience compressive and tensile stresses simultaneously from two directions. Considering the economic preference for thin steel plates, evaluating the elastic critical local buckling stresses in the panel zone under biaxial normal stress may provide essential information to structural engineers. In this study, an elastic buckling analysis based on the energy method is performed to clarify the impact of panel geometry and boundary conditions on the elastic local buckling stresses of oblique panel zones. As confirmed, the buckling stresses derived from the energy method could simulate the local buckling stresses with accuracy comparable to that of finite element analysis, and an engineer-friendly design formula was proposed. Finally, we determined the correlation of the buckling stresses under biaxial stresses and presented a method for evaluating this correlation. Engineers can utilize the provided design equations to more efficiently and accurately calculate buckling loads, facilitating safer and more economical design of structures with oblique plates.

By repeated unloading and loading of the excavation dynamic and static loads, repeated train dynamic and static loads of multi-factors, the underpass tunnel, cross tunnel engineering influence area rock layer, the existing tunnel structure of the three constitutes a multifaceted structure, multi-factor interaction system. Existing tunnels into the prediction theory model of the new tunnel excavation process of dynamic and static loads, dynamic and static loads of existing tunnels are mostly analyzed individually, the results of synergistic analysis needs to be improved. Based on the theory of the current layer method, the paper comprehensively considers the stiffness of the existing tunnel, the stiffness of the new tunnel, the excavation method load and the existing tunnel load, coupled with Peck's empirical formula, the theoretical model of deformation prediction for excavation of a two-lane highway tunnel under the tunnel through the existing railroad is proposed, and verified and optimized by numerical calculations and monitoring data, which proves the applicability and reliability of the theoretical model in the similar strata and the project promotion.

So called Higuchi’s method of fractal dimension estimation is widely used and the term Higuchi’s fractal dimension even occurs in many publications. This paper deals with this method from mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. Definition of Higuchi’s dimension was comparated with mathematical definition of the distance and dimension. It is showed, that the definition of the Higuchi’s dimension does not satisfy axioms of distance and dimension. So called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.

High entropy alloys have excellent wear resistance, so they have great application prospects in the fields of wear resistance and surface protection. In this study, the wear resistance of FeNiCrCoCu high entropy alloy coating was systematically analyzed by molecular dynamics method. FeNiCrCoCu high entropy alloy was used as a coating material to adhere to the surface of Cu matrix. The friction and nano indentation simulation of this coating material were carried out by controlling the ambient temperature. The influence of temperature on its friction properties was analyzed from five aspects: lattice structure, dislocation evolution, friction coefficient, hardness and elastic modulus. The results show that with the increase of temperature, the disorder of the lattice structure increases, which leads to the increase of the tangential force and the friction coefficient in the friction process. At 300K and 600K, the ordered lattice structure of the high entropy alloy coating material is basically the same, and thus their hardness is basically the same. However, the dislocation density at 600K is significantly reduced compared with that at 300K, resulting in the increase of the elastic modulus of the material from 173GPa to 219GPa. At the temperatures of 900K and 1200k, lattice disorder take place rapidly, and dislocation density also decreases significantly, resulting in a significant decrease in the hardness and elastic modulus of the material. When the temperature reaches 900K, the wear resistance of the FeNiCrCoCu high entropy alloy coating decreases sharply. This work is of great value to the analysis of wear resistance of high entropy alloy at high temperature.

Currently, the design and construction of embankments of roads, railroads and hydraulic structures are based on regulatory documents developed 25-30 years ago. For the construction of granite massifs it is necessary to use sandy soils, the distribution of which in the Arctic zone of Siberia in the areas of construction is not more than 1.5%. In this case, the range of transport of sand in the alluvial area is 35 kilometers, in the rest of the area - an average of 60 kilometers. Large volumes of soil massifs require large amounts of transportation units, fuel consumption and are accompanied by large emissions of hydrocarbons into the atmosphere. Over the past 15 years, the authors have developed designs and technologies that significantly reduce the energy consumption during the construction of soil embankments. Combined structures are cages made of geosynthetic materials filled with unsuitable melted and frozen overmoistened clay and peaty soils. This allowed the use of soils within the construction sites and thereby reduce the range of transportation from 0.2 to 2.0 kilometers. As an example, when reducing the range of transportation from 25 km to 1 km, the energy consumption is reduced by a factor of 21. The use of geosynthetics made it possible to set the initial parameters of the water-heat regime control process, which increased the life cycle of the embankment from 2 to 5 times in comparison with traditional soil massifs and reduced the consumption of energy for repair and maintenance of linear transport structures. This article gives a theoretical substantiation of water-heat regime management, based on which new designs and technologies have been proposed and tested in Siberia in 2008-2013. The results of the tests confirm the theoretical research. Thus, the use of combined constructions of geosynthetics and inapplicable soils not only reduces the distance of transportation, but also reduces the volume of earthworks. It reduces the consumption of energy by 1.5-2 times.

Motivated by diffraction experiments on the $\left(2\sqrt{3}\times \sqrt{3}\right)\mathrm{R}{30}^{\circ }$ reconstructed Si(111) due to deposition of rare earth elements (Dy, Tb) and silicide formation we analyse the splitting and non-splitting of superstructure spots. For this purpose, we model diffraction patterns for one dimensional structures generated by the binary surface technique and use supercell models to keep the analysis simple. Diffraction pattern are calculated in the framework of the kinematical diffraction theory and they are analyzed as a function of the domains and domain boundaries. Basic properties of the diffraction pattern are analyzed for model systems of a two-fold and a three-fold periodicity. The rules derived from these calculations are applied to the "real-world" system of Si(111)-($\left(2\sqrt{3}\times \sqrt{3}\right)\mathrm{R}{30}^{\circ }$)-RESi$2_{}$ (RE = Dy or Tb). Depending on the combination of domains and domain boundaries of different types a plethora of different features are observed in the diffraction patterns. These are analyzed to determine the sizes of both domain boundaries and domains from experimentally observed splitting of specific superstructure spots.

Femtosecond laser two-photon polymerization (TPP) technology, known for its high precision and capability to fabricate arbitrary 3D structures, has been widely applied in the production of various micro-nano optical devices, achieving significant advancements particularly in the field of photonic wire bonding (PWB) for optical interconnects. Currently, research on optimizing both the optical loss and production reliability of polymeric photonic wires is still in its early stages. One of the key challenges is that inadequate metrology methods cannot meet the demand for multiphysical measurements in practical scenarios. This study utilizes in-situ scanning electron microscopy (SEM), for the first time, to monitor the working PWBs fabricated by TPP technology at the microscale. Optical and mechanical measurements are made simultaneously to evaluate the production qualities and to study the multiphysical coupling effects of PWBs. The results reveal that photonic wires with larger local curvature radii are more prone to plastic failure, while those with smaller local curvature radii recover elastically. Furthermore, larger cross-sectional dimensions contribute dominantly to the improved mechanical robustness. The optical loss deterioration of the elastically deformed photonic wire is only temporary, which can be fully recovered when the load is removed. After further optimization based on the results of multiphysical metrology, the PWBs fabricated in this work achieve a minimum insertion loss of 0.6 dB. In this study, the multiphysical analysis of PWBs carried out by in-situ SEM metrology offers a novel perspective for optimizing the design and performance of microscale polymeric waveguides, which could potentially promote the mass production reliability of TPP technology in the field of chip-level optical interconnection.

People have always hoped to be able to fill an entire plane with ``single unit cells'' without periodicity. This wish was realized after the mathematician discovered a 13-sided ``single unit cell'' named `einstein'. These non-periodic tessellations generally exhibit anisotropic properties, making them superior in terms of mechanical performance compared to periodic structures. From the perspective of information entropy, the reason behind the improved mechanical properties of these structures is the higher entropy associated with non-periodic configurations. To quantify the disorder of non-periodic structures, we propose an entropy expression for the `einstein' metamaterial. To demonstrate the mechanical properties of these high-entropy structures, we fabricate specimens using 3D printing and conducte mechanical experiments. For comparative analysis, we also use ABAQUS to perform finite element analysis of the problem. The research results reveal that the mechanical properties of high-entropy structures created by the non-periodic stacking of cells are significantly improved compared to those of low-entropy structures created by periodic stacking. The conclusions drawn from the study of individual issues are generalizable and may be of assistance in future material and structural design.

SiC ceramics are excellent materials applied at high temperatures because of their light weight, excellent high temperature strength, and high thermal shock resistance. For better engineering properties, we made SiC with fractal lattices. Stress-strain behavior and modulus changes from room temperature to 1,250oC were analyzed using LAMMPS S/W, a molecular dynamics program. As a result of this study, it was confirmed that the modulus of elasticity of SiC crystals changed in the range of about 475 GPa to 425 GPa as it increased from room temperature to 1,250 oC, The stress-displacement characteristics of SiC crystals, which could not be measured at a high temperature of 1,000 oC or higher, could be ensured.

Histones are keys to many epigenetic events and their complexes have therapeutic and diagnostic importance. The determination of the structures of histone complexes is fundamental in the design of new drugs. Computational molecular docking is widely used for the prediction of target-ligand complexes. Large, linear peptides like the tail regions of histones are challenging ligands for docking due to their large conformational flexibility, extensive hydration, and weak interactions with the shallow binding pockets of their reader proteins. Thus, fast docking methods often fail to produce complex structures of such peptide ligands at a level appropriate for drug design. To answer this challenge, and improve the structural quality of the docked complexes, post-docking refinement has been applied using various molecular dynamics (MD) approaches. However, a final consensus has not been reached on the desired MD refinement protocol. In the present study, MD refinement strategies were systematically explored on a set of problematic complexes of histone peptide ligands with relatively large errors in their docked geometries. Six protocols were compared that differ in their MD simulation parameters. In all cases, pre-MD hydration of the complex interface regions was applied to avoid the unwanted presence of empty cavities. The best-performing protocol achieved a median of 32 % improvement over the docked structures in terms of the change of root mean squared deviations from the experimental references. The influence of structural factors and explicit hydration on the performance of post-docking MD refinements was also discussed to help their implementation in future methods and applications.

Magnaporthe oryzae is a filamentous heterothallic ascomycete fungus globally distributed in rice-growing regions and serves as the causative agent of rice blast disease. Populations shaped by environmental factors and human intervention play important roles in the formation of genetic structure. In this study, population structures and spatiotemporal dynamics were investigated based on the large-scale whole genomic sequences of rice-infecting M. oryzae around the world. By analyzing the genetic structures, we identified divergent clades that crossed geographic boundaries. While we observed associations between the isolates and their geographic origins, we also found that there were frequent migration events occurring worldwide. The populations in Asia demonstrated the highest genetic diversity due to the continent’s history of rice domestication, followed by separate gene flows to Africa, North America, South America and Europe. Within Asia, China was the migration origin, facilitating gene flows to Japan and South Korea. Additionally, our analysis of the evolutionary history of global M. oryzae populations provided insights into the population expansion that has taken place in recent decades. Overall, our findings indicate that human-mediated gene flows played a pivotal role in shaping the genetic structure of M. oryzae.

The pursuit of materials that offer both wear comfort and protection for functional and protective clothing has led to the exploration of weft-knitted spacer structures. Traditional cushioning materials such as spacer fabrics and laminated foam often suffer from deformation under compression stresses, thus compromising their protective properties. This study investigates the enhancement of the force absorption, stress-strain and thermal properties of weft-knitted spacer fabrics with inlays. Surface yarns with optimal stretchability and thermal properties are used and combined with elastic yarns in various patterns to fabricate nine different inlay samples. The mechanical and thermal properties of these samples are systematically analyzed, including their compression, stretchability, thermal comfort and surface properties. The results show that the inlay spacer fabric exhibits superior compression properties and thermal conductivity compared to traditional laminated foam and spacer fabrics, while maintaining stretchability, thus providing a better performance than traditional fabrics for protective clothing and wearable cushioning products. This study further confirms that the type of inlay yarn and inlay structure are crucial factors that significantly influence the thermal, tensile and compressive properties of fabric. This research provides valuable insights into the design and development of advanced textile structures to improve wear comfort and protection in functional garment applications.

In the conservation of monumental heritage, the collection and utilization of information are of primary importance. The Heritage Building Information Modeling (HBIM) procedure harnesses the potential of three-dimensional models, offering significant advantages in accessing documentation, interoperability, multidimensionality of intervention design, cost evaluation and maintenance management. Attention here is focused on the Certosa di Pisa, a large historical complex built in the 14th century as a monastery of the Carthusian order, currently in a state of deterioration and in need of restoration and re-functionalization. The multifaceted nature of this monumental complex, with its intricate interplay of architectural elements spanning different historical periods and featuring diverse techniques, poses a significant challenge for structural safety assessment. This case study presents an opportunity to explore an HBIM approach to streamline the diagnostic process and facilitate the intervention design phase. The goal is achieved by utilizing an accurate 3D model enriched with data from multiple sources and automating certain operations for structural assessment. The usefulness of the HBIM methodology is highlighted as a valuable tool in the realm of Cultural Heritage structures for both technicians and scholars alike.

The intestinal microbial community of aquatic animals is closely related to the environment and thus affects the health of aquatic animals. Here we investigated annual variation of intestinal bacteria community structures of Ruditapes philippinarum cultured using two different methods, bottom sown and raft hanging. Bacterial diversity of seawater and sediment in different seasons was examined as well. Correlation between R. philippinarum intestinal bacteria community structures and environmental factors was analyzed. The results showed that in the two aquculture areas where R. philippinarum was differentially cultured, bacteria community structure of seawater and sediment both altered with seasons. However, neither seasonal changes nor difference in culture methods could significantly affect the intestinal bacteria community structures of R. philippinarum. Additionally, in terms of the alpha diversity of intestinal bacteria communities, there was no significant difference in R. philippinarum cultured using the two methods. For benthic cultured clams, alpha diversity of the intestinal bacterial communities was often higher than that of the environmental bacterial communities. For raft hanging cultured calms, Alpha diversity of the intestinal bacterial communities was normally comparable with that of the environmental counterparts. Beta diversity analysis showed that the intestinal bacterial community structure of R. philippinarum was mainly determined by both deterministic and stochastic processes. Correlation analysis showed that the intestinal bacterial community structures of R. philippinarum were determined by a variety of environmental factors. For clams collected from the benthic culture area, the intestinal bacterial structure was more correlated with the physicochemical properties of sediment in comparing with those of seawater. For clams collected from the raft-culture area, the intestinal bacterial structure was mainly determined by the phsicochemical characteristics of seawater. This study helps us to better understand the bacterial community structure in complex aquaculture ecosystems, providing a reference for healthy shellfish aquaculture and ecosystem protection in aquaculture area.

The construction time of concrete structures in hydraulic tunnels is long, the construction environment is complex, and there are many influencing factors. The requirements for construction quality are high, not only to meet the strength requirements, but also to meet the design requirements of erosion resistance, crack resistance, and seepage resistance according to its specific operating environment. Therefore, evaluating the construction quality of concrete structures in hydraulic tunnels is of great significance. Considering the randomness and fuzziness of factors affecting the construction quality of concrete structures in hydraulic tunnels, this paper proposes a comprehensive evaluation model based on Combined Weighting (CWM) and Uncertainty Measurement Theory (UM). The IAHP method and CRITIC method are used to determine the subjective and objective weights of evaluation indicators, combined weighting is based on the principle of minimum entropy, and the UM method is used to evaluate the construction quality level. Finally, taking a hydraulic tunnel as an example, its construction quality grade is calculated to be III according to the evaluation model proposed in this paper, which matches with the engineering reality, and a comparative study is made with the mixture element topology theory at the same time. It is verified that the evaluation model can scientifically and reasonably evaluate the construction quality level of concrete structures in hydraulic tunnels.

Tertiary lymphoid structures (TLSs) have become the focus of antitumor immunity. However, the prognostic significance of TLSs in epithelial ovarian cancer (EOC) treated with primary debulking surgery (PDS) or interval debulking surgery (IDS) remains unelucidated. This retrospective study examined the prognostic value of TLSs in tumor tissues obtained during PDS and IDS. Pathological specimens were collected from patients with EOC who underwent PDS or IDS between 2017 and 2020 at the National Cancer Center Hospital East. The correlation of tumor-infiltrating lymphocyte frequency, TLS presence, and PD-L1 expression with progression-free survival (PFS) and overall survival (OS) and the correlation between TLS and PD-L1 expression were analyzed. Overall, 25 specimens (15 from PDS and 10 from IDS) were analyzed. The presence of TLS was associated with a significantly longer OS in patients who underwent PDS but not in patients who underwent IDS. No correlation was identified between TLS and PFS in patients with PDS or with IDS. However, TLS was positively correlated with PD-L1 positivity. The prognostic impact of TLS, specifically in pre-chemotherapy specimens, and a positive correlation between TLS and PD-L1 indicate the potential of TLS as a meaningful biomarker for understanding antitumor immunity and developing immunotherapy for EOC.

The fundamental period is one of the most important parameters for the design of new structures , as well as the estimation of the capacity of existing ones. However, its calculation requires the solution of an eigenvalue problem. Especially for new buildings, this can involve material and geometric parameters that are not known beforehand. Thus, to estimate it, various design codes and researchers have adopted a several approximate analytical equations based on a number of key structural parameters. To this end, the present study introduces a novel methodology for the derivation of analytical equations for the fundamental period of Reinforced Concrete (RC) structures. The methodology is based on Machine Learning (ML) explainability techniques and specifically the so-called SHapley Additive exPlanations (SHAP) values. The novel methodology allows these equations to be constructed sequentially and in an informed manner, controlling the balance between accuracy and complexity. An extended dataset comprised of 4026 data points is employed. The results showed excellent accuracy, with a coefficient of determination R2≈0.95. This demonstrates the potential applicability of the proposed methodology in a wide array of similar engineering challenges.

In contemporary construction, the prevalence of vibration serviceability issues in lightweight and slender structures has become increasingly common, owing to advancements in building materials and construction methods. While these structures often meet the criteria for ultimate limit states, they can still elicit complaints due to excessive vibrations induced by human activity. To address this challenge, the Integral Resonant Control (IRC) technique has emerged as a favored approach for actively damping vibrations in various systems. This study introduces a fresh perspective on implementing a multi-input multi-output (MIMO) IRC scheme for active vibration control (AVC) specifically tailored for pedestrian structures utilizing inertial mass actuators. Building upon a common framework and design methodology outlined in previous research, this work presents a novel application of MIMO IRC for AVC. The designed controller is rigorously tested and implemented on a laboratory floor structure to validate its efficacy.

This paper intoduces a non-standard research technique to clarify how complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using fractal dynamical models with and without stochastic forces. This method for conducting research involves tracing the his- torical evolution of understaning an empirical medical process faciltated by the fractal calculus perspective. Herein we trace the analysis of the time series for heart rate varability (HRV) developed for diagnosing the cardiovascular health of a patient. This is done herein by introducing four (one empirical which en- tails three theoretical fractal models) distinct but related fractal models each one introduced to solve a particular problem arising from a fundamental defect in the previous model but in generalizing a model at one stage to resolve the problem associated with the defect another is invariably introduced by the re- placement model. It is through the utilization of the fractional calculus that the necessity for rethinking how to systematically incorporate additonal layers of complexity are revealed ultimately resulting in a 'complete' description of its empirical dynamics in fractal terms.

Wagyu beef is gaining worldwide popularity, primarily due to the fineness of its marbling. Cur-rently, the evaluation of this marbling is performed visually by graders. This method has several issues: varying evaluation standards among graders, reduced accuracy due to long working hours and external factors causing fatigue, and fluctuations in grading standards due to the grader's mood at the time. This paper proposes the use of fractal analysis for the grading evaluation of beef marbling to achieve automatic grading without the inconsistencies caused by human factors. In the experiments, cross-sectional images of the parts used for visual judgment were taken, and fractal analysis was performed on these images to evaluate them using fractal dimensions. The results confirmed a correlation between the marbling evaluation and the fractal dimensions, demonstrating that quantitative evaluation can be achieved, moving away from qualitative visual assessments.

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), s_ex, and the pair-correlation contribution, s₂. Thus, the RMPE represents the net contribution to s_ex due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1 < d < 3 has been proposed [Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction ϕ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δs_min at a packing fraction ϕ_min, and then rapidly increases, becoming positive beyond a certain packing fraction ϕ₀. Interestingly, while both ϕ_min and ϕ₀ monotonically decrease as dimensionality increases, the value of Δs_min exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d ≃ 2.38. A plot of the scaled RMPE Δs/|Δs_min| shows a quasiuniversal behavior in the region −0.14 ≲ ϕ − ϕ₀ ≲ 0.02.

In the current work, the stable queueuing system's Generalised Z-Entropy (GZE) of Rényian formalism is examined in its fractal dimension. Notably, fractal dimension’s resulting behaviour that corresponds to the GZE parameters is examined through numerical tests. This research makes a substantial generalization in the literature by fusing fractal geometry and information theory to shed light on how entropy and complexity interact. More fundamentally, the significant role of fractal dimension to advance Big Data Analytics(BDAs) is highlighted. Closing remarks combined with open problems and the next phase of research are provided.

Molecular visualisation is fundamental in the current scientific literature, textbooks and dissemination materials, forming an essential support for presenting results, reasoning on and formulating hypotheses related to molecular structure. Visual exploration has become easily accessible on a broad variety of platforms thanks to advanced software tools that render a great service to the scientific community. These tools are often developed across disciplines bridging computer science, biology and chemistry. Here we first describe a few Swiss Army knives geared towards protein visualisation for everyday use with an existing large user base, then focus on more specialised tools for peculiar needs that are not yet as broadly known. Our selection is by no means exhaustive, but reflects a diverse snapshot of scenarios that we consider informative for the reader. We end with an account of future trends and perspectives.

Surveys on the optimum seismic design of structures reveal that many investigations focus on how to minimize its initial cost while satisfying the performance constraints. Although reducing the initial cost while complying with the requirements of earthquake design codes of practice will significantly guarantee the life safety of occupants against earthquakes, it may still cause considerable economic losses to residents and fatalities. Accordingly, calculating the possible earthquake damages caused during the structure's lifetime may become essential from the optimal Life Cycle Cost (LCC) design point of view. LCC analysis is used to evaluate economic feasibility including construction, operation, occupancy, maintenance and end-of-life costs. For optimization, the population-based, meta-heuristic algorithm based on the Ideal Gas Molecular Movement (IGMM), has established its capability in solving highly nonlinear mono and multi-objective engineering problems. Therefore, this paper investigates the LCC -based mono and multi-objective optimum design of a 3-D four-story concrete building structure combined with the Endurance Time (ET) competence. The results show that, apart from substantially reducing the total number of analyses required, the proposed technique significantly affected dipping minor injury cost, rental, and income costs by 22%, 16%, and 16%, respectively. In total, a 10% reduction in all structural life-cycle costs was achieved, which could well be considered significant.

Gracilaria lamaneiformis, a red seaweed, is an abundant source of bioactive polysaccharides with significant health-promoting properties. Nevertheless, the broad application of G. lamaneiformis in the nutraceutical and pharmaceutical sectors remains constrained due to the absence of comprehensive data. This review provides a detailed examination of the preparation methods, structural characteristics, and biological activities of G. lamaneiformis polysaccharides (GLP). We explore both conventional and advanced extraction techniques, highlighting the efficiency and yield improvements achieved through methods such as microwave-, ultrasonic-, and enzyme-assisted extraction. The structural elucidation of GLP using modern analytical techniques, including high-performance liquid chromatography, gas chromatography, and nuclear magnetic resonance spectroscopy, is discussed, providing comprehensive insights into their molecular composition and configuration. Furthermore, we critically evaluate the diverse biological activities of GLP, including their antioxidant, anti-inflammatory, antitumor, and gut microbiota modulation properties. This review underscores the therapeutic potential of GLP and suggests future research directions to fully harness their health benefits.

The present paper proposes a fractal analysis of the Covid-19 dynamics in 45 European countries. We introduce a new idea of using the box-counting dimension of the epidemiologic curves as a means of classifying the Covid-19 pandemic in the countries taken into consideration. The classification can be a useful tool in deciding upon the quality and accuracy of the data available. We also investigated the reproduction rate, which proves to have significant fractal features, thus enabling another perspective on this epidemic characteristic. Moreover, we studied the correlation between two meteorological parameters: global radiation and daily mean temperature and two Covid-19 indicators: daily new cases and reproduction rate. The fractal dimension differences between the analysed time series graphs could represent a preliminary analysis criterion, increasing research efficiency. Daily global radiation was found to be stronger linked with Covid-19 new cases than air temperature (with a greater correlation coefficient -0.386, as compared with -0.318), and consequently it is recommended as the first-choice meteorological variable for prediction models.

Suitable soil structure and nutrient security are important for plant growth and development, characteristics of soil fractal dimension and distribution of physical and chemical properties and their interactions play an important role in studying the stability of soil structure and water and fertilizer cycles. As a sustainable management model, intercropping has positive benefits for erosion control, spatial optimization of resources, as well as improving system productivity. The effects of four intercropping methods on soil fractal dimension and physicochemical properties were investigated by intercropping Salvia miltiorrhiza with forage and S. miltiorrhiza with forest under typical karst rock desertification habitats in Guizhou. The results showed that soil nutrient content of intercropping was significantly higher than that of monoculture, the organic carbon content of soil grown under forest is higher than other treatments, and there was a non-significant change in soil water content of intercropping compared with monoculture. The soil fine-grained matter of intercropping was significantly higher than that of monoculture, while the soil fractal dimension showed a tendency to become larger with the increase of fine-grained matter. The intercropping planting, due to its component types and spatial and temporal configurations, leads to differences in soil water and fertilizer interactions, which can be combined with other ecological restoration measures to optimize the composite model and jointly promote the restoration and development of ecologically fragile areas.

Waterbomb structures are origami-inspired deformable structural components used in new types of robots. They have a unique radially deployable ability that enables robots to better adapt to their environment. In this paper, we propose a series of new waterbomb structures with square, rectangle, and parallelogram base units. Through quasi-static axial and radial compression experiments and numerical simulations, we prove that the parallelogram waterbomb structure has a twist displacement mode along the axial direction. Compared with the square waterbomb structure, the proposed optimal design of the parallelogram waterbomb structure reduces the critical axial buckling load-to-weight ratio by 55.4% and increases the radial stiffness-to-weight ratio by 67.6%. The significant increase in the radial stiffness-to-weight ratio of the waterbomb structure and decrease in the critical axial buckling load-to-weight ratio make the proposed origami pattern attractive for practical robotics applications.

This study addresses the critical need for standardizing Building Information Modeling (BIM) Execution Plans (BEPs) in the Architecture, Engineering, Construction, and Operations (AECO) sector. By analyzing 36 BEP documents from international organizations, we identify key elements and propose a comprehensive framework aimed at enhancing digital transformation and collaboration in complex construction projects. This research employs scientometric analysis to map the evolution of BEP standards and integrates empirical data from industry surveys to validate the proposed framework. Our findings highlight the benefits of standardized BEPs in reducing inefficiencies and improving project outcomes, thereby providing a significant contribution to the field of BIM implementation.

We address the problem of finding a unique graph embedding that best describes a graph's "topology". This issue is of particular interest in the chemistry of materials. Graphs that admit a tiling in 3-dimensional Euclidean space are termed tessellate, those that do not decussate. We give examples of decussate and tessellate graphs that are finite and 3-periodic. We conjecture that a graph has at most one tessellate embedding. We give reasons for considering this the default "topology" of periodic graphs.

The Svenonius theorem establishes the correspondence between definability of relations in a countable structure and automorphism groups of these relations in the extension of the structure. This correspondence may help in finding the description of the definability lattice constituted by all definability spaces (reducts) of the original structure. However, the major difficulty here is the necessity to consider the extensions which generally are obscure and hardly amenable to classification. Because of that results on definability lattices were obtained only for $\omega$-categorical structures (i.\,e. those in which all elementary extensions are isomorphic to the structure itself). All known definability lattices for such structures proved to be finite. In this work we introduce the concept of upwards complete structure as such in which all its extensions are isomorphic. Further we define upwards completions structures. For such structures Galois correspondence between definability lattice and the lattice of closed supergroups of automorphism group of the structure is an anti-automorphism. These lattices could be infinite in general. We describe the natural class of structures which have upwards completion, that is discretely homogeneous graphs, present the explicit constrcution of their completion and automorphism groups of completions. We establish the general \emph{localness} property of discretely homogeneous graphs and present the examples of completable structures and their completions.

A multiscale model that enables quantitative understanding and prediction of the size effect on scattering properties of micro- and nanostructures is crucial for the design of LED surface textures optimized for high light extraction efficiency (LEE). In this paper, a hybrid process for combining full-wave finite-difference time-domain simulation and a ray-tracing technique based on a bidirectional scattering distribution function model is proposed. We apply this method to study the influence of different pattern sizes of a patterned sapphire substrate on GaN-based LED light extraction from the microscale to the nanoscale. The results show that near-wavelength–scaled patterns with strong diffraction are not expected to enhance LEE. By contrast, microscaled patterns with optical diffusion behavior have the highest LEE at a specific aspect ratio, and subwavelength-scaled patterns that have antireflection properties show marked enhancement of LEE for a wide range of aspect ratios.

In this paper, we investigate various graphene monolayer nanomesh structures (diodes) formed only by nanoholes, with a diameter of just 20 nm and etched from the graphene layer in different shapes (such as rhombus, bow-tie, rectangle, trapezoid, and triangle), and their electrical properties targeting electromagnetic energy harvesting applications. In this respect, the main parameters characterizing any nonlinear device for energy harvesting are extracted from tens of measurements performed on a single chip containing the fabricated diodes. The best nano-perforated graphene structure is the triangle nanomesh one, which exhibits remarkable performance in terms of its characteristic parameters, i.e., a 420 Ω differential resistance for optimal impedance matching to an antenna, a high responsivity greater than 1000 V/W, and a low noise equivalent power of 847 pW/√Hz at 0 V.

The structure of arylpiperazine moieties as an important pharmacophore could generate wide pharmacological activities．Arylpiperazine derivatives referred in this paper possessed antitumor activity. The title compounds were crystallized by slow evaporation. 2-(4-(2-(4-Phenylpiperazin-1-yl)ethyl)benzyl)isoindoline-1,3-dione(1), 2-(4-(2-(4-(4-Bromophenyl)piperazin-1-yl)ethyl)benzyl)isoindoline-1,3-dione (2) and 2-(4-(2-(4-(4-Chlorophenyl)piperazin-1-yl)ethyl)benzyl)isoindoline-1,3-dione (3) crystallizes in the triclinic space group P-1 with two molecules in the unit cell. The unit cell parameters for 1 are a = 6.9159(14) Å, b = 9.999(2) Å, c = 16.925(3) Å, α = 88.25(3)°, β = 85.14(3) °, γ = 79.22(3) °. The unit cell parameters for 2 are a = 6.9995(14) Å, b = 9.919(2) Å, c = 17.671(4) Å, α= 97.55(3)°, β = 92.19(3) °, γ = 102.23(3) °. The unit cell parameters for 1 are a = 6.9872(14) Å, b = 9.863(2) Å, c = 17.557(4) Å, α=96.81(3)°, β = 91.89(3) °, γ = 101.74(3) °. Pi-pi interactions were observed between molecules, and compound 2 and 3 showed halogen interactions between molecules nearby, which was different from compound 1.

This review contains a popular presentation of the history of carbon nanostructure discovery, a short description of the main approaches to production and investigation of such objects and consideration of the most perspective ways of their applied usage.

This is a study on fractals existing in music. The application case is the composition DIAPHONIES of Michael Paouris. Sliding-window fractal analysis indicate areas of continuous fractality dipped in non-fractal areas of possibly deterministic and stochastic nature. Diverging cases of pronounced non-fractal areas are addressed and also areas of mixed fractality and non-fractality. Many segments exhibit persistency-P (2

(RADA)4 nanoscaffolds are excellent candidates for use as peptide delivery vehicles: they are relatively easy to synthesize with custom bio-functionality, and assemble in situ to allow a focal point of release. This enables (RADA)4 to be utilized in multiple release strategies by embedding a variety of bioactive molecules in an all-in-one ‘construct’. One novel strategy focuses on the local, on-demand release of peptides triggered via proteolysis of tethered peptide sequences. However, the spatial-temporal morphology of self-assembling nanoscaffolds may greatly influence the ability for enzymes to both diffuse into as well as actively cleave substrates. Fine structure and its impact on overall affect on peptide release is poorly understood. In addition, fractal networks observed in nanoscaffolds are linked to the fractal nature of diffusion in these systems. Therefore, matrix morphology and fractal dimension of virgin (RADA)4 and mixtures of (RADA)4 and matrix metalloproteinase 2 (MMP-2) cleavable substrate modified (RADA)4 were characterized over time. Sites of high (GPQG+IASQ, CP1) and low (GPQG+PAGQ, CP2) cleavage activity were chosen. Fine structure was visualized using established according to established methods. After 2 hrs of incubation, nanofiber networks showed an established fractal nature, however nanofibers continued to bundle in all cases as incubation times increased. It was observed that despite extensive nanofiber bundling after 24 hrs of incubation time, the CP1 and CP2 nanoscaffolds were susceptible to MMP-2 cleavage. The properties of these engineered nanoscaffolds characterized herein illustrate that they are an excellent candidate as an enzymatically initiated peptide delivery platform.

The astro-structures with the shape of comet and semi-circle, are found in the electronegative inductively coupled plasmas (ICPs), e.g., Ar/O2 and Ar/SF6. They are formed by means of the self-coagulation theory. This theory is built and based on two-dimensional fluid model simulation dynamic data of the above ICP sources. Concretely, quasi-Helmholtz equation is constructed through the free diffusion transport component and a novel negative chemical source term. The absolute value of recombination rate is higher than the attachment rate and so the net source of simulated anion is negative. This is quite a new chemical phenomenon in the electronegative and gaseous discharging plasmas when compared to the previously reported normal positive chemical source that will generate ambi-polar diffusion potential. In electronegative plasma, the self-coagulation is ambi-polar to sustain the electrical neutrality. Besides, when the anions are accelerated by ambi-polar potential before self-coagulated, the self-coagulation is again advective which leads to the formation of blue sheath. At the ambi-polar self-coagulation of high electronegativity, the electrons dynamics are relatively decoupled from ions and meanwhile they have their own relatively weak, spontaneous, and monopolar self-coagulation in the periphery of astro-structure. At the ambi-polar self-coagulation, both the anion and cation are individually treated as mass point models that carry charge (point charge models, more precisely). When the charge amounts of two individual astr-structures, e.g., semi-circle SF3+ and Ar+, are equal, the coagulated profile of heavy species SF3+ collapses by the expelling effect of Coulomb force that exists between the two point-charges. This is an anti-collective behavior of astro-structure, instead of the collective interaction of plasma, since the collapse of coagulated heavy species creates spatially dispersed charge density that cannot be shielded. The simulation shows that the lighter the species, the easier it self-coagulates, determined by the inertial effect of density quantity. The discharge picture of electronegative plasma is combined by a dynamic continuum transport (e.g., forming the ellipse background) and the mechanical balance contained in the static self-coagulation process (proven by dimensional analysis of continuity equation). The popular astro-structure of electronegative ICP source awaits urgently for the validation of experiment.

This study reports on the development of bio-based hydrophobic coatings for packaging papers through deposition of polyhydroxybutyrate (PHB) particles in combination with nanofibrillated cellulose (NFC) and plant wax. In a first approach, PHB particles in micrometer range (PHB-MP) were prepared through a phase-separation technique providing internally nanosized structures. The particles were transferred as a coating by dip-coating filter papers in the particle suspension, followed by sizing with a carnauba wax solution. This approach allowed partial to almost full surface coverage of PHB-MP over the paper surface resulting in static water contact angles of 105° to 122° and 129° to 144° after additional wax coating. In a second approach, PHB particles with submicron sizes (PHB-SP) were synthesized by an oil-in-emulsion (o/w) solvent evaporation method, and mixed in aqueous suspensions with 0 to 7 wt% NFC. After dip-coating filter papers in PHB-SP/NFC suspensions and sizing with a carnauba wax solution, static water contact angles of 112° to 152° were obtained. The intrinsic properties of the particles were analyzed by scanning electron microscopy, thermal analysis and infrared spectroscopy, indicating higher crystallinity for PHB-SP than PHB-MP. The chemical interactions between the more amorphous PHB-MP particles and paper fibers were identified as an esterification reaction, while the morphology of the NFC fibrillar network was playing a key role as binding agent in the retention of more crystalline PHB-SP at the paper surface, hence contributing to higher hydrophobicity.

The novel coronavirus has presented specimen-access challenges to geoscientific researchers, including paleobiologists interested in fossil ammonoids. Ammonoid sutures are geometric patterns formed by the intersection of the septa and the shell wall, and have long been a diagnostic tool for ammonite researchers for such applications as species identification, taxonomic relationships, ontogenetic change, functional and evolutionary morphology, and other aspects of ammonoid paleobiology. Without access to specimens in museum and institutional collections, researchers must rely on previously published illustrations and photographs of ammonoid sutures. However, many of these illustrations were published decades ago without an index of scale. Suture tracings lacking a scale bar are not usable by researchers interested in applying the quantitativeness of fractal geometry to the interpretation of septal complexity. Additonally, distortion of the marginal elements of suture geometry occurs due to shell curvature near the venter and umbilicus. The revised approach described here eliminates the problem of missing scale information in fractal analysis of ammonite sutures, making use of just the lateral lobe and adjacent saddle. Our revised method’s non-requirement of a full hemisuture also facilitates comparisons among sutures within an ontogenetic sequence, or sutures from multiple ammonite taxa.

Interest grows in designing silicon-on-insulator slot waveguides to trap optical fields in subwavelength-scale slots and developing their optofluidic devices. However, it is worth noting that the inherent limitations of the waveguide structures may result in high optical losses and short optical paths, which challenge the device performance in optofluidics. Incorporating the planar silicon-based slot waveguide concept into a silica-based hollow-core fiber can provide a perfect solution to realize an efficient optofluidic waveguide. Here we propose a subwavelength-scale liquid-core hybrid fiber (LCHF), where the core is filled with carbon disulfide and surrounded by a silicon ring in a silica background. The waveguide properties and the Stimulated Raman Scattering (SRS) effect in the LCHF are investigated. The fraction of power inside the core of 56.3% allows an improved sensitivity in optical sensing; while the modal Raman gain of 23.60 m-1·W-1 is 2 times larger than that generated around a nano fiber with the interaction between the evanescent optical field and the surrounding Raman media benzene-methanol, which enables a significant low-threshold SRS effect. Besides, this in-fiber structure features compactness, robustness, flexibility, ease of implementation in both trace sample consumption and reasonable liquid filling duration, as well as compatibility with optical fiber systems. The detailed analyses of the properties and utilizations of the LCHF suggest a promising in-fiber optofluidic platform, which provides a novel insight into optofluidic devices, optical sensing, nonlinear optics, etc.

Facility Management (FM) has increasingly focused on using Building Information Modeling (BIM) in large-scale development projects. To successfully integrate BIM in the FM sector, cooperation among different participants involved in various project stages must be improved. The objective of this digital revolution in FM is to enhance the efficacy of planning, constructing, and managing assets, benefiting all parties involved. However, the utilization of BIM in FM is limited due to factors such as incomplete owner understanding, insufficient data accessibility, and stakeholders' unfamiliarity with BIM procedures and standardization. Although the FM industry acknowledges BIM's significance, achieving successful implementation remains challenging. Facility managers lack a clear understanding of BIM's benefits in expediting operations and cost efficiency and the necessary skills for efficient utilization. To address this constraint, it is essential to develop an Employee’s Information Requirement (EIR) at the outset of a project, serving as a strategic plan and providing a comprehensive vision for all parties involved, particularly large-scale projects. Two essential technologies that facilitate the transition towards building operations are BIM and the Internet of Things (IoT). Incorporating these technologies is crucial to reducing time, expenses, and operational challenges throughout any project. The aim of this research is to create a Digital-Trio workflow, as a new expression, by providing a methodology for using facility management with BIM through the integration of EIR and IoT, maximizes the benefit of stakeholders strategically and operationally. It also explores how the preparation of the EIR by communicating with all parties will definitely improve the design process, sustainability, efficiency, cost, and time for any project, especially megaprojects.

To date, the development of unmanned technologies using autonomous underwater vehicles (AUV) has become an urgent demand for solving the problem of inspection of industrial sub-sea structures. A key issue here is precise localization of AUVs relative to underwater objects. However, the well-known challenges of recognizing and coordinating underwater objects (impossibility to use GPS, undercurrents, etc.) do not allow high-precision navigation if based solely on a standard suite of AUV navigation tools (sonars, etc.). An alternative is a technology of processing of optical images that, at short distances, can provide higher accuracy of AUV navigation compared to a technology of acoustic measurement processing. In this study, in the context of the problem of subsea production system inspection, we propose a method to recognize underwater objects and provide coordinate reference of AUV to them, based on stereo-image processing. Its distinctive features are the use of a non-standard technique for generating a geometric model of an object from its views (foreshortening) taken from positions of a pre-made overview trajectory, the use of various characteristic geometric elements when recognizing objects, and the original algorithms for comparing visual data of the inspection trajectory with an a priori model of the object.

Waste glycerol can be subjected to various processing operations, including purification and re-fining, to obtain glycerol of appropriate purity. In addition, alternative methods of utilising waste glycerol are also being sought, e.g. by converting it into other valuable chemical products or biofuels. Therefore, various technologies are being developed to utilise this type of waste effectively and sustainably. The production of value-added products from waste glycerol is an important issue that determines the improvement of the economic viability of biofuel production and corresponds to the model of a waste-free and emission-free circular economy. This paper characterised the mechanisms and evaluated the efficiency of existing methods of microbiological utilisation of waste glycerol into liquid biofuels, including biodiesel, bioethanol and biobutanol, and identified further directions for the production of value-added products. In addition, a bibliographical analysis of publications re-lated to the production of liquid fuels and economically valuable products from glycerol was carried out, the progress of research and application work was assessed and directions for future research were identified.

Abstract—In this paper, decidability of the structures of real, rational, integer and natural numbers will be studied in different languages. Decidability or undecidability of mathematical structures is one of the fundamental and sometimes very difficult problems of mathematical logic, where several examples of problems in this field are still open and unresolved even after decades. One of the goals of Mathematical Logic is the axiomatization of mathematical theoriesTarski has proved the decidability of the theory of real and complex numbers in the language of addition and multiplication, and it is proved that theories of natural, integer, and rational numbers, in the language of addition and multiplication, are undecidable (Theorems of Gödel and Robinson). We will review The following problemes: The Main Problem 1: ⟨Q; ⊑⟩ is decidable? Problem 2: an explicit axiomatization for ⟨Z; \times⟩? and we will study boolean algebras. Boolean algebras are famous mathematical structures.Tarski showed the decidability of the elementary theory of Boolean algebras.In this paper, we study the different kinds of Boolean algebras and their properties. And we present for the first-order theory of atomic Boolean algebras a quantifier elimination algorithm. The subset relation is a partial order and indeed a lattice order,And I will prove that the theory of atomic Boolean lattice orders is decidable, and furthermore admits elimination of quantifiers. So the theory of the subset relation is decidable. And we will study decidability of atomlss boolean algebra.

Five years ago, the concept of addressed fiber Bragg structures (AFBS) was proposed, which simultaneously perform the functions of a two-frequency radiation shaper, the difference frequency of which is the AFBS address, and a sensitive element, since the value of the difference frequency is invariant to measured physical fields, and the set of difference frequencies, moreover, is orthogonal in the array of such sensors, enabling their address multiplexing. In this article, we provide an overview of the theory and technology of AFBS, including the structures with three or more spectral components with various combinations of difference frequencies, symmetrical and asymmetric, performing the functions of the address and converting information signals to the low-frequency range at the same time, along with other functions. The subjects of interrogation of these structures, their fabrication and calibration are discussed as well. We also consider a wide range of applications in which AFBS can be used, covering such areas as oil and gas production, power engineering, transport, medicine, etc. In addition, the prospects of AFBS further development are proposed.

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

The interlaminar strength of mechanically interlocked polymer-metal-interfaces is strongly dependent on the surface structure of the metal component. Therefore, this contribution assesses the suitability of the fractal dimension for quantification of the surface structure as well as interlaminar strength prediction of aluminum/polyamide 6 polymer-metal-hybrids. Seven different surface structures, manufactured by blasting, combined blasting and etching, thermal spraying and laser ablation, are investigated. The experiments are carried out on a novel butt-bonded hollow cylinder testing method that allows shear and tensile strength determination with one specific specimen geometry. The fractal dimension of the metal surfaces is derived from cross-sectional images. For comparison, the surface roughness slope is determined and related to the interlaminar strength. Finally, a fracture analysis is conducted. For the investigated material combination, the experimental results indicate that the fractal dimension is an appropriate measure for predicting the interlaminar strength

Sehezar area is located in southern Tonokabon in Mazandaran province, north of Iran, near the Tarom – Hashdtjin belt. The existence of granitoid masses in the region can be important in terms of the potential of mineralization. Geochemical anomaly separation from the background is one of the important steps in mineral exploration. In the past decades, geochemical anomalies have been identified by means of various methods. Some of these separation methods include: statistical analysis methods (like univariate, bivariate, multivariate statistics), spatial statistical methods and fractal and multi-fractal methods. To identify the anomalous area, 71 stream sediment samples were collected from the area and analyzed by the ICP-MS method, and then interpreted. Initially, data were normalized and afterwards, univariate analysis (threshold limit and screening (P.N) methods) was used, in which results of the probable and definite anomaly of the threshold method were confirmed by the P.N screening method. Finally, the maps of the anomal zones were drawn. Then, bivariate analysis (Pearson correlation coefficients) and multivariate analysis on normal data were performed on SPSS software, in which factor analysis and cluster analysis were used for multivariate analysis. As a result of using the factor analysis method, six factors were identified and factor maps were drawn by the Surfer software. Also, by using cluster analysis, the variables were divided into two groups. In order for a better separation of the geochemical anomaly from the background, in addition to the threshold method, the Concentration - Area fractal method was used. Here, the fractal geometry using full-logarithmic graphs of the Concentration - Area obtained is capable of separating the stairs of different sections (background, threshold, and anomaly) with respect to the angle coefficient of the Concentration - Area plot. Then, in conclusion, results of these methods were compared and investigated, and finally, the anomalies area maps of the Au, Ag, Cu, Fe, W elements were drawn by Concentration - Area fractal and threshold methods and anomalous zones were introduced.

The article deals with auxetic structures made on the basis of suitably connected rigid rotating squares (from Grima and Evans), with axes of rotation on the squares’ surface. The geometric model and the resulting relationships that allow for the determination of Poisson’s ratio are considered in detail. It is demonstrated that changing the rotation axis position does not affect the negative Poisson’s ratio, equal to -1. The models built confirm the initial considerations and can offer new application possibilities.

The establishment of an isolation layer in submarine mining has long presented an enduring challenge. In the context of this research, we conducted a similarity simulation test to preliminarily ascertain the interplay between the thickness and extent of the isolation layer. Subsequently, we introduce an innovative approach that integrates fractal theory and the bonded block model (BBM) to simulate undersea isolation layer mining. The validation of this method hinges on on-site borehole scanning and displacement monitoring, which serve to depict the intricate fractal evolution of fractures and predict the optimal thickness of the isolation layer. Our findings affirm the robustness and validity of this method. Evaluation of the fractal dimensions of fractures reveals that a critical threshold of 1.7 exists to prevent structural failure of the isolation layer, while a limit of 1.5 is necessary to avert significant water ingress. Remarkably, the correlation dimension of the settlement time series closely aligns with the fractal dimension of the fractures, underscoring the feasibility of ensuring the safety of isolation layer mining through real-time settlement monitoring.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

In this article, the evolution in space and in time of the coronavirus pandemic is studied by utilizing a neural network with a self-organizing nature for the spatial analysis of data, and a fuzzy fractal method for capturing the temporal trends of the time series of the countries. Self-organizing neural networks possess the capability for clustering countries in the space domain based on their similar characteristics with respect to their coronavirus cases. In this form enabling finding the countries that are having similar behavior and thus can benefit from utilizing the same methods in fighting the virus propagation. To validate the approach, publicly available datasets of coronavirus cases worldwide have been used. In addition, a fuzzy fractal approach is utilized for the temporal analysis of time series of the countries. Then, a hybrid combination of both the self-organizing maps and the fuzzy fractal approach is proposed for efficient COVID-19 forecasting of the countries. Relevant conclusions have emerged from this study, that may be of great help in putting forward the best possible strategies in fighting the virus pandemic. A lot of the existing works concerned with the Coronavirus have look at the problem mostly from the temporal viewpoint that is of course relevant, but we strongly believe that the combination of both aspects of the problem is relevant to improve the forecasting ability. The most relevant contribution of this article is the proposal of combining neural networks with a self-organizing nature for clustering countries with high similarity and the fuzzy fractal approach for being able to forecast the times series and help in planning control actions for the Coronavirus pandemic.

Chikungunya virus (CHIKV) is a mosquito borne RNA virus that poses an emerging threat to humans. As other RNA viruses, CHIKV encodes an error-prone RNA polymerase which, in addition to full-length genomes, gives rise to truncated, non-functional genomes coined defective viral genomes (DVGs). DVGs have been intensively studied in the context of therapy, as they can inhibit viral replication and dissemination in their hosts. In this work, we interrogate the influence of viral RNA secondary structures on the production of CHIKV DVGs. We experimentally map RNA secondary structures of CHIKV genome using selective 2′-hydroxyl acylation analyzed by primer extension and mutational profiling (SHAPE-MaP), which couples chemical labelling with next-generation sequencing. We correlate the inferred secondary structure with preferred deletion sites of CHIKV DVGs. We document an increased probability of DVG generation with truncations at unpaired nucleotides within the secondary structure. We then generated a CHIKV mutant bearing synonymous changes at the nucleotide level to disrupt existing RNA secondary structure (CHIKV-D2S). We show that CHIKV-D2S presents altered DVG generation compared to wild-type virus, correlating with its change in RNA secondary structure obtained by SHAPE-MaP. Our work thus demonstrates that RNA secondary structure impacts CHIKV DVG production during replication.

The fractal dimension of geomagnetic variations at the Baigazan magnetic station at Russian Altay for 2011-2013 was calculated using the Higuchi method. The daily variation of Higuchi Fractal Dimension (HFD) for the D,H,Z-components of the geomagnetic field has been investigated, its contribution to the variability of HFD is from 30 to 40 percent of the total variance. A correlation analysis of the fractal dimension of the variations of the D,H,Z-components with Auroral Electrojet (AE) index and solar wind characteristics was carried out. A negative correlations with logarithms of AE-index, interplanetary magnetic field (IMF) strength and solar wind velocity were found. About 25 percent of the fractal dimension variance is controlled by the variability of these characteristics. Pair and partial correlation coefficients for these parameters were calculated for every month of 2011-2013.

The discovery of a simple numerical formula for the projection of all the atomic mass of life-sustaining CONHSP bioatoms leads to the emergence of a set of Nested CODES unifying all the biological, genetic and genomic components by unifying them from bioatoms up to 'to whole genomes. In particular, we demonstrate the existence of a digital meta-code common to the three languages ​​of biology that are RNA, DNA and amino acid sequences. Through this meta-code, genomic and proteomic images appear almost analogous and correlated. The analysis of the textures of these images then reveals a binary code as well as an undulatory code whose analysis on the human genome makes it possible to predict the alternating bands constituting the cariotypes of the chromosomes. The application of these codes to perspectives in astrobiology, in Cancers basic research and the emergence of binary codes and regions of local stability (voting process), whose fractal nature we demonstrate, is illustrated.

Understanding how novel structures arise is a central question in evolution. The carapace of the waterflea Daphnia is a bivalved “cape” of exoskeleton that surrounds the animal, and has been proposed to be one of many novel structures that arose through repeated co-option of genes that also pattern insect wings. To determine whether the Daphnia carapace is a novel structure, the expression of pannier, the Iroquois gene aurucan, and vestigial are compared between Daphnia, Parhyale, and Tribolium. The results suggest that the Daphnia carapace did not arise by cooption, but instead represents an elongated ancestral exite (lateral lobe or plate) that emerges from a proximal leg segment that was incorporated into the Daphnia body wall. The Daphnia carapace therefore appears to be homologous to the Parhyale tergal plate and the insect wing. In addition, the vg-positive region that gives rise to the Daphnia carapace also appears to be present in Parhyale and Tribolium, which do not form a carapace. Thus, rather than a novel structure resulting from gene co-option, the carapace appears to have arisen from an ancient, conserved developmental field that persists in a cryptic state in other arthropod lineages, but in Daphnia became elaborated into the carapace. Cryptic persistence of serially homologous developmental fields may thus be a general solution for the origin of many novel structures.

A construction for the systems of natural and real numbers is presented in Zermelo-Fraenkel Set Thoery, that allows for simple proofs of the properties of these systems, and practical and mathematical applications. A practical application is discussed, in the form of a Simple and Linear Fast Adder (Patent Pending). Applications to finite group theory and analysis are also presented. A method is illustrated for finding the automorphisms of any finite group $G$, which consists of defining a canonical block form for finite groups. Examples are given, to illustrate the procedure for finding all groups of $n$ elements along with their automorphisms. The canonical block form of the symmetry group $\Delta_4$ is provided along with its automorphisms. The construction of natural numbers is naturally generalized to provide a simple and sound construction of the continuum with order and addition properties, and where a real number is an infinite set of natural numbers. A basic outline of analysis is proposed with a fast derivative algorithm. Under this representation, a countable sequence of real numbers is represented by a single real number. Furthermore, an infinite $\infty\times\infty$ real-valued matrix is represented with a single real number. A real function is represented by a set of real numbers, and a countable sequence of real functions is also represented by a set of real numbers. In general, mathematical objects can be represented using the smallest possible data type and these representations are calculable. In the last section, mathematical objects of all types are well assigned to tree structures in a proposed type hierarchy.

Metaheuristic algorithms are widely used as optimization methods, due to their global exploration and exploitation characteristics, which obtain better results than a simple heuristic. The Stochastic Fractal Search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic-stochastic diffusion property, an improved Dynamic Stochastic Fractal Search (DSFS) optimization algorithm is presented. The DSFS algorithm was tested with benchmark functions, such as the multimodal, hybrid and composite functions, to evaluate the performance of the algorithm with dynamic parameter adaptation with type-1 and type-2 fuzzy inference models. The main contribution of the article is the utilization of fuzzy logic in the adaptation of the diffusion parameter in a dynamic fashion. This parameter is in charge of creating new fractal particles, and the diversity and iteration are the input information used in the fuzzy system to control the values of diffusion.

An extension of the models used to generate fractal traffic flows is presented by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated by the model, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

In addition to image filtering in the spatial and frequency domains, fractal characteristics induced algorithms offers considerable flexibility in the design and implementations of image processing solutions in areas such as image enhancement, image restoration, image data compression and spectrum of applications of practical interests. Facing up to a real-world problem of identifying workpiece surface defects, a generic adaptive fractal filtering algorithm is proposed, which shows advantages on the problems of target recognition, feature extraction and image denoising at multiple scales. First, we reveal the physical principles underlying between signal SNR and its representative fractal dimension indicative parameters, validating that the fractal dimension can be used to adaptively obtain the image features. Second, an adaptive fractal filtering algorithm (Abbreviated as AFFA) is proposed according to the identified correlation between the image fractal dimensions and the scales of objects, and it is verified by a benchmarking image processing case study. Third, by using the proposed fractal filtering algorithm, surface defects on a flange workpiece are identified. Compared to conventional image processing algorithms, the proposed algorithm shows superior computing simplicity and better performance Numerical analysis and engineering case studies show that the fractal dimension is eligible for deriving an adaptive filtering algorithm for diverse-scale object identification, and the proposed AFFA is feasible for general application in workpiece surface defect detection.