The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

Biohydrogen is a versatile energy carrier for the generation of electric energy from renewable sources. Hydrogenases can be used in enzymatic fuel cells to oxidize dihydrogen. The rate of electron transfer (ET) at the anodic side between the [NiFe]-hydrogenase enzyme distal iron-sulfur cluster and the electrode surface can be described by the Marcus equation. All parameters for the Marcus equation are accessible from DFT calculations. The distal cubane FeS-cluster has a three cysteine and one histidine coordination [Fe₄S₄](His)(Cys)₃ first ligation sphere. The reorganization energy (inner- and outer-sphere) is almost unchanged upon a histidine-to-cysteine substitution. Differences in rates of electron transfer between the wild-type enzyme and the all-cysteine mutant can be rationalized by a diminished electronic coupling between the donor and acceptor molecules in the [Fe₄S₄](Cys)₄ case. The fast and efficient electron transfer from the distal iron-sulfur cluster is realized by a fine-tuned protein environment which facilitates the flow of electrons. This study enables the design and control of electron transfer rates and pathways by protein engineering.

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent's next action by introducing two new classes of games: ’invertible games’ and ‘cyclical games'. By explicitly expanding out the mutual information between past states and the next action we show under what circumstances these expressions can be simplified. These information measures are then applied to the Traveler's Dilemma game and the Prisoner's Dilemma game, the Prisoner's Dilemma being invertible, to illustrate their use. In the Prisoner's Dilemma a novel connection is made between the computational principles of logic gates and both the structure of games and the agents' decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: ‘Tit-for-Tat' and ’Win-Stay, Lose-Switch'.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Keywords: olfactory rehabilitation; chronic pain; fMRI;

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss further possible utilizations in other fields of data processing.

Background and Objectives: Knee osteoarthritis (KOA) is a degenerative disease that is targeting continuously people of different ages, but especially the elderly population, the number of which tends to increase continuously at the global level. Apart from age, excess weight can influence the evolution of the disease, with obesity being associated with a weak inflammation stage, and an imbalance between pro-inflammatory and anti-inflammatory cytokines. The present work aimed to identify specific biomarkers alike ACRP-30, IL-10, TNF-α, and IL-6 in synovial fluid and correlate them with patients’ clinical data. Materials and Methods: 24 subjects with KOA and over 50 years of age are involved in the present study. All patients performed a supine X-ray at the target knee. Ultrasound was performed using an ESAOTE MyLab Omega (ESAOTE Spa, Italy) ultrasound device and a 6-19 MHz linear array transducer. Results: The obtained results highlighted a significant correlation between age and adiponectin level (p=0.0451, r=-0.412). Also, the IL-10 values are lower in cases where the intensity of the pain is more pronounced (p=0.0405, r=-0.421). In addition, analyzing the data by gender, it was observed that in the case of males, stiffness is more related to age (p=0.0079, r=0.7993), compared to women (p=0.0203, r=0.6223). In the case of women, the progression of the disease tends to increase more intensively total WOMAC score’s values (p=0.00031, r=0.8342), compared with men (p=0.0289, r=7013). Regarding interleukins and BMI, significant correlations were observed only in the case of men. Conclusions: A significant correlation between age and adiponectin, and adiponectin and IL-6, suggests that advanced age may contribute to adiponectin reduction. Comparing men with women, it was observed that men's age is more related to rigidity, and IL-6 and IL-10 are directly correlated to BMI and women seem to be more sensitive to pain and stiffness.

The paper presents the prediction of hydrodynamic characteristics of different rudder -plane configurations behind a submarine in deep water through the Reynolds-Averaged Navier-Stokes method in Ansys Fluent Solver. The hydrodynamic force and moment acting on the Cross-plane, X-plane, and Y-plane rudder configurations are analyzed for estimating hydrodynamic coefficientsfor predicting the advantages of each configuration to control the ship. The obtained results show that X-force of the X-plane rudder configuration is larger than the force acting on the Cross-plane rudder and Y-plane rudder configurations. However, Y-force, and Z-force of the X-plane rudder configuration are significantly greater than the Y-force of the left configurations. The same tendency can be seen in the moment of the X-plane rudder about the y-axis and z-axis. The roll moment induced by the Y-plane and Cross-plane rudder configurations is significantly larger than the case of the X-plane rudder configuration.

This article introduces a new fractional approach to the concept of information dimension of complex networks, based on a (q,q′)-entropy proposed in the literature. The q parameter measures how far is the number of subsystems (for a given size ε) from the mean number of overall sizes. The q′ (interaction index) measures when the interactions between subsystems are greater (q′>1), lesser (q′<1) or equal to the interactions into these subsystems. The computations of the proposed information dimension are carried out on several real-world and synthetic complex networks. The results from the proposed information dimension are compared with those from the information dimension based on the Shannon entropy.

The study shows that the volumes and surfaces of the $n$-simplices, $n$-orthoplices, $n$-cubes, and $n$-balls are holomorphic functions of $n$, which makes those objects omnidimensional. Furthermore, the volume of an $n$-simplex is shown to be a bivalued function of $n$, and thus the surfaces of $n$-simplices and $n$-orthoplices are also bivalued functions of $n$. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about $n$-balls reveal previously unknown properties of these geometric objects in negative dimensions. In particular, for $0 < n < 1$, the volumes of the omnidimensional polytopes are larger than those of circumscribing $n$-balls, while their volumes and surfaces are smaller than the volumes of inscribed $n$-balls. Reflection relations around $n = 0$ for volumes and surfaces of these polytopes inscribed in and circumscribed about $n$-balls are disclosed. Specific products and quotients of volumes and surfaces of the omnidimensional polytopes and $n$-balls are shown to be independent of the gamma function.

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

Microwave technology has a potential application in the extraction of zinc from sulphide ores, knowledge of the dielectric properties of these ores plays a major role in the microwave design and simulation for any process. The dielectric properties of zinc sulfide concentrate for two different apparent densities—1.54 and 1.63 g/cm³—have been measured by using the resonance cavity perturbation technique at 915 and 2450 MHz during the roasting process for the temperature ranging from room temperature to 850 °C. The variations of dielectric constant, the dielectric loss factor, the dielectric loss tangent and the penetration depth with the temperature, frequency and apparent density have been investigated numerically. The results indicate that the dielectric constant increases as the temperature increases and temperature has a pivotal effect on the dielectric constant, while the dielectric loss factor has a complicated change and all of the temperature, frequency and apparent density have a significant impact to dielectric loss factor. Zinc sulfide concentrate is high loss material from 450 to 800 °C on the basis of theoretical analyses of dielectric loss tangent and penetration depth, its ability of absorbing microwave energy would be enhanced by increasing the apparent density as well. The experimental results also have proved that zinc sulfide concentrate is easy to be heated by microwave energy from 450 to 800 °C. In addition, the experimental date of dielectric constant and loss factor can be fitted perfectly by Boltzmann model and Gauss model, respectively.

Primary biliary cholangitis (PBC) is a cholestatic liver disease characterized by immune-mediated injury to small bile ducts. Although PBC is an autoimmune disease, the results of traditional immunosuppressive therapy are disappointing. Nearly 40% of PBC patients do not respond to the first-line drug UDCA. Without appropriate intervention, PBC patients would eventually progress to liver cirrhosis and even death. There is an urgent need to develop new therapies. The gut-liver axis emphasizes the interconnection between the gut and the liver, and there is increasing evidence that gut microbiota and bile acids play an important role in cholestatic diseases. Dysbiosis of gut microbiota, imbalance of bile acids, and immune-mediated bile duct injury constitute the triad of pathophysiology in PBC. Understanding the gut microbiota-bile acid network and corresponding immune functions in PBC provides a new perspective for its treatment strategies. Therefore, we summarize the latest advancements in research of gut microbiota and bile acids in PBC and, for the first time, explore the potential of immune factors related to them as novel immunotherapy targets. This article discusses potential therapeutic approaches focusing on regulating gut microbiota, maintaining bile acid homeostasis, their interactions, and related immune factors.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

This paper provides orthogonal moments (OM) such as, Zernike Moments(ZM), Psuedo Zernike Moments(PZM) and Orthogonal Fourier Mellin Moments(OFMM) for the analysis of melanoma images. The moment invariants may vary with respect to geometric variations. For the analysis of orthogonal moments hundred random melanoma images and hundred non-melanoma images have been taken into consideration from the database of 570 melanoma images and 250 non-melanoma images respectively. Orthoganal moments have been computed by varying the phase angles from 10° to 40° with an equal interval of 10° degree for the orders 2, 4,8,16,32,64,128,256 respectively. For the optimal OMs Particle Swarm Optimization (PSO) technique have been used. These set of extracted optimal OMs have been further applied to classify melanoma images. Support Vector Machine (SVM) has been used for the classification of [1]sensitivity=88.78%.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

Graph symmetry detection, similarity, and identity measures have been extensively studied in graph automorphism and isomorphism problems. Nevertheless, graph isomorphism and automorphism detection remain an open (unsolved) problem for many decades. In this paper, a new optinalytic coefficient termed as an optical moment coefficient was introduced for optinalysis. Its characteristic efficiency was tested for bijective property, invariance, deterministic polynomiality and non-polynomiality. The test results show that the new optical moment coefficient is very efficient for symmetry detections, similarity and identity measures between two isometric isomorphs and automorphs; and deterministic on polynomial and non-polynomial graph models.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

Apple replant disease (ARD) is a complex issue caused by various fungal, oomycetes pathogens and parasites which can differ in their abundance between sites within a geographic region. Knowledge of the specific etiology of ARD at a particular site is required in order to develop commercially viable soil management strategies to combat specific/individual components of the disease. In this study we analyzed the soil from six ARD sites for the presence of fungal, bacterial and oomycetes communities and plant parasitic nematodes. Five fungal, and 17 bacterial classes were differentially represented in the microbiomes from different locations. Mortierellomycetes was the most abundant fungal taxa represented followed by Sordariomycetes. Mortierella exigua a fungal endophyte was the most abundant fungal amplicon sequence variant (ASV) in the core microbiome. Proteobacteria was the most prevalent phylum identified in orchard soils. Several potential phytopathogenic fungi involved in ARD and endophytes including Fusarium oxysporum, F. solani, Nectria ramulariae, Ilyonectria robusta and Nectriaceae were identfied in the orchard soil. Pythium attrantheridium (Globisporangium attrantheridium), P. monospermum and P. ultimum (Globisporangium ultimum) were the most abundant oomycete taxa identified in these soil samples. Six different groups of plant-parasitic nematodes were found across the six orchards soil. Root-lesion nematodes, Pratylenchus spp., which are commonly associated with ARD, were identified in all orchards soil at population densities ranging from 12 to 33/100 cm3 soil. This research contributes valuable understanding of the ARD complex as the apple industry needs alternative approaches to combat the disease.

Background: Clinical trails have revealed that patients with depression generally accompanied with learning and memory impairment, which critically impact on individual’s health and development. Danggui-Shaoyao-San (DSS), a famous Chinese complex prescription, significantly overcame depression and relieved cognitive disorder based on previous research and publication. However, its effectsand potential mechanism against chronic restraint stress (CRS) remained unknown. Methods: CRS animal model was established and mice were divided to six groups while they were oral administrated with Danggui-Shaoyao-San at doses of 1.25, 2.5 and 5 g/kg for 14 days. Emotional and cognitive performances were detected by behavior tests, meanwhile neural plasticity and its molecular mechanism were examined by Dil staining, western blot and immunofluorescence. Results: DSS treatment dose-dependently improved locomotion ability in open filed test, overcame depression behavior in forced swimming test and elevated plus maze test, enhanced learning and memory ability in Morris water maze test. CRS decreased number of total spines and mushroom spines, while DSS treatment dose-dependently restored these by Dil staining. Expression of BDNF and GluR1 were significantly down-regulated in CRS group, which were significantly normalized by DSS. Conclusions: DSS treatment dose-dependently reversed CRS-induced cognitive impairments by inducing structural remodeling of neurons.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

This paper describes the first results of an Image Recognition Based Location (IRBL) for mobile application focusing on the procedure to generate a Database of range images (RGB-D). In an indoor environment, to estimate the camera position and orientation, a prior spatial knowledge of the surrounding is needed. In order to achieve this objective a complete 3D survey of two different environment (Bangbae metro station of Seoul and E.T.R.I. building in Daejeon – Republic of Korea) was performed using LiDAR (Light Detection And Ranging) instrument and the obtained scans were processed in order to obtain a spatial model of the environments. From this, two databases of reference images were generated using a specific software realized by the Geomatics group of Politecnico di Torino (ScanToRGBDImage). This tool allow to generate synthetically different RGB-D images) centered in the each scan position in the environment. Later, the external parameters (X, Y, Z, ω, φ, κ) and the range information extracted from the DB images retrieved, are used as reference information for pose estimation of a set of acquired mobile pictures in the IRBL procedure. In this paper the survey operations, the approach for generating the RGB-D images and the IRB strategy are reported. Finally the analysis of the results and the validation test are described.

Some peptide-based drugs including oxytocin, vasopressin, ziconotide, pramlintide, nesiritide, and octreotide, contain one intramolecular disulfide bonds. A novel and reusable monodispersed silica nanosphere-supported Pt(IV) complex (SiO2@TPEA@Pt(IV)) was synthesized via a four-step procedure and used for formation of intramolecular disulfide bonds in peptides. TEM and chemical mapping results for the Pt(II) intermediates and for SiO2@TPEA@Pt(IV) show that the silica nanospheres possess a monodisperse spherical structure and contain uniformly distributed Si, O, C, N, Cl, and Pt. The valence state of Pt on the silica nanospheres was characterized by XPS. The Pt(IV) loaded on SiO2@TPEA@Pt(IV) was 0.15 mmol/g, as determined by UV-vis spectrometry. Formation of intramolecular disulfides in six dithiol-containing peptides of variable lengths by use of SiO2@TPEA@Pt(IV) was investigated and the relative oxidation yields were determined by HPLC. In addition, peptide 1 (Ac-CPFC-NH2) was utilized to study the reusability of SiO2@TPEA@Pt(IV). No significant decrease in the relative oxidation yield was observed after ten reaction cycles. Moreover, the structure of SiO2@TPEA@Pt(IV) after being used ten cycles was determined to be similar to its initial one, demonstrating the cycling stability of the complex.

The spin magnetic moments and spin g factors (g_s = -2) of electron, muon and tau are explained based on the electric charges (EC) and lepton charges (LC) in terms of the three-dimensional quantized space model. The spin g factors of electron, muon and tau are g_s = -2 which is the sum of the EC g factor (g_EC = -1) and the LC g factor (g_LC = -1). The spin g factor (g_s = -2) of the electron is predicted by the Dirac’s equation. The orbit g factors of electron, muon and tau are g_L = g_EC = -1 from the EC g factor (g_EC = -1) without the contribution of the LC g factor (g_LC = -1). The spin g factors of the elementary fermions are calculated from the equation of g_s = g_EC + g_LC + g_CC where g_EC = EC/|EC|, g_LC = LC/|LC| and g_CC = CC/|CC|. For example, the spin g factors of the neutrinos and dark matters are g_s = -1. The spin g factors of the u and d quarks are g_s = 0 and g_s = -2, respectively. The g factor problem of neutrinos with the non-zero LC charges are solved by the LC Coulomb force of F_c(LC) ≈0. It is, for the first time, proposed that the binary motion (fluctuations) of the m_EC and m_LC masses for the electron, muon and tau leptons make the anomalous g factor. This binary motion could be originated from the virtual particle processes including the photons. Also, the weak force (beta) decay is closely related to the binary motion of the m_EC and m_LC for the electron, muon and tau leptons.

In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-diffusion; (iv)~hydrodynamic fully developed turbulence, and (v)~plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon Permutation Entropy ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

The conventional well placement was done manually by using a numerical reservoir simulator, and it required a lengthy trial-and-error process. It required great experience and expertise to manipulate the variables and uncertainties that lie on the reservoir to determine the best placement of the well. In addition, the traditional gradient-based methods such as Line-search and Trust-region were not viable in terms of maximum results obtained. Gradient-based methods were too dependent on the surface gradient of the solution and may only converge to local optima instead of global optima. Complex reservoirs have rough surfaces with high uncertainties, which hinders the traditional gradient-based method from converging to global optima. Thus, genetic algorithms were utilized to automate the manual trial-and-error process and to overcome the limitations of the traditional gradient-based method. The objectives of this study were to analyse the effect of different initial well placement distributions, the number of random solution sizes, and the crossover rate on cumulative oil production. A synthetic reservoir model built using CMG Builder was used as the testing platform for the optimization problems. Well-placement parameterization and optimization set-up were carried out using the CMG CMOST optimization tool. The integration of CMG IMEX and CMOST optimized cumulative oil production based on the objectives of the study. The results obtained showed that the higher number of random solutions used resulted in higher cumulative oil production, with more generations needed to reach the optimum solution. It can be concluded that the larger number of random solutions used increased the probability of reaching the optimum solution, but will take more generations.

In this paper, we succeed to discover the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of concerned model. Finally, this technique is simple, fruitful and reliable to handle the nonlinear FPDEs.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

An analysis is presented of the possible existence of a second anomalous dipole moment of Dirac’s particle next to the one associated with the angular momentum. It includes a discussion why, in spite of his own derivation, Dirac has doubted about its relevancy. It is shown why since then it has been overlooked and why it has vanished from leading textbooks. A critical survey is given on the reasons of its reject, including the failure of attempts to measure and the perceived violations of time reversal symmetry and charge-parity symmetry. It is emphasized that the anomalous electric dipole moment of the pointlike electron (AEDM) is fundamentally different from the quantum field type electric dipole moment of an electron (eEDM) as defined in the standard model of particle physics. The analysis has resulted into the identification of a third type Dirac particle, next to the electron type and the Majorana particle. It is shown that, unlike as in the case of the electron type, its second anomalous dipole moment is real valued and is therefore subject to polarization in a vector field. Examples are given that it may have a possible impact in the nuclear domain and in the gravitational domain.

Furthermore, the nasal congestion typical of rhinitis can contribute to upper airway obstruction and sleep-disordered breathing. A vicious circle is created between asthma and sleep-disordered breathing: uncontrolled asthma and sleep-disordered breathing can worsen each other. In children with genetic obesity, despite alterations in the immune system, fewer allergies are found compared to the general population. The causes of this reduced allergenicity are unclear but probably involve genetic, immunological, and environmental factors. Further studies are needed to understand the mechanisms. The study emphasizes the importance of jointly evaluating and managing allergies, obesity, and sleep-disordered breathing in children, considering their close interconnection.

Based on the dynamic strength variation mechanism of concrete under complex loading conditions, two approaches were devised: numerical testing and CT scanning, guided by the principle of minimizing energy dissipation. A methodology for calculating concrete's failure area and measuring its strength was developed. The analysis delves into the mechanisms behind failure patterns and variations in concrete specimen strength, focusing on crack initiation, development, and the resultant failure surface formed by crack propagation, along with the stress distribution in concrete specimens subjected to diverse loading conditions. Through evaluating the strength and computed failure area of concrete specimens, it is evident that the loading method influences both the strength and failure area of concrete specimens. In general, a larger failure area correlates with a higher measured strength.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

Fibrodysplasia Ossificans Progressiva (FOP) is an enigmatic, ultra-rare genetic disorder characterized by progressive heterotopic ossification, wherein soft connective tissues undergo pathological transformation into bone structures. This incapacitating process severely limits patient mobility and poses formidable challenges for therapeutic intervention. Predominantly caused by missense mutations in the ACVR1 gene, the disorder has hitherto defied comprehensive mechanistic understanding and effective treatment paradigms. This write-up offers a comprehensive overview of the contemporary understanding of FOP's complex pathobiology, underscored by advances in molecular genetics and proteomic studies. We shed light on targeted therapy, spanning genetic therapeutics, enzymatic and transcriptional modulation, stem cell therapies, and innovative immunotherapies. We also focused on the intricate complexities surrounding clinical trial design for ultra-rare disorders like FOP, addressing fundamental statistical limitations, ethical conundrums, and methodological advancements essential for the success of interventional studies. We advocate for the adoption of a multi-disciplinary approach that converges bench-to-bedside research, clinical expertise, and ethical considerations to tackle the challenges of ultra-rare diseases like FOP and comparable ultra-rare diseases. Overall, this article serves a dual role: as a definitive scientific resource for ongoing and future FOP research and as a call to action for innovative solutions to address methodological and ethical challenges that impede progress in the broader field of medical research for ultra-rare conditions.

An analysis is presented of the possible existence of a second anomalous dipole moment of Dirac’s particle next to the angular one. It includes a discussion why, in spite of his own derivation, Dirac has doubted about its relevancy. It is shown why since then it has been overlooked and why it has vanished from leading textbooks. A critical survey is given on the reasons of its reject, including the failure of attempts to measure and the perceived violations of time reversal symmetry and chargeparity symmetry. It is emphasized that the anomalous electric dipole moment of the pointlike electron (AEDM) is fundamentally different from the quantum field type electric dipole moment of an electron (eEDM) as defined in the standard model of particle physics and that its measurement requires different instrumentation. A proposal has been described how to prove or disprove its existence by experiment. Moreover, by reference from literature, the possible impact is discussed in the nuclear domain and in the gravitational domain.

In particle physics, spin is an intrinsic form of angular momentum carried by the elementary particles. It is believed that spin is a solely quantum-mechanical phenomenon, which does not have a counterpart in classical mechanics. We have derived the simplest equations of spin and magnetic moment of a charged elementary particle. These formulas enable us to understand the physical nature of the spin and the structure of elementary particles. It is shown that the electron and muon are in the shape of a thin ring with a circular cross section (torus), and the proton is in the form of a ring with a non-circular cross section (toroid). The connection between the photon’s spin of and the propagation of electromagnetic waves is considered.

This communication explores the transition from Cognitive Behavioural Therapy (CBT) to a more holistic model, named Complex Therapy, developed by Tullio Scrimali for explaining and treating mental disorders. The Author delves into the limitations of traditional CBT and introduces an innovative framework that integrates multiple therapeutic modalities. While CBT is based on the study and modification of behaviour and cognition, Complex Therapy includes, in its focus, the theory of human relationships, the attachment theory, neuroscience, applied neuroscience, complex systems theory and ecology.Complex Therapy addresses the multifaceted nature of mental health issues by combining evidence-based techniques with personalized care strategies. The goal is to enhance patient outcomes through a tailored, comprehensive treatment plan that adapts to the evolving needs of individuals facing mental health challenges.Two innovative and original items which Scrimali has developed, which are a device for Applied Neuroscience MindLAB Set and a new botanical drug, NegEnt, are presented and discussed.The topic also describes, an original and integrated protocol, named Negative Entropy, the author has developed for treating a challenging disorder, such as schizophrenia, he renamed Entropy of Mind.

A hybrid material, consisting of commercially available nitrocellulose (NC) membrane non-covalently modified with amino-polyethylene glycol functionalized reduced graphene oxide (NH2-PEG-rGO) nanoparticles, was successfully synthesized for oligonucleotide extraction. Fourier Transform Infrared Spectroscopy (FTIR) confirmed the modification of the NC membrane, revealing characteristic peaks of both compounds NC and NH2-PEG-rGO. Scanning Electron Microscopy (SEM) exhibited morphological changes in the NC/NH2-PEG-rGO hybrid membrane, marked by the introduction of NH2-PEG-rGO particles, resulting in a distinctly smothered surface compared to the porous surface of the NC control membrane. Wettability assays revealed hydrophobic behavior for the NC/NH2-PEG-rGO hybrid membrane, with a water contact angle exceeding 90°, contrasting with the hydrophilic behavior characterized by a 16.7° contact angle in the NC membrane. The performance of the NC/NH2-PEG-rGO hybrid membrane was evaluated for the extraction of ssDNA with fewer than 50 nucleotides from solutions containing various ionic species (MnCl2, MgCl2, and MnCl2/MgCl2). The NC/NH2-PEG-rGO hybrid membrane exhibited optimal performance when incubated in MgCl2, presenting the highest fluorescence emission at 525 relative fluorescence units (r.f.u.). This corresponds to the extraction of approximately 610 pg (≈13%) of the total oligo-DNA, underscoring the efficacy of the pristine material, which extracts 286 pg (≈6%) of oligo-DNA in complex solutions.

Dental agenesis is one of the most common developmental anomaly in humans and it is frequently as-sociated with several other oral abnormalities. The present case describes nonfamilial agenesis of per-manent teeth in a twenty-one-year-old boy, with no apparent systemic abnormalities. The treatment in-cluded a personalized and interdisciplinary approach by the means of endodontics, orthodontics, im-plants supported restorations and prosthetic treatments. The treatment plan was thoroughly elaborated using photographic analysis, study models, orthopantomogram, CBCT and cephalograms. Virtual smile design, diagnostic waxing, and mock-up previsualized the treatment objectives. The edentulous spaces were reconstructed by inserting dental implants, and monolithic Zirconia implant supported restorations. The final results showed a highly aesthetic and functional rehabilitation. Periodic checkups have shown that the stability of the result is well maintained and that the implant supported restorations are an op-timal solution for patients with multiple anodontia.

Human papillomavirus (HPV) uses the cellular trafficking machinery to reach the cell nucleus and initiate a successful infection. The HPV capsid consists of two proteins: L1 (the major capsid protein) and L2 (minor capsid protein), and L2 is known to be responsible for trafficking the viral genome to the nucleus. From previous studies, we know that many cellular proteins interact with L2 and are involved in the trafficking process at different stages of the infectious entry process. To further investigate how HPV-16 achieves successful viral entry, we have performed a mass spectrometry analysis to identify novel interacting proteins that associate with incoming HPV-16 virions. We show that HPV-16 pseudovirions interact with a group of cellular cargo proteins (COPI), and here we confirm that this is mediated by the direct binding of L2, but not L1, to the COPB1 subunit. We also show that the ability of L2 to interact with COPB1 is conserved in both low- and high-risk HPV types. Furthermore, we also show that the interaction is essential for successful infection entry of multiple HPV types, thereby identifying a novel constituent of the infectious entry pathway of the HPV.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

Aiming at the limitations of single-functionality, limited applicability, and complex designs prevalent in current metasurfaces, we propose a terahertz multifunctional and multiband tunable metasurface utilizing a VO2-metal hybrid structure. This metasurface structure comprises a top VO2-metal resonance layer, a middle polyimide dielectric layer, and a gold film reflective layer at the bottom. This metasurface exhibits multifunctionality, operating independently of polarization and incident angle. The varying conductivity states of the VO2 layers, enable the metasurface to achieve various terahertz functionalities, including single-band absorption, broadband THz absorption, and multiband perfect polarization conversion for linear (LP) and circularly polarized (CP) incident waves. Finally, we believe that the functional adaptability of the proposed metasurface expands the repertoire of options available for future terahertz device designs.

The precise regulation of hinge moment and pitch angle driven by the pitch regulated mechanism is crucial for modulating thrust requirements and ensuring stable attitude control in Martian coaxial rotorcraft. Nonetheless, the aerodynamic hinge moment in rotorcraft presents time-dependent dynamic properties, posing significant challenges for accurate measurement and assessment for such characteristics. In this study, we delve into the detailed aerodynamic hinge moment characteristics associated with the pitch regulated mechanism of Mars rotorcraft under a spectrum of control strategies. A robust computational fluid dynamics model has been developed to simulate rotor’s aerodynamic loads, accompanied by a quantitative hinge moment characterization that takes into account the effects of varying rotor speeds and pitch angles. Our investigation has yielded a thorough understanding of the interplay between aerodynamic load behavior and rotor surface pressure distributions, leading to the creation of an empirical mapping model for hinge moments. To validate our findings, we engineered a specialized test apparatus capable of measuring the hinge moments of the pitch regulated mechanism, facilitating empirical assessments under replicated atmospheric conditions of both Earth and Mars. The result indicates aerodynamic hinge moments depend non-linearly on rotational speed, peaking at a 0° pitch angle and showing minimal sensitivity to pitch under 0°. Above 0°, hinge moments decrease, reaching a minimum at 15° before rising again. Simulation and experimental comparisons demonstrate that under Earth conditions, the aerodynamic performance and hinge moment errors are within 8.54% and 24.90%, respectively. For Mars conditions, errors remain below 11.62%, proving the CFD model’s reliability. This supports its application in the design and optimization of Mars rotorcraft systems, enhancing their flight control through accurate prediction of aerodynamic hinge moments across various pitch angles and speeds.

Redox mediators comprising I–, Co3+, and Ti3C2Tx MXene were applied to dye-sensitized solar cells (DSCs). In the as-prepared DSCs (I-DSCs), wherein hole conduction occurred via the redox reaction of I−/I3− ions, the power conversion efficiency (PCE) was not altered by the addition of Ti3C2Tx MXene. The I-DSCs were exposed to light to produce Co2+/Co3+-based cells (Co-DSCs), wherein the holes were transferred via the redox reaction of Co2+/Co3+ ions. A PCE of 9.01% was achieved in a Co-DSC with Ti3C2Tx MXene (Ti3C2Tx-Co-DSC), which indicated an improvement from the PCE of a bare Co-DSC without Ti3C2Tx MXene (7.27%). It was also found that the presence of Ti3C2Tx MXene in the redox mediator increased the hole collection, dye regeneration, and electron injection efficiencies of the Ti3C2Tx-Co-DSC, leading to an improvement in both the short-circuit current and the PCE when compared with those of the bare Co-DSC without MXene.

Background: Asthma is a widespread chronic respiratory disease that poses a significant public health challenge. The current study investigated the associations between air pollution and asthma severity among individuals residing near the Sohar industrial port (SIP) in Oman. Despite the presence of multiple major industrial complexes in Oman, limited knowledge regarding their impact on respiratory health is accredited. Hence, the primary objective of this study is to offer valuable insights into the respiratory health consequences of industrial air pollution in Al Batinah North. Methods: The state health clinics' records for patient visits related to asthma were collected for the timeframe spanning 2014 to 2022. Exposure was defined as the distance from SIP, Majan Industerial Area (MIA) and Sohar Industerial Zone (SIZ) to determine high, intermediate, and low exposure zones (12 km, respectively). Exposure effect modifications by age, gender, and smoking status were also examined. Results: The conducted cross-sectional study of 410 patients (46.1% males and 53.9% females) living in over 17 areas around SIP revealed that 73.2% of asthmatics were under 50 years old, with severity significantly associated with closeness to the port. Risk ratios were estimated to be (RR:2.42; CI95%: 1.01–5.78), (RR:1.91; CI95%: 1.01–3.6), and (RR:1.68; CI95%: 0.92–3.09) for SIP, MIP and SIZ areas, respectively, compared to the control area. Falaj Al Qabail (6.4 km) and Majees (6 km) had the highest number of asthma patients (N. 69 and N. 72), and highest percentages of severe asthma cases among these patients (28% and 24%) with significant risk ratios (RR:2.97; CI95%: 1.19–7.45 and RR:2.55; CI95%: 1.00–6.48), correspondingly. Moreover, severe asthma prevalence peaked in the 25-50 age group (RR:2.05; CI95%: 1.26–3.33), and this linkage between asthma and age was much more pronounced in males than females. Smoking and exposure to certain contaminant (dust and smoke) increased also the risk of severe asthma symptoms, but their effects were less important in the high risk zone, suggesting much more important risk factor. A neural network model accurately predicted asthma risk (94.8% accuracy), with proximity to Sohar Industrial Port as the most influential predictor. Conclusion: The study highlights the High asthma burden near Sohar Industrial Port, linked to port proximity and smoking and wind direction as major risk factors. These findings inform vital public health policies to reduce air pollution and improve respiratory health in the region, prompting national policy review.

Cranberries are rich in bioactive constituents reported to influence a variety of health benefits, ranging from improved immune function and decreased infections to reduced cardiovascular disease and more recently cancer inhibition. A review of cranberry research targeting cancer revealed positive effects of cranberries or cranberry derived constituents against 17 different cancers utilizing a variety of in vitro techniques; whereas, in vivo studies supported the inhibitory action of cranberries toward cancers of the esophagus, stomach, colon, bladder, prostate, glioblastoma and lymphoma. Mechanisms of cranberry-linked cancer inhibition include cellular death induction via apoptosis, necrosis and autophagy; reduction of cellular proliferation; alterations in reactive oxygen species; and modification of cytokine and signal transduction pathways. Given the emerging positive preclinical effects of cranberries, future clinical directions targeting cancer or premalignancy will be considered

In traditional finance, option prices are typically calculated using crisp sets of variables. However, in a proposed new approach, the assumption is made that these parameters have a degree of fuzziness or uncertainty associated with them. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. To determine the belief degree associated with a particular option price, an interpolation search algorithm was proposed recently[1]. Interpolation is a mathematical technique used to estimate values between known data points. In this case, the algorithm is applied to determine the belief degree associated with a specific option price within the range of possible prices. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. It allows them to consider their risk preferences and beliefs about the uncertain parameters when selecting an option price. In this paper, we will review a unified framework for combining fractional Brownian motion with fuzzy processes and obtain a joint measure space. We start by constructing a product measure space that captures the randomness and fuzziness inherent in the respective processes. We begin with the usual Kolmogorov filtered probability space (Ω, F, ℙ), where ℙ represents the probability measure, Ω is the set of all possible outcomes or states that a random process can take and {Ft, t ∈ [0, T]} is an information filtration. We will review the work of Merton (1976) on option pricing when the underlying stock returns have jumps [2] and expand it to fuzzy fractional processes.

Volatility estimation and quantile regression are relevant active research areas in statistics, machine learning and econometrics. In this work, we propose two procedures to estimate local variances in generic regression problems by using of kernel smoothers. The proposed schemes can be applied in multidimesional scenarios (not just for time series analysis) and easily in a multi-output framework, as well. Moreover, they allow the possibility of providing uncertainty estimation using a generic kernel smoother technique. Several numerical experiments show the benefits of the proposed methods, even comparing with benchmark techniques. One of these experiment involves a real dataset analysis.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

Drag-dominant tidal turbine energy holds tremendous clean energy potential but faces significant hurdles as unsuitability of Disk Actuator theory due to the varying swept blockage area, unaccounted bypass flow downstream interaction and rotor parasitic drag whereas Blade Element Momentum theory is computably effective for majorly 3-blade lift-dominated aerofoil. This study proposes a novel method to find the optimal TSR of any turbine with a cost-effective and user-friendly Moment Balancing algorithm to support robust tidal energy development. Performance analysis CFD study of Pinwheel and Savonius tidal turbines was carried out. Dynamic TSR matrix was developed with varying rotational speeds and fluid velocities for reliability, unlike previous works simulated at a fixed fluid velocity. Novel parameters such as thrust and idle moment are introduced as functions of only inlet fluid velocity and rotational speed respectively. These relationships are verified through regression analysis, and the turbines' net moment equations are established based on these parameters. Rotational speed was a reliable predictor for Pinwheel's idle moment, while inlet velocity was a reliable predictor for thrust moment in both models. The optimal (Cp, TSR) values for Pinwheel and Savonius turbines were (2.37, 0.223) and (0.63, 0.16) respectively, within an acceptable error range for experimental validation.

The bipartite entanglement is comprehensively investigated in the mononuclear molecular complex (Et3NH)[Ni(hfac)2L], where HL denotes 2-(2-hydroxy-3-methoxy-5-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-3-oxide-1-oxyl and hfacH stands for hexafluoroacetylacetone. From the magnetic point of view, the molecular compound (Et3NH)[Ni(hfac)2L] consists of an exchange-coupled spin-1 Ni2+ magnetic ion and a spin-12 nitronyl-nitroxide radical substituted nitrophenol. The nickel-radical molecular complex affords an experimental realization of a mixed spin-(12, 1) Heisenberg dimer with a strong antiferromagnetic exchange coupling J/kB= 505 K and two distinct g-factors gRad=2.005 and gNi=2.275. By adopting this set of magnetic parameters we demonstrate that the Zeeman splitting of a quantum ferrimagnetic ground-state doublet due to a weak magnetic field may substantially reinforce the strength of bipartite entanglement at low temperatures. The molecular compound (Et3NH)[Ni(hfac)2L] maintains sufficiently strong thermal entanglement even at room temperature, vanishing only above 546 K. Specifically, the thermal entanglement in the nickel-radical molecular complex retains approximately 40% of the maximum value corresponding to perfectly entangled Bell states at room temperature, which implies that this magnetic compound provides suitable platform of a molecular qubit with potential implications for room-temperature quantum computation and quantum information processing.

This paper aims to demonstrate that, beyond the small world of Riemann-Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to the different paths taken. Notions of time and scale sequences are introduced and general associated basic derivatives, namely right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to get both known and new fractional order derivatives. Several fractional derivatives are considered, mainly: Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

The analytical method for the calculation of the properties of a bolted connection established by the structural Eurocodes proposes the T-stub as a component for the characterization of the tension and compression zones in moment joints. In this article, a review of the state of the art on the T-stub component is developed, where the works developed since it was initially defined, and from the perspectives of formulation, experimentation and numerical simulation are summarized and discussed. Additionally, possible future lines of work are proposed.

We consider fractional integral operators $(I-T)^d, d \in (-1,1)$ acting on functions $g: \mathbb{Z}^{\nu} \to \mathbb{R}, \nu \ge 1 $, where $T $ is the transition operator of a random walk on $\mathbb{Z}^{\nu}$. We obtain sufficient and necessary conditions for the existence, invertibility and square summability of kernels $\tau (\mathbf{s}; d), \mathmb{s} \in \mathbb{Z}^{\nu}$ of $(I-T)^d $. Asymptotic behavior of $\tau (\mathbf{s}; d)$ as $|\mathbf{s}| \to \infty$ is identified following local limit theorem for random walk. A class of fractionally integrated random fields $X$ on $\mathbb{Z}^{\nu}$ solving the difference equation $(I-T)^d X = \varepsilon$ with white noise on the right-hand side is discussed, and their scaling limits. Several examples including fractional lattice Laplace and heat operators are studied in detail.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

The goal of this study was to analyze the instability during stepping of young and older adults at fast and spontaneous speed. To this aim, the anteroposterior and the mediolateral distances between the body center of mass (COM) and the minimum moment axis (MMA) were computed. A total of 15 young adults (25y.o. [19-29]) and 15 older adults 68.7y.o. [63-77] volunteered for this study. For the computation of the distances, a complete biomechanical protocol combining two force platforms and a 3D motion capture analysis system was setup. The subjects were equipped with 47 reflective markers and were modeled as a frictionless multibody with 19 segments, 18 joints and 42 degrees of freedom and were asked to perform a stepping at both speeds. The stepping was divided in 5 phases with successive swing and double stance phases. The greater instability was observed during the swing phases. The distances indicate a significant higher instability at fast speed for both groups (p &lt; 0.001) for all the phases. The anteroposterior distance also increases significantly for older adults highlighting greater instability while no differences were observed for the mediolateral distance all along the 5 phases suggesting higher risks of backward of forward falls during stepping.

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

This work is a top-level summary of several contributions published in the last three decades. It makes the case that complex dynamics of nonlinear systems lies at the heart of foundational physics.

Magneto-electrochemistry (MEC) is a unique paradigm in science, where electrochemical experiments are carried out as a function of an applied magnetic field, creating a new horizon of potential scientific and technological applications. Over the time, detailed understanding of this research domain was developed to identify and rationalize the possible effects exerted by a magnetic field on the various microscopic processes occurring in an electrochemical system, such as: electrolyte properties governed by charge-transfer process (electric conductivity, viscosity, and diffusivity), mass transfer, electrochemical kinetics and on the structure/quality of products formed either at the working electrode or in the electrochemical cell. Particularly, magnetic field controlled chiral architecture obtained from deposited metal, alloys and catalyst and their excellent enantio-recognition in experimental frame is highly appealing. Interestingly, Hall effect was also demonstrated in electrolytic medium via an impressive experimental technique which is being employed for further theoretical understanding in the field of magneto-electrochemical science. Later, a highly reproducible local temperature variation was observed in electrochemical electrolytes exposed to perpendicular magnetic and electric fields. However, until recent studies, none of the above mentioned reports considered the possibility of a spin-dependent related charge-transfer process. Recent experimental and theoretical studies reveal that electron’s transmission through chiral molecules is spin-selective and this effect has been referred to as chiral-induced spin-selectivity (CISS) effect. The CISS effect pave the way for the building up of a system characterized by a net magnetic moment exploiting the spin-filtering ability of chiral molecules. This interplay between chirality and magnetism may shed light on fundamental scientific aspects underlying the enantio-recognition and highly efficient electron-transfer that occurs in biological process.

The allosteric SERCA (Sarcoplasmic/Endoplasmic Reticulum Ca2+-ATPase) activator CDN1163 has been recently added to the group of pharmacological tools for probing SERCA function. We chose to investigate the effects of the compound on T lymphocyte Ca2+ stores, using the well-described Jurkat T lymphocyte as a reliable cell system for Ca2+ signaling pathways. Our study identified the lowest concentrations of the SERCA inhibitors thapsigargin (TG) and 2,5-di-(tert butyl)-1,4-benzohydroquinone (tBHQ) capable of releasing Ca2+, permitting the differentiation of the TG-sensitive SERCA 2b Ca2+ store from the tBHQ-sensitive SERCA 3 Ca2+ store. We proceeded to test the effects of CDN1163 on Ca2+ stores, examining specific actions on the SERCA 2b and SERCA 3 Ca2+ pools using our low dose SERCA blocker regimen. In contrast to previous work, we find CDN1163 exerts complex time-sensitive and SERCA isoform-specific actions on Ca2+ stores. Surprisingly, short-term exposure (0-30 minutes) to CDN1163 perturbs T cell Ca2+ stores by suppressing Ca2+ uptake with diminished Ca2+ release from the SERCA 2b-controlled store. Concomitantly, we find evidence for a SERCA-activating effect of CDN1163 on the SERCA 3 regulated store, given the observation of increased Ca2+ release inducible by low dose tBHQ. Intriguingly, longer-term (&gt;12 hours) CDN1163 exposure reversed this pattern, with increased Ca2+ release from SERCA 2b-regulated pools, yet decreased Ca2+ release responses from tBHQ-sensitive SERCA 3 pool. Our results reveal differential effects of CDN1163 on Ca2+ stores regulated by distinct SERCA isoforms, prompting the need for careful interpretation of the compound’s effects, particularly in cells expressing multiple SERCA isoforms.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

Recent technological advancements in conservation genetics and genomics have resulted in diverse tools for aiding conservation of species. The precision and resolution of high throughput sequencing technologies provide valuable insights to aid conservation decisions, but these technologies are often financially unfeasible or unavailable in resource constrained countries. Inter-Simple Sequence Repeat (ISSR) markers, when combined with sensitive automated detection systems, provide a simple, cheap means to investigate genetic diversity and discriminate closely related species. Here we apply this technology to assess genetic diversity and taxonomic delimitation in the Encephalartos eugene-maraisii species complex, a highly threatened, taxonomically dubious group of cycads in South Africa. Silica dried cycad leaflets were extracted using the Oktopure robot employing Sbeadex chemistry and amplified with fluorescently tagged ISSR primers. Band presence was scored with an ABI 3130 genetic sequencer under three different fluorescence cut-off values. Phenetic analyses were performed in NTSYS software while Bayesian analysis was performed in STRUCTURE, and haplotype network analysis, AMOVA and Tajima’s D statistic was computed with PopART. Our analyses support taxonomic singularity of E. dyerianus, E. dolomiticus and E. eugene-maraisii. Relationships between E. nubimontanus and E. cupidus remain uncertain. E. middelburgensis samples showed no clustering but had poor amplification success. This study demonstrated the suitability of automated ISSR fingerprinting as a method for plant conservation studies, especially in resource-constrained countries.

Alterations in the composition and diversity, metabolism, and products of the microbiome, and of the gut microbiome (GM), have been shown to be closely associated with the onset and progression of many human diseases, including cancer (i.e. hematological neoplasms). Acute lymphoblastic leukemia (ALL) is the most common form of childhood malignancy. Affected cases present typical alterations of GM, followed by inflammation, which contribute to its progression, response to therapy, as well as possible relapses. Recent evidence also reports that GM influences the development and functions of the newborn's hematopoietic system through the process of developmental programming during fetal life, as well as its susceptibility to the onset of onco-hematological pathologies, namely ALL. Furthermore, in children with ALL, GM has been found to vary in composition, variety, and functions during the clinical stages of ALL, and such variation may influence and predict the complications and prognosis of ALL after chemotherapy treatment or stem cell hematopoietic transplant. Here, we suggest some therapeutic strategies, which can be applied at two levels of intervention to recover the microbiome, and consequently prevent/delay ALL or arrest its progression.

Direct yaw moment control (DYC) is an effective way to alter the behaviour of electric cars with independent drives. Controlling the torque applied to each wheel can improve the handling performance of a vehicle making it safer andfaster on a race track. The state-of-the-art literature covers the comparison of various controllers (PID, LPV, LQR, SMC, etc.) using ISO manoeuvres. However, more advanced comparison on important characteristics of the controllers performance is missed, such as the robustness of the controllers under changes in the vehicle model, steering behaviour, use of the friction circle and, ultimately, lap time on a track. In this study, we have compared the controllers according to some of the aforementioned parameters on a modelled race car. Interestingly, best lap times are not provided by perfect neutral or close-to-neutral behaviour of the vehicle, but rather by allowing certain deviations from the target yaw rate. In addition, a modified PID controller showed that its performance is comparable to other more complex control techniques such as MPC.

The dorsal column nuclei complex (DCN-complex) includes the dorsal column nuclei (DCN, referring to the gracile and cuneate nuclei collectively), external cuneate, X, and Z nuclei, and the median accessory nucleus. The DCN are organised by both somatotopy and modality, and have a diverse range of afferent inputs and projection targets. The functional organisation and connectivity of the DCN implicate them in a variety of sensorimotor functions, beyond their commonly accepted role in processing and transmitting somatosensory information to the thalamus, yet this is largely underappreciated in the literature. To consolidate insights into their sensorimotor functions, this review examines the morphology, organisation, and connectivity of the DCN and their associated nuclei. First, we briefly discuss the receptors, afferent fibres, and pathways involved in conveying tactile and proprioceptive information to the DCN. Next, we review the modality and somatotopic arrangements of the remaining constituents of the DCN-complex. Finally, we examine and discuss the functional implications of the myriad of DCN-complex projection targets throughout the diencephalon, midbrain, and hindbrain, in addition to their modulatory inputs from the cortex. The organisation and connectivity of the DCN-complex suggest that these nuclei should be considered a complex integration and distribution hub for sensorimotor information.

Research on titanium oxo complexes (TOCs) are usually focused on their structure and photocatalytic properties. Findings from these investigations spurred our interest in exploring also their potential biological activities. In this study, we focused on the synthesis and structure of a compound with the general formula [Ti8O2(OiPr)20(man)4] (1), which was isolated from the reaction mixture of titanium(IV) isopropoxide with mandelic acid (Hman) in a molar ratio of 4:1. The structure (1) was determined using single-crystal X-ray diffraction, while spectroscopic studies provided insights into its physicochemical properties. To assess the potential practical applications of (1), its microcrystals were incorporated into a polymethyl methacrylate (PMMA) matrix, yielding composite materials of the type PMMA + (1) (2 wt.%, 5 wt.%, 10 wt.%, and 20 wt.%). The next stage of our research involved the antimicrobial activity evaluation of the obtained materials. Investigations carried out demonstrated antimicrobial activity of pure (1) and its composites (PMMA + (1)) against both Gram-positive and Gram-negative strains. Furthermore, MTT tests conducted on the L929 murine fibroblast cell line confirmed the lack of cytotoxicity of these composites. Our study identified (1) as a promising antimicrobial agent, also for producing composite coatings.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

The dynamics of surface and sub-surface water events can lead to slope instability resulting in anomalies such as slough slides on earthen levees. Early detection of these anomalies by a remote sensing approach could save time versus direct assessment. We have implemented a supervised Mahalanobis distance classification algorithm for the detection of slough slides on levees using complex polarimetric Synthetic Aperture Radar (polSAR) data. The classifier output was followed by a spatial majority filter post-processing step which improved the accuracy. The effectiveness of the algorithm is demonstrated using fully quad-polarimetric L-band Synthetic Aperture Radar (SAR) imagery from the NASA Jet Propulsion Laboratory’s (JPL’s) Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR). The study area is a section of the lower Mississippi River valley in the southern USA. Slide detection accuracy of up to 98 percent was achieved, although the number of available slides examples was small.

This paper seeks to fill in the gaps of modern relativistic Cosmology by utilizing the total symmetry between space and time dimensions and re-interpreting the scale factor of the Universe as a gravitational potential generated by the mass/energy of the entire Universe as a whole. The gradient of this potential is along the cosmological time dimension through which the Universe is falling. This gradient gives us an arrow of time, we find explanations for why the Universe began expanding and why the expansion is accelerating without the need for a Cosmological Constant. In a finite time, the gradient will point in the opposite direction of time turning the expanding Universe into a collapsing one where it is shown that when placing the Schwarzschild metric in the dynamic Cosmological background, gravity becomes repulsive and things like would-be Black Holes become White Holes. The model naturally describes a Universe and an anti-Universe (consisting of antimatter) moving in opposite directions of time that collide at the end of collapse, annihilating and subsequently pair producing two new Universes as the cycle begins again. It is shown that the model's Hubble diagram fits the currently available supernova and quasar data. It is found that Dark Matter can perhaps be understood as ordinary matter that is not connected to us with null geodesics.

Accurately estimating a person's age is crucial for identity verification at all critical checkpoints, including airports, land borders, and seaports. Human gait may be used as a biometric identifier and indicator of age, among other things. This study aims to develop methods for estimating a person's age by observing their walk. In this paper, a novel technique for preprocessing the proposed gait dataset has been used by utilizing a combination of the gait energy image (GEI), the accumulated frame difference energy image (AFDEI), and the invariant moment of the image. The proposed technique outperformed state-of-the-art methods in terms of accuracy. The proposed method was tested and evaluated using a convolutional neural network (CNN), and it achieved an average accuracy of 90.35% across 14 different view angles within 5 K-Fold, the proposed method resulted in 94.68% and 94.54% in 30º and 75º view degree respectively. concluding that the approach is effective and promising for estimating age using human gait.

The purpose of this paper is to investigate the effect of a varying moment on the rotation angle of a large tethered satellite that is orbiting a planet. Two different types of orbits were investigated: a simple circular orbit and an elliptical orbit. Cases with zero and non-zero initial angular rotation velocity were investigated as well. This investigation will assist satellite docking missions. The large rigid tethered satellite is a futuristic concept, and this investigation is meant to assist possible docking missions to the satellite. To simplify the problem, the rotation is constrained to the orbital plane.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Real and complex analytic functions are largely studied in the field of complex analysis and are seen as very useful tools in solving problems in mathematics, physics and engineering. Real and complex numbers are a subset of semi-structured complex numbers (a new number set created to algebraically solve division by zero). Nevertheless, the properties of analytic functions made up of semi-structured complex variables (called semi-structured complex analytic functions) is yet to be explored. This limits the range of possible problems that can be resolved using analytic functions). In this regard, the aim of this paper was to expound upon the properties of semi-structured complex analytic functions and show their application in solving engineering problems. The results of this paper included (1) developing a full set of Cauchy–Riemann Equations for the semi-structured complex -space; (2) define sufficient and necessary conditions for a semi-structured complex function to be analytic; (3) determine the relationship between semi-structured complex analytic functions, Laplace’s Equations and Poisson’s Equations; and (5) provide an example of the use of these functions.

Polyelectrolyte-drug complexes are interesting alternatives to improve unfavourable drugs properties. Vancomycin (VAN) is an antimicrobial used in the treatment of methicillin-resistant Staphylococcus aureus pulmonary infections in patients with cystic fibrosis. It is generally administered intravenously with high incidence of adverse side effects, which could be reduced by intrapulmonary administration. Currently, there are no commercially available inhalable formulations containing VAN. Thus, the present work focuses on the preparation and characterization of an ionic complex between hyaluronic acid (HA) and VAN with potential use as inhalable formulations. Particulate-solid HA-VAN25 complex by spray drying from an aqueous dispersion was obtained. FTIR spectroscopy and thermal analysis confirmed the ionic interaction between HA and VAN, while an amorphous diffraction pattern by X-ray was observed. The powder density, geometric size and morphology showed a suitable aerosolization and aerodynamic performance of the powder, indicating the capability of reaching the deep lung. An in vitro extended-release profile of VAN from the complex was obtained, exceeding 24 hours. Microbiological assays against methicillin-resistant and -sensitive reference strains of Staphylococcus aureus, showed that VAN preserves its antibacterial efficacy. In conclusion, HA-VAN25 exhibited interesting properties for the development of inhalable formulations with potential efficacy and safety advantages over conventional treatment.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Burkholderia are a group of Gram-negative bacteria that can cause a variety of diseases in at-risk populations. B. pseudomallei and B. mallei, the etiological agents of melioidosis and glanders, respectively, are the two clinically relevant members of the B. pseudomallei complex (Bpc). The development of vaccines against Bpc species has been accelerated in recent years, resulting in numerous promising subunits and glycoconjugate vaccines incorporating a variety of antigens. However, a second group of pathogenic Burkholderia species exists known as the Burkholderia cepacia complex (Bcc), a group of opportunistic bacteria which tend to affect individuals with weakened immunity or cystic fibrosis. To date there have been few attempts to develop vaccines to Bcc species. Therefore, the primary goal of this review is to provide a broad overview of the various subunit antigens that have been tested in Bpc species, their protective efficacy, study limitations, and known or suspected mechanisms of protection. Then, we assess the reviewed Bpc antigens for their amino acid sequence conservation to homologous proteins found in Bcc species. We propose that protective Bpc antigens with a high degree of Bpc-to-Bcc sequence conservation could serve as components of a pan-Burkholderia vaccine capable of protecting against both disease-causing groups.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

The Fusarium fujikuroi species complex (FFSC) includes socioeconomically important pathogens that cause disease and/or mycotoxin contamination on numerous crops. Here, we used comparative genomics to elucidate processes underlying the ability of pine-associated and grass-associated FFSC species to colonize tissues of their respective plant hosts. We characterized the identity, possible functions, evolutionary origins, and chromosomal positions of the host-range-associated genes encoded by the two groups of fungi. The 72 and 47 genes identified as unique to the respective genome groups were potentially involved in diverse processes, ranging from transcription, regulation, and substrate transport, through to virulence/pathogenicity. Most emerged early during the evolution of Fusarium/FFSC and were subsequently retained only in some lineages, while some had origins outside Fusarium. Although differences in the densities of these genes were especially noticeable on the conditionally dispensable chromosome of F. temperatum (representing the grass-associates) and F. circinatum (representing the pine-associates), the host-range-associated genes tended to be located towards the subtelomeric regions of chromosomes. Taken together, these results demonstrate that multiple mechanisms drive the emergence of genes in grass- and pine-associated FFSC taxa examined and highlighted the diversity of molecular processes potentially underlying niche-specificity in these and other Fusarium species.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.