The design is described of a readily useable technology for routine paddock-scale soil porosity estimation. The method is non-contact (proximal) and typically from sensors mounted on a small farm vehicle around 1 m above the soil surface. Challenges arise from the need to have a compact low-power rigid structure and to allow for pasture cover and surface roughness. The high-frequency regime for acoustic reflections from a porous material is a function of the porosity , the tortuosity , and the angle of incidence . There is no dependence on frequency, so measurements must be conducted at two or more angles of incidence in order to obtain two or more equations in the unknown soil properties and . A system requiring a single transmitter/receiver pair to be moved from one angle to another is not viable for rapid sampling. Therefore, the design includes at least two transmitter/reflector pairs placed at identical distances from the ground so that they would respond identically to power reflected from a perfectly reflecting surface. A single 25 kHz frequency is a compromise which allows for the frequency-dependent signal loss from a natural rough agricultural soil surface. Multiple-transmitter and multiple-microphone arrays are described which give a good signal to noise ratio while maintaining a compact system design. The resulting arrays have a diameter of 100 mm. Pulsed ultrasound is used so that the reflected sound can be separated from sound travelling directly through the air horizontally from transmitter to receiver. The average porosity estimated for soil samples in the laboratory and in the field is found to be within around 0.04 of the porosity measured independently. This level of variation is consistent with uncertainties in setting the angle of incidence, although assumptions made in modelling the interaction of ultrasound with the rough surface no doubt also contribute.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

Matrices and their inverses allow accurate calculations to be produced quickly and compactly and can be used to control any process represented by a system of equations. Singular matrices require extensive workarounds (costing time and money) to solve these systems of equations because they have no inverse. Finding their inverse involves division by zero. Nevertheless, recently a new number set called semi-structured complex numbers was developed to enable division by zero in algebraic equations. The aim of this research was to demonstrate that the inverse of a singular matrix can be found using semi-structured complex numbers. This research reveals (1) Singular matrices and their inverses can be used to find a unique solution to a pair of simultaneous equations that appear to have infinitely many solutions or appear to have no solution; (2) Singular matrices map coordinates in projective space to coordinates in Euclidean space and their inverse maps coordinates in Euclidean space to coordinates in projective space; (3) the inverse of a singular matrix proves that parallel lines in Euclidean space do not intersect but in projective space intersect at a “point at infinity” and (4) collinear lines that intersect at infinitely many points in Euclidean space only intersect at one point in projective space.

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

Here, using the theory of electrical-quantum modelling of the neutron and proton as a three-phase alternating current electrical generator, we will analyse the proton decay and the inverse neutron decay and determine the following subatomic particles, Dproton, Protoniu, Dneutron and Neutroniumd.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

We provide representations for the generalized Drazin inverse of an anti-triangular matrix of the form $\left( \begin{array}{cc} a&b\\ 1&0 \end{array} \right)$ in a Banach algebra $\mathcal{A}$, under the condition that $ab=ba$. Specifically, we present the representation of Drazin inverse for these types of anti-triangular matrices in Banach algebras.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

The continuous casting process of helical fiber reinforced metal matrix composites was proposed, and the experimental equipment was designed and manufactured. The relationship model be-tween the process parameters and the helical shape of the fibers in the metal matrix is analyzed by differential geometry. Helical carbon fiber reinforced lead matrix composites were prepared under different conditions. When the melting temperature and cooling intensity were increased, the helical radius of helical carbon fiber in lead matrix was increased. When the fiber rotation speed was increased, the helical radius was decreased, and the helical pitch was de-creased proportionally. The experimental results are consistent with the process model. Carbon fiber rein-forced aluminum composites were prepared. Scanning electron microscopy showed that the infiltration between the aluminum matrix and the carbon fiber was not complete. As the volume fraction of carbon fiber which was added in composites is too small, the mechanical properties of the composites have not been significantly improved.

In this paper, we provide alternative proofs to some results proposed in the article "New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions" authored by Yogesh J. Bagul.

Lignin fibers typically influence the mixture performance of stone matrix asphalt (SMA), such as strength, stability, durability, noise level, rutting resistance, fatigue life, and water sensitivity. However, limited studies were conducted to analyze the influence of fibers on the percent voids in mineral aggregate in bituminous mixture (VMA) during the mixture design. This study analyzed the effect of different fibers and fiber contents on the VMA in SMA mixture design. A surface-dry condition method test and Marshall Stability test were applied on the SMA mixture with four different fibers (i.e., flocculent lignin fiber, mineral fiber, polyester fiber, blended fiber). The test results indicated that the bulk specific gravity of SMA mixtures and asphalt saturation decreased with the increasing fiber content, whilst the percent air voids in bituminous mixtures (VV), Marshall Stability and VMA increased. Mineral fiber had the most obvious impact on the bulk specific gravity of bituminous mixtures, while flocculent lignin fiber had a minimal impact. The mixture with mineral fiber and polyester fiber had significant effects on the volumetric properties, and, consequently, exhibited better VMA over the conventional SMA mixture with lignin fiber. Modified fiber content range was also provided, which will widen the utilization of mineral fiber and polyester fiber in the applications of SMA mixtures. The mixture evaluation suggested no statistically significant difference between lignin fiber and polyester fiber on the stability. The mineral fiber required a much larger fiber content to improve the mixture performance than other fibers. Overall, the results can be a reference to guide SMA mixture design.

While the number of publications on wine and health is steadily increasing, ranging from molecular level to epidemiological studies, often with contradictory results, little attention has been given to an holistic approach. In this review some unusual concepts are considered, such as phytocomplex, vehicle and the Matrix effect. As an example, three mono/polyphenols present in wine, Tyrosol, Hydroxytyrosol and Resveratrol, have been selected and the consequences of respecting, disregarding or ignoring the Matrix effect are shown. Underestimation of the wine Matrix effect could lead to deceiving results, as in the case of de-alcoholized wine or wine-compound-based nutritional supplements,or in emphasizing a single component toxic activity, in this case alcohol, ignoring the specific protective action at molecular level of other compounds (polyphenols) present in the same Matrix. The dark side of Matrix effect is also discussed. It is suggested that specificity of wine should be always taken in consideration by public health Authorities.

The inverse system identification toolbox named INVSID 1.0 for MATLAB, which is used to identify the inversion of single-input single-output systems, is developed. The complete process of developing the toolbox is demonstrated. Afterwards, a numerical example is illustrated to describe how the toolbox can be used to solve inverse identification problems. Simulation results demonstrate the effectiveness of the toolbox.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

In this note we generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several inverses. The higher idempotents are introduced, and their commutation leads to unique inverses in the multi-relational formulation, and then further to the higher inverse semigroups. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle as introduced: the expressions should not depend of the numerical arity values, which allows us to provide natural and correct binary limits. In the first definition no idempotents can be defined, analogously to the binary semigroups, and therefore the uniqueness of inverses can be governed by shifts. In the second definition called sandwich higher regularity, we are able to introduce the higher polyadic idempotents, but their commutation does not provide uniqueness of inverses, because of the middle terms in the higher polyadic regularity conditions.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

The poly lactic acid (PLA) is one of the most used bio-derived thermoplastic polymers in 3D and 4D printing applications. The determination of PLA surface properties is of capital importance in 3D/4D printing technology. (1) Background: The surface thermodynamic properties of PLA polymer were determined by using the inverse gas chromatography (IGC) technique at infinite dilution. The determination of the retention volume of polar and non-polar molecules adsorbed on the PLA particles filling the column allowed us to obtain the dispersive, polar, and Lewis’s acid-base surface properties at different temperatures from 40 °C to 100 °C. (2) Methods: the applied surface method was based on our recent model that used the London dispersion equation and the new chromatographic parameter function of the deformation polarizability and the harmonic mean of the ionization energies of the PLA polymer and organic molecules. (3) Results: The application of this new method led to the determination of the dispersive and polar free surface energy of adsorption of molecules on the polymeric material, as well as the glass transition and the Lewis acid-base constants. (4) Conclusions: four interval temperatures were distinguished showing four zones of the variations of the surface properties of PLA as a function of the temperature before and after the glass transition.

This article presents a novel resolution of the Collatz Conjecture, centered on the concept of Generative Completeness of the inverse Collatz function. We introduce and rigorously prove that for all N ∈ ℕ⁺, there exists a minimal generator m_N = 1 such that all positive integers up to N can be generated through successive applications of the inverse Collatz function G. This key property, which we term "Generative Completeness", forms the cornerstone of our proof. Building upon this foundation, we establish several crucial results: The boundedness of all Collatz sequences The existence and uniqueness of cycles in Collatz sequences The nature of the unique cycle as {1, 4, 2} We then present three distinct approaches to resolving the Collatz Conjecture, all fundamentally rooted in the Generative Completeness property. These diverse methods not only prove the conjecture but also provide deep insights into the structure of Collatz sequences.

This paper addresses the Collatz Conjecture, an open question in mathematics that postulates all positive integers will eventually reach one when a pair of specific operations are repeatedly applied. Despite its apparent simplicity, the conjecture lacks a formal proof. To tackle this enigma, we introduce Algebraic Inverse Trees (AITs), data structures that trace inverse operations of the Collatz sequence. This new approach not only elaborates our unique methodology but also sheds light on the underlying complexities of the Collatz Conjecture.

This study provides an in-depth review of the available literature on metal composite material machining, focusing on traditional machining operations such as turning, milling, shaping, drilling, and grinding. The motivation for the study is that this composite type has emerged as a vital material in applications requiring functionality, resilience, cost-effective operation, low consumption of energy and lightweight. Despite its superior characteristics, the manufacturing complexity and poor machinability of metal matrix composites have been the primary barriers to its adoption. Nevertheless, there is a reduction of exceptional efficiency, increase in surface roughness, tool wear and so on in metal matrix composites throughout machining. As a result, this review gives a comprehensive investigation of metal matrix composite machining and effect on process parameters and procedures. Furthermore, this study distinguishes metal matrix composites towards sustainable manufacturing and the metals employed by the researchers, as well as the gaps discovered for future recommendations in metal-based composites.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

Background: This study attempted to construct musculoskeletal JEM using KWCS data and use it to evaluate the burden of these disorders in Korean workers. Methods: This study was conducted using data from the second to the sixth KWCS, and a total of 210,500 people were included. The jobs of the subjects were reclassified based on the unit groups of the 7th Korean Standard Classification of Occupation (KSCO). The intensity of exposure to work-related risk factors for musculoskeletal disorders was classified into ‘high’, ‘moderate’, and ‘low’ for the body segments involving the ‘upper extremities and neck’, ‘lower back’, and ‘lower extremities’. Results: The time of exposure was longest in the standing posture and repetitive hand and arm movements. An analysis of the intensity of exposure by body segments revealed that the highest intensity of exposure was to the upper extremities. For the upper extremities and neck, and the lower back, there was a exposure-response relationship in the association between intensity of exposure and musculoskeletal symptoms. However, for the lower extremities, there was a exposure-response relationship only at high exposure. Conclusion: In this study, a JEM for work-related risk factors for musculoskeletal disorders was constructed for the first time in Korea. The intensity of exposure to musculoskeletal risk factors was estimated for each occupation. The JEM constructed in this study is expected to have high applicability for assessing the risk of musculoskeletal disorders for each job with respect to the upper extremities and neck, and lower back.

The ECM is composed of a considerable number of biochemically and structurally diverse constituents. ECM is a highly dynamic system that constantly receives and sends biological, chemical and mechanical signals. Several studies suggest that mechanical signals derived from the extracellular microenvironment regulate skin regeneration and wound healing. We evaluated effects of a mixture of biomolecules extracted and purified from bovine colostrum on restoring the mechanical properties of ECM. Test measuring collagen contraction showed a significant difference in contraction activation in samples treated with the 2% colostrum derivative mixture compared to the control. The analysis of the supernatant showed an inhibition of metalloproteinase-2 expression and an increase in collagen secretion by fibroblasts in treatment samples. Our hypothesis is that the molecules extracted and purified from bovine colostrum restore the ECM environment qualitative and quantitative characteristics, thus guaranteeing through a mechanical action the restoration of the wound due to the transduction of the signal activated by the integrins.

The release of the active substance from the matrix modified-release tablets based on Kollidon®SR and chitosan depends on its solubility in the dissolution medium and on the composition of the matrix-forming polymers. The study is based on new oral matrix tablets based on Kollidon®SR and chitosan, formulated to optimize the low oral bioavailability of chlorzoxazone, a non-steroidal anti-inflammatory drug, a class II Biopharmaceutical Classification System. Nine types of chlorzoxazone matrix tablets were obtained using the direct compression method, and their combination at 1:1, 1:2, 1:3 chlorzoxazone/ excipients, 20%-40% (w/w) Kollidon®SR, 3-7% (w/w) chitosan and the auxiliary substances were formulated in constant concentrations. Pharmaco-technical characterization included the analysis of flowability and compressibility properties (flow time, friction coefficient, angle of repose, Hausner ratio, Carr Index), and of pharmaco-chemical characteristics (mass and dose uniformity, thickness, diameter, mechanical strength, Friability, degree of softening, in vitro release profile) of the tablets. Based on the initial evaluation of the pharmaco-technical analysis, pharmaco-chemical characteristics, and in vitro release profile, only three matrix tablet formulations (F1b, F2b, and F3b) were further tested. They were evaluated through Fourier-transform infrared spectrometry, X-ray Diffraction, thermogravimetry, differential scanning calorimetry, and in vitro dissolution tests. The three formulations were comparatively studied regarding the release kinetics of active substances using in vitro release testing. The results were analyzed by fitting into four representative mathematical models for the modified release oral formulations. In vitro kinetic study reveals a complex mechanism of release occurring in the first (0 - 2 hours) and second (2.0 hours – 36 hours) steps of drug release. Two factors have been calculated to assess the release profile of chlorzoxazone: f1 - the similarity factor and f2 - the factor difference. The results have shown that both Kollidon®SR and chitosan may be used as matrix-forming agents when combined with chlorzoxazone. In vitro dissolution tests revealed the F2b sample, data suggesting a faster drug release. The three formulations showed optimum pharmaco-technical properties and in vitro kinetic study, and they had tremendous potential to be used in oral pharmaceutical products for the controlled delivery of chlorzoxazone.

Electrowetting display (EWD) device is a new type of electrowetting-on-dielectric (EWOD) equipment which can achieve a paper-like display effect under the control of electric field. In this microfluidic system, the stability of grayscale could be affected by various factors, such as the physicochemical properties of materials, device structure, and electric field distribution. To improve the grayscale stability of active matrix electrowetting displays (AM-EWDs), the impact of different polarities of driving voltage on oil backflow was investigated in this study. Based on the driving principles of AM-EWD, an optimized inter-frame bipolar reset driving waveform was designed to overcome oil backflow. The proposed driving waveform maintained the stability of the oil state by periodically and rapidly releasing trapped charges in the dielectric layer through a reverse driving voltage. Additionally, the effect of feed through voltage on the pixel driving voltage was eliminated by compensating for the driving voltage on common electrode. Finally, the performance of the designed driving waveform was evaluated with a 6-inch AM-EWD driving platform. Compared to the conventional unipolar reset driving waveform, the backflow speed decreased by 2.70 a.u./s. The standard deviation of the display luminance was also reduced by 11.24 a.u. Experimental results indicated that both the oil backflow speed and the fluctuation range of luminance were effectively suppressed by the proposed driving waveform.

In this paper, the neural network is developed for solving the inverse photoacoustic problem aiming to estimate thermo-elastic properties and thickness of a semiconductor sample. The idea was that these sample properties be estimated from the phase characteristic because the phase measurements are more sensitive. The neural network has been trained on a large basis of photoacoustic phases calculated from a theoretical Si n-type model in the range of 20Hz to 20kHz, on which random Gaussian noise has been applied. It is shown that high accuracy and precision could be reached in solving of inverse photoacoustic problem using only phase measurement.

The surface thermodynamic properties of polymers and copolymers modified by supramolecular structures are very used in several industrial processes, such as selective adsorption, paints, coatings, colloids, and adhesion applications. Background: Inverse gas chromatography at infinite dilution was proved to be the best technique to determine the surface properties of solid surfaces by studying the adsorption of some model polar and non-polar organic molecules adsorbed on solid surfaces by varying the temperature. Methods: The retention volume of adsorbed solvents is a precious parameter to obtain the London dispersive and polar free energies and the London dispersive surface energy of styrene–divinylbenzene copolymer modified by supramolecular structure of melamine using the Hamieh thermal model and our new methodology consisting in the separation of the two polar and dispersive free energy of interaction. This led to the determination of the polar acid and base surface energy, and the Lewis’s acid-base constants of the various solid materials. Results: all surface energetic properties of styrene–divinylbenzene copolymer modified by melamine at different percentages were determined as a function of temperature, following our new methodology. Conclusions: It was observed that the styrene–divinylbenzene copolymer exhibited the highest London dispersive surface energy which decreased when the melamine percentage increased. All materials presented higher Lewis’s basicity and this Lewis’s basicity increased with the percentage of melamine.

This article presents a new methodology for modeling and analyzing discrete dynamic systems through the construction of inverse algebraic models, giving rise to the Theory of Inverse Discrete Dynamical Systems. Key concepts such as inverse modeling, structural analysis in inverse algebraic trees, and the establishment of topological equivalences for the analytical transfer of properties between the canonical system and its inverted counterpart are introduced. Central theorems on homeomorphic invariance and topological transport are demonstrated, consolidating the validity of transferring cardinal attributes between both equivalent dynamic representations. As a concrete application, an alternative proof of the historic Collatz Conjecture is presented through the rigorous construction of the associated inverse model and the analytical transfer of properties exhibited in the inverted tree structure. Furthermore, evidence has been presented on Conway's Conjecture in the Game of Life through meticulous inverse modeling in bounded cases, overcoming initial limitations of the theory in combinatorial explosions. Although a complete proof of the conjecture is not achieved, this positively expands the modeling and analysis capacity of the methodology. The impact of properly applying this novel theory to expand understanding and solve open problems in discrete dynamical systems seems vast and profound.

Ultrafast pump-probe spectroscopic studies allow for deep insights into the mechanisms and timescales of photophysical and photochemical processes. Extracting valuable information from these studies, such as reactive intermediates' lifetimes and coherent oscillation frequencies, is an example of the inverse problems of chemical kinetics. This article describes a consistent approach for solving this inverse problem that avoids the common obstacles of simple least-squares fitting that can lead to unreliable results. The presented approach is based on the regularized Markov Chain Monte Carlo sampling for the strongly nonlinear parameters, allowing for a straightforward solution of the ill-posed nonlinear inverse problem. The software to implement the described fitting routine is introduced and the numerical examples of its application are given. We will also touch on critical experimental parameters, such as the temporal overlap of pulses and cross-correlation time and their connection to the minimal reachable time resolution.

This investigation mainly focused on the microstructural analysis of Al based hybrid metal matrix composites. Aluminium as base metal and reinforced with 2% B4 C, ZrO2 (2%,4%,6%), SiC (4%,8%,12%). Specimens were manufactured by using conventional stir casting technique. Hybrid metal matrix composites were examined by using Scanning electron microscope. This research explained XRD, EDS and Fractography analysis. This investigation shows the reinforced material has given better results in all aspects than pure Al6061 alloy and homogeneous dispersion of particles inside the matrix. Porosity, delamination, cracks, particle distributions were observed through microstructural analysis. Additionally determined the crystal size of pure Aluminium 6061 alloy and hybrid composites.

Titanium-based metal-matrix composites manufactured by additive manufacturing offer tremendous lightweighting opportunities. However, processing high reinforcement content remains challenging. This study reports an improved manufacturing process for Ti-TiC enabling high reinforcement content and significant fracture strain concurrently: mechanical blending, followed by laser powder bed fusion and a single heat treatment. As-built microstructure shows both un-melted TiC particles and sub-stoichiometric TiC dendrites resulting from a partial dissolution of TiC particles. The heat treatment is shown to fully convert TiC dendrites into equiaxed TiC grains. Reduction of the C/Ti ratio in TiC during the process results in an increase in the reinforcement content, from a nominal 12 vol% to an effective 21.5 vol%. Ti-TiC tensile samples reached fracture strains of up to 1.7%, Young’s moduli of up to 149 GPa and ultimate tensile strengths of up to 827 MPa. Lower TiC initial powder size distributions displayed the best mechanical performance.

This article aims to analyze household energy data to predict electricity self-sufficiency and identify the key features that impact it. For this purpose, we use SHAP (Shapley Additive Explanations), LightGBM (Light Gradient Boosting Machine), and a correlation heatmap-based framework to analyze 12 months of energy and questionnaire survey data collected from over 200 smart houses in Kitakyushu, Japan. We use the SHAP summary plot to identify the impact-wise order of key features influencing the electricity self-sufficiency rate (ESSR). Using SHAP, we demonstrated that key features are; housing types, average monthly electricity bill, floor heating, electric capacity, number of washing and drying machines, fee plans, occupation of household head, total floor area, average monthly gas bill, cooking equipment, etc. Furthermore, we adopted the LightGBM classifier with $\ell^1$ regularization to extract the most significant features and predict the electricity self-sufficiency rate of households. This LightGBM-based model can also predict the electricity self-sufficiency rate of households that did not participate in the questionnaire survey. A heat map is also used to analyze the correlation among household variables. The findings discussed in this article offer valuable insights for energy policymakers to achieve the targets of energy self-sufficient houses.

Several Lung diseases can result in lung damage structural changes, with lung transplantation as a only therapeutic option when the disease reaches an advanced progression, unfortunately, the success of lung transplantation is limited. In this context, lung bioengineering is considered a potential therapeutic alternative and the current approach is based on the use of the natural extracellular matrix (ECM) of the decellularized lung. The use of undifferentiated cells to seed an ECM can be a more practical strategy for lung bioengineering but the sterilization of the organ for this recellularization process is still a challenge. In this sense, Low-Level Laser Therapy (LLLT) can emerge as a potential treatment alternative. Therefore, the objective of this study was to verify if LLLT, can optimize lung recelularization with mesenchymal stem cells by cytokine modulation. For this, we decellularized lungs from C57BL/6 mice perfusing SDS 1% via pulmonary artery, sterilized with LLL (660nm, 100mW, 30s). Whole lung scaffolds were recellularized: (1) Recellularized Lung (2) Recellularized Lung + LLLT. Mesenchymal stem cells derived from human tooth pulp (DPSc) were seeded into lungs and incubated for 24 hours at 37ºC, 5% CO₂, in a bioreactor-like conditions, maintaining CPAP at 20cmH2O, 90% O2, and LLL at wavelength of 808nm, 100mW, 30s. Culture medium were analyzed at 24 hours. H&E, immunostaining, SEM and ELISA assay were performed. We produced viable biological scaffolds absent of DNA content, preserving glycosaminoglycans and collagen I, III and IV, fibronectin, laminin and elastin and lung structure (SEM). The levels of IL-6 and IL-8 were stable during the 24 hours of culture. IFN-γ levels showed significant difference in the DPSc and DPSc+LLLT group in the 24-hour evaluation. The levels of IL-10 decreased after LLLT. These findings highlight LLLT's role in cytokine regulation and contamination prevention during lung recellularization with mesenchymal stem cells. Overall, these results demonstrated that LLLT's modulated cytokine levels and could prevent contamination during the lung recellularization process with mesenchymal stem cells, offering promise for enhanced therapeutic strategies in lung bioengineering.

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

Seismic velocity inversion is one of the most critical issues in the field of seismic exploration and has long been the focus of numerous experts and scholars. In recent years, the advancement of machine learning technologies has infused new vitality into the research of seismic velocity inversion and yielded a wealth of research outcomes. Typically, seismic velocity inversion based on machine learning lacks control over physical processes and interpretability. Starting from wave theory and the physical processes of seismic data acquisition, this paper proposes a method for seismic velocity model inversion based on Physical Embedding Recurrent Neural Networks. Firstly, the wave equation is a mathematical representation of the physical process of acoustic waves propagating through a medium, and the finite difference method is an effective approach to solving the wave equation. With this in mind, we introduce the architecture of recurrent neural networks to describe the finite difference solution of the wave equation, realizing the embedding of physical processes into machine learning. Secondly, in seismic data acquisition, the propagation of acoustic waves from multiple sources through the medium represents a high-dimensional causal time series (wavefield snapshots), where the influential variable is the velocity model, and the received signals are the observations of the wavefield. This forms a forward modeling process as the forward simulation of the wavefield equation, and the use of error back-propagation between observations and calculations as the velocity inversion process. Through time-lapse inversion and incorporating the causal information of wavefield propagation, the non-uniqueness issue in velocity inversion is mitigated. Through mathematical derivations and theoretical model analyses, the effectiveness and rationality of the method are demonstrated. In conjunction with simulation results for complex models, the method proposed in this paper can achieve velocity inversion in complex geological structures.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

In Indonesia, types of meat are still identified manually due to increasing prices for beef and buf-falo ahead of Idul Fitri. Traders mix beef with pork to thwart the beef scam. Haar wavelet and GLCM, GLCM with angles of 0°, 45°, 90°, and 135°, as well as matrices using contrast, correlation, energy, homogeneity, and entropy, are used in feature extraction. The following are the results of meat image classification testing using k-NN, Haar wavelet, and GLCM: The k-NN algorithm shows superiority in identifying fresh (99%), frozen (99%), and rotten (96%) meat texture images with the most fantastic accuracy results in every situation. Meanwhile, GLCM routinely provides good results, especially regarding the texture image of fresh meat (183.21) and rotten meat (115.79). However, despite delivering less throughput than k-NN and GLCM, Haar wavelets are still helpful, especially when dealing with fresh meat texture images (89,96).

The thermal surface properties of graphenes and carbon materials are of crucial importance in chemistry of materials, chemical engineering, and many industrial processes. (1) Background: The determination of these surface properties is carried out using inverse gas chromatography at infinite dilution which leads to the retention volume of organic solvents adsorbed on solid surfaces. This experimental and fundamental parameter actually reflects the surface thermodynamic interactions between injected probes and solid substrates. (2) Methods: The London dispersion equation and the Hamieh thermal model were used to quantify the London dispersive and polar surface energy of graphenes and carbon fibers as well their Lewis acid-base constants by introducing the coupling amphoteric constant of materials. (3) Results: The London dispersive and polar acid-base surface energies, the free energy of adsorption, the polar enthalpy and entropy, and the Lewis acid-base constants of graphenes and carbon materials were determined. (4) Conclusions: it was showed that graphene exhibited the highest values of London dispersive surface energy, polar surface energy, and Lewis’s acid-base constants. These highest characteristics of graphene justify its great potentiality and uses in many industrial applications.

Thin people who undergo implant insertion into the chest wall face a high risk of implant exposure to the external environment. Five months after an 8-year-old boy underwent implantable cardioverter-defibrillator (ICD) implantation in a subcutaneous pocket in the left anterolateral chest wall to manage long QT syndrome, ICD replacement became necessary owing to exposure risk from distal and lateral thinning of the ICD pocket. Pocket rupture and exposure would increase the risk of infection; therefore, we performed ICD removal and primary pocket closure. Two weeks later, a new suprafascial pocket was created, acellular dermal matrix (ADM) was attached to the inner wall to prevent ICD protrusion, and a new ICD was inserted. One year postoperatively, the ADM was engrafted, and no complications were observed. A thin subcutaneous layer increases the risk of ICD implantation complications. Inner wall strengthening with ADM can help prevent pocket rupture.

The transformation of the states of polarization of electromagnetic waves that interact with polarimetrically linear media can be represented by means of the associated Mueller matrix. A global measure of the ability of a linear medium to modify the states of polarization of incident waves, due to any combination of enpolarizing, depolarizing and retarding properties, is introduced as a distance of the Mueller matrix to the identity matrix. This new descriptor, called the polarizing power, is applicable to any Mueller matrix and can be expressed as a function of the degree of polarimetric purity and the trace of the Mueller matrix. The graphical representation of the feasible values of the polarizing power provides a general view of its main peculiarities and features. The values of the polarizing power for several typical devices are analyzed.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

The temperature effect plays an important role for an accurate determination of the polar free energy, polar thermodynamic parameters, and enthalpic and entropic Lewis’s acid base properties of oxides, polymers and composites polymers/oxides. The adsorption of polymers on other solid surfaces is crucial in many industrial applications, coatings, paints, catalysis, colloids and adhesion processes. (1) Background: Inverse gas chromatography at infinite was used for the physico-chemical characterization of solid substrates by determining the thermodynamic parameters of adsorption of model organic solvents on solid surfaces such as polymers, metallic oxides, carbon fibers, pharmaceutical or 3D/4D printing substrates. (2) Methods: A new method based on the London dispersion equation was applied with a new parameter associating the deformation po-larizability and the harmonic mean of the ionization energies of solvent. More accurate values of the dispersive and polar interaction energies of the various organic solvents adsorbed on PMMA in bulk phase and PMMA/silica at different recovery fractions were obtained as well as the Lewis acid-base parameters and the transition temperatures of the different composites. (3) Results: This new methodology gave very interesting results on the behavior of PMMA adsorbed on silica. An important effect of the temperature and the recovery fraction on the various physicochemical and thermodynamic properties was highlighted. The variations of all interaction parameters showed the presence of three transition temperatures for the different PMMA adsorbed on silica with the various coverage rates with a shift of these temperatures for a recovery fraction of 31% (4) Con-clusions: An important variation of the polar enthalpy and entropy of adsorption, the Lewis ac-id-base parameters and the intermolecular separation distance as a function of the temperature and the recovery fraction of PMMA on silica.

This study outlines a 3-step production process for Ti-TiC Metal Matrix Composite (MMC) employing powder Mechanical Blending, Laser Powder Bed Fusion (LPBF), and a heat treatment. A TiC fraction of more than 20 vol% was formed in-situ through the reaction of titanium with carbon during the LPBF process. The manufactured MMC pieces showed a record stiffness and fracture strain combination. The LPBF energy density impacted strongly porosity type. The as-built microstructure displayed an homogeneous distribution of sub-stoichiometric TiC dendrites which were fully converted into equiaxed TiC grains during the heat treatment. The TiC C/Ti ratio was found to be close to 0.5, resulting in an effective reinforcement content nearly twice the one expected for stoichiometric TiC, leading to stronger reinforcement. The mechanical analysis revealed a Young’s modulus of up to 149 GPa and an ultimate tensile strength of up to 770 MPa, indicating a 27% and 34% improvement, respectively, compared to commercially pure Titanium produced by LPBF and heat treated in the same conditions. A fracture strain of up to 2.8% was achieved. The combination of in-situ formation of defect-free TiC reinforcement and subsequent heat treatment enables to reach an exceptional ductility, considering the 20 vol% reinforcement content.

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

The spread of high-performance personal computers, frequently equipped with powerful Graphic Processing Units (GPU), raised the interest on a set of techniques able to extract models of electromagnetic phenomena (and devices) directly from available examples of the desired behavior. Such approaches are collectively referred to as Machine Learning (ML). A typical representative ML approach is the so called “Neural Network” (NN). Using such data-driven models allows evaluating the output in a much shorter time when a theoretical model is available, or allows predicting the behavior of the systems and devices when no theoretical model is available. With reference to a simple yet representative benchmark electromagnetic problem, some of the possibilities and the pitfalls of the use of NN for the interpretation of measurements (inverse problem) or to obtain the required measurements (optimal design problem) are discussed. The investigated aspects include the choice of the NN model; the generation of the dataset(s); the selection of hyperparameters (hidden layers, training paradigm). Finally, the capabilities in the handling of ill-posed problems are critically revised.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

Uterine tube extracellular matrix is a key component that regulates tubal tissue physiology, and it has a region-specific structural distribution, which are directly associated to their functions. Considering this, application of biological matrices in culture systems is an interesting strategy to develop biomimetic tubal microenvironments and enhance their complexity. However, there are no established protocols to produce tubal biological matrices that consider the organ morphophysiology for such applications. Therefore, this study aimed to establish region-specific protocols to obtain decellularized scaffolds derived from porcine infundibulum, ampulla, and isthmus to provide suitable sources of biomaterials for tissue-engineering approaches. Porcine uterine tubes were decellularized in solutions of 0.1% SDS and 0.5% Triton X-100. Decellularization efficiency was evaluated by DAPI staining and DNA quantification. We analyzed ECM composition and structure by optical and scanning electronic microscopy, FTIR and Raman spectroscopy. DNA and DAPI assays validated the decellularization, presenting significative reduction of cellular content. Structural and spectroscopy analyses revealed that produced scaffolds remained well structured and with ECM composition preserved. YS and HEK293 cells were used to attest cytocompatibility, allowing cell survival and successful interaction with the scaffolds. These results suggest that such matrices are applicable for future biotechnological approaches in the reproductive field.

In this study, in order to determine the effect of matrices shape on percolation threshold values, computer simulations were performed using the Monte Carlo method for a 200x200 square-shaped matrix and rectangular matrices containing the same number of nodes as the square matrix. Based on the simulations, the average values of percolation thresholds and standard deviations for current flow along and across the matrices were determined. It was determined that for a square-shaped matrix, the average values of percolation thresholds in both directions of current flow were the same. Extending the rectangular matrix while reducing its height causes the average value of the percolation threshold in the direction of current flow along the matrix to increase from 0.592740 to 0.759847, while in the transverse direction it decreases from 0.592664 to 0.403614. The values of the classical asymmetry coefficients of the probability distributions of percolation thresholds for both directions of current flow were determined. Histograms of the probability distributions of percolation threshold values for square-shaped matrix and rectangular matrices were made and compared with normal distributions. It was found that the occurrence of two percolation thresholds in rectangular layers should be considered when analyzing electrical conductivity measurements of nanocomposite thin films.

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

Hydrogels can be considered as mimics of extracellular matrix (ECM).Cytoskeleton through integrins is connected with ECM and cytoskeleton tension depends on ECM stiffness.A number of age-related diseases depend on cellular processes related with cytoskeleton function.Some examples of cancer initiation and progression and heart disease in relationship with ECM stiffness has been analysed.Incorporation of rigid particles in ECM can increase ECM stifness and to promote formation of internal residual stresses. Water migration, changes of water binding energy to biomactomolecules, changes of the state of water from tightly bound water to free and loosely bound water changes stiffness of ECM. Risks related with rigid particles incorporation into ECM have been also iscussed.

Inverse gas chromatography at infinite dilution was used to determine the surface thermodynamic properties of silica particles and PMMA adsorbed on silica, and more particularly, to quantify the London dispersive energy γsd, the Lewis acid γs+ and base γs- polar surface energies of PMMA/silica composites as a function of the temperature and the recovery fraction θ of PMMA. The polar acid–base surface energy γsAB and the total surface energy of the different composites were then deduced as a function of the temperature. In this paper, the Hamieh thermal model was used to quantify the surface thermodynamic energy of poly methyl methacrylate (PMMA) adsorbed on silica particles at different recovery fractions. A comparison of the new results was carried out with those obtained by applying other molecular models of the surface areas of organic molecules adsorbed on the different solid substrates. An important deviation of these molecular models from the thermal model was proved. The determination of γsd, γs+, γs-, and γsAB of PMMA in both bulk and adsorbed phases showed an important non-linearity variation of these surface parameters as a function of the temperature. The presence of maxima in the curves of γsd(T) highlighted the second order transition temperatures in PMMA showing beta-relaxation, glass transition and liquid-liquid temperatures. These three transition temperatures depended on the adsorption rate of PMMA on silica. The proposed method gave a new relation between the recovery fraction of PMMA and its London dispersive energy showing an important effect of the temperature on the surface energy parameters of adsorption of PMMA on silica. A universal equation relating γsd(T,θ) of the systems PMMA/silica to the recovery fraction and the temperature was proposed.

This research was devoted to study the effect of the tacticity of PMMA on the surface physicochemical properties such as the London dispersive component of the surface energy of the polymer, the polar and dispersive free energies, the Lewis’s acid-base surface parameters, and the Lewis acid and base surface energies of atactic, isotactic and syndiotactic PMMAs as a function of the temperature. Inverse gas chromatography (IGC) at infinite dilution was used to determine the surface thermodynamic properties of PMMA at different tacticities. The experimental values of the net retention time and volume of model organic molecules adsorbed on the atactic, isotactic and syndiotactic PMMAs, were obtained by IGC technique at infinite dilution. The London dispersion interaction energy was used for the separation of the polar and dispersive energy of the different n-alkanes and polar solvents adsorbed on the different PMMA surfaces. The London dispersive surface energy γ_s^d (T) of PMMAs was determined by applying the Hamieh thermal model that took into account the effect of the temperature on the surface area of adsorbed molecules. The obtained results showed non-linear variations of γ_s^d (T) of atactic, isotactic, and syndiotactic PMMAs with three maxima characterizing the three transition temperatures of PMMAs, T_g, T_g and T_(liq-liq) with a shift of these temperatures with the isotactic and syndiotactic PMMAs. It was showed that the polar interaction free energy ∆G_a^p (T) also showed the presence of the three above transition temperatures of the polymers. The study showed an important non-linearity variation of the different acid-base parameters in the various polymer surfaces proving the highest effect of the temperature and the tacticity on these parameters. The determination of the enthalpic and entropic Lewis’s acid-base parameters showed an amphoteric character for the different PMMAs. The basicity of the atactic PMMA was about four times larger than its acidity outside the neighborhood of the transition temperatures of the polymer. Whereas, the isotactic PMMA was about 2 to 2.5 times more basic than acid, while the syndiotactic PMMA exhibited the highest basicity by showing a surface 5 to 8 times more basic than acid. However, the Lewis acid-base parameters strongly depended on the temperature and sudden variations of these surface parameters were observed around the transition temperatures largely depending on the PMMA tacticity. The determination of the polar acid and base surface energies of the three PMMAs led to the same previous transition temperatures with an important effect of the tacticity of PMMA on the values of these acid-base surface energies.

Cells actively sense differences in topology, matrix elasticity and protein composition of the extracellular microenvironment and adapt their function and morphology. In this study, we focus on the cross-talk between matrix stiffness and protein coating density that regulate morphology and proliferation dynamics of single myocytes. For this, C2C12 myocytes were monitored on L-DOPA functionalized hydrogels of 22 different elasticity and fibronectin density compositions. Static images were recorded and statistically analyzed to determine morphological differences and to identify the optimized extracellular matrix (ECM). Using that information, selected ECMs were used to study the dynamics before and after cell proliferation by statistical comparison of distinct cell states. We observed a fibronectin density independent increase of the projected cell area until 12 kPa. Additionally, changes in the fibronectin density led to an area optimum at about 2.6 μg/cm, which was confirmed by an independent F-actin analysis, revealing a maximum actin filament to cell area ratio of 7.5 %. The proliferation evaluation showed an opposite correlation between cell spreading duration and speed to the matrix elasticity and protein density, which did not affect the cell cycle duration. In summary, we identified an optimized ECM composition, while independent matrix properties regulate distinct cell characteristics.

The correct selection of the value of p is a complex and iterative procedure that requires experience in the interpretation of the obtained interpolated maps. Inverse Distance Weighting is a method applied to the porosities of the K and L hydrocarbon reservoirs, discovered in the Neogene (Lower Pontian) subsurface sandstones in the northern Croatia (Pannonian Basin System). They represent small and large data samples. Also a standard statistical analysis of the data was made, followed by the qualitative-quantitative analysis of the maps, based on the selection of different values of the power distance exponent (p-value) for the K and L reservoirs maps. According to the qualitative analysis, for a small data set, p-value could be set on 1 or 2 giving the most optimal result, while for a large data set, a p value of 3 and 4 could be applied. By quantitative analysis, for the case of small data p=2 is recommended, resulting in a root mean square error value of 0.03458, a mean absolute error of 0.02013 and a median absolute deviation of 0.00546. Oppositely, a p-value of 3 and 4 is selected as appropriate for a large data set, with root mean square errors of 0.02435 and 0.02437, mean square errors of 0.01582 and 0.01509 and median absolute deviations 0.00896 and 0.00444. Eventually for a small data set, it is recommended to use a p-value of 2, and for a large data set, a p-value of 3 or 4.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.

Inverse optimal control is a method for recovering the cost function used in an optimal control problem in expert demonstrations. Most studies on inverse optimal control have focused on building the unknown cost function through the linear combination of given features with unknown cost weights, which are generally considered to be constant. However, in many real-world applications, the cost weights may vary over time. In this study, we propose an adaptive online inverse optimal control approach based on a neural-network approximation to address the challenge of recovering time-varying cost weights. We conduct a well-posedness analysis of the problem and suggest a condition for the adaptive goal, under which the weights of the neural network generated to achieve this adaptive goal are unique to the corresponding inverse optimal control problem. Furthermore, we propose an updating law for the weights of the neural network to ensure the stability of the convergence of the solutions. Finally, simulation results for an example linear system are presented to demonstrate the effectiveness of the proposed strategy. The proposed method is applicable to a wide range of problems requiring real-time inverse optimal control calculations

This article proposes application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using the deep learning. In general, the spots represent vague figures in abstract “information spaces” or crisp figures with lack of in-formation about their shapes and are adequate for representation human mental images and reasoning in Artificial Intelligence (AI). However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, basing on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Also, we defined L4 vectors, L4 matrices, and mathematical operations on them. Developed apparatus can be used in AI, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates application of spot-based inverse Radon algorithm for binary image reconstruction.

As many if not most ligands at G protein-coupled receptor antagonists are inverse agonists, we have systematically reviewed inverse agonism at the nine adrenoceptor subtypes. Except for β3-adrenoceptors, inverse agonism has been reported for each of the adrenoceptor subtypes, most often for β2-adrenoceptors, including endogenously expressed receptors in human tissues. As with other receptors, detection and degree of inverse agonism depends on the cells and tissues under investigation, i.e. is greatest when the model has a high intrinsic tone/constitutive activity for the response being studied. Accordingly, it may differ between parts of a tissue, for instance atria vs. ventricles of the heart, and within a cell type between cellular responses. The basal tone of endogenously expressed receptors often is low, leading to less consistent detection and smaller extent of observed inverse agonism. The extent inverse agonism depends on specific molecular properties of a compound but clusters by chemical class. While inverse agonism is a fascinating facet in attempts to mechanistically understand observed drug effects, we are skeptical whether an a priori definition of extent of inverse agonism in the target product profile of a developmental candidate is a meaningful option in drug discovery and development.

We present an improved algorithm for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithm is much more accurate than the famous fast inverse square root algorithm and has a similar computational cost. The presented modification concern Newton-Raphson corrections and can be applied when the distribution of these corrections is not symmetric (for instance, in our case they are always negative).

Matrix metalloproteinases (MMPs) have been demonstrated to have both detrimental and protective functions in inflammatory diseases. Several MMP inhibitors, with the exception of Periostat®, have failed in Phase III clinical trials. As an alternative strategy, recent efforts have been focussed on the development of more selective inhibitors or targeting other domains than their active sites (e.g., exosites, ectosites) through specific small molecule inhibitors or monoclonal antibodies. Here, we present some examples that aim to better understand the mechanisms of conformational changes/allosteric control of MMPs functions. In addition to MMP inhibitors, we discuss unbiased global approaches such as proteomics and N-terminomics to identify new MMP substrates and achieve a better understanding of the roles of these proteases in diseases.

Introduction: Depending on the kind of cancer and neurological disorders, there might be a direct or inverse link between neurodegeneration and cancer. The inverse interaction between cancer and Alzheimer's pathology has garnered substantial interest in medical research. While this inverse interaction between Alzheimer's pathology and cancer presents a fascinating scientific puzzle, there is still limited information and studies on the potential mechanisms involved in this inverse rela-tionship. Aim: This study aims to identify potential genes from Alzheimer's disease that may protect against cancer. Method: The Gene Expression Omnibus (GEO) database provided the Alzheimer's pathology dataset, and GEO 2R was utilized to examine genes that were differentially expressed. The expression of upregulated Alzheimer's pathology genes in breast, colorectal, and prostate cancer was compared using VENN 2.1, colorectal, and prostate cancer was compared using VENN 2.1, and colorectal and prostate cancers were compared using VENN 2.1. Results: Among the upregulated genes associated with Alzheimer's disease, 25 genes are shared among breast cancer, colorectal cancer, and prostate cancer, while 28 of these genes were exclusive to Alzheimer's dis-ease. Gene expression profiling interactive analysis among the shared genes revealed that AQP1, C4A, CSRP2, CRYAB, MACF1, HSPB2, and NEAT1 were downregulated in breast, colorectal, and prostate cancers. These genes have varying roles in cancer progression and suppression. Functional analysis of Alzheimer's disease-related upregulated genes revealed that C1orf56 and HIST1H2AC control cell proliferation, with HIST1H2AC playing a role in necroptosis. Additionally, C1orf56 worked as an oncogenic modifier to support DNMT3B's tumor suppressor properties. Conclusion: Given the role of HIST1H2AC and C1orf56 in the negative control of cell proliferation and their upregulation in Alzheimer's disease, there is a need to further investigate HIST1H2AC and C1orf56 as potential tumor suppressors responsible for Alzheimer's disease and cancer inverse association.

In this paper, at first, a color image of a car is taken. Then the image is transformed into a grayscale image. After that, the motion blurring effect is applied to that image according to the image degradation model described in equation 3. The blurring effect can be controlled by a and b components of the model. Then random noise is added in the image via Matlab programming. Many methods can restore the noisy and motion blurred image; particularly in this paper Inverse filtering as well as Wiener filtering are implemented for the restoration purpose. Consequently, both motion blurred and noisy motion blurred images are restored via Inverse filtering as well as Wiener filtering techniques and the comparison is made among them.

Introduced in 1967 by Lov\'{a}sz, graph exponentiation has received little attention over the past several decades. Since graph exponentiation produces large graphs and any graph can be constructed utilizing its adjacency matrix, we provide a four step linear construction algorithm that generates the adjacency matrix for the graph exponential.

Biofilm matrix is akin to bacterial abodes, primarily composed of proteins, polysaccharides, extracellular DNA, and lipids, providing essential structural support to bacteria. While some biofilm matrix offers significant benefits, such as engineered biofilm reactors that assist in water pollutant removal, others pose risks to human health, potentially leading to conditions like lung infections. Realizing the potential of advantageous biofilm matrix and mitigating the harmful effects of detrimental ones necessitates a comprehensive and systematic exploration of this intricate domain. To facilitate this examination, our study leveraged a dataset of the 1000 most pivotal papers in the field and conducted an exhaustive bibliographic review. This paper serves as a valuable resource for understanding the current progress in biofilm matrix research and delving into vital avenues for future exploration in this dynamic field.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

Metal matrix composite are used in such fields of technology, such as: aerospace, electronics, energy, industry, defense, automotive, aviation, shipbuilding, and more. Composite coatings of ceramic - metals is used primarily to enhance the durability of machine parts. Therefore, new materials are permanently looked for, what has resulted in the past in development of composite materials. The coatings dispersed are consisting of metallic matrix (metals and their alloys) and small non-metallic particles. The deposition of ceramic particles simultaneously with metallic matrix leads often to composite coatings possessing properties much better than those of metallic coating. The nickel and less often, other iron group elements are usually used as a matrix and Al2O3 as tough particles. The welding technology of applying alloy and composite coatings is widely used. The technology of infrasound thermal spraying of metal matrix composite coatings was presented. It is a simple technology and a very useful one in ship machinery regeneration during the cruise craft (e.g. internal combustion engines, torque pumps, separators). The metal matrix composite coatings must undergo finishing due to high surface roughness after application. In the article to used finishing by plastic working and machining of coatings nickel matrix composite was proposed.

The direct measurements of the magnetocaloric effect were performed in Heusler Ni44.4Mn36.2Sn14.9Cu4.5 alloy at cryogenic temperatures in magnetic fields up to 10 T. The maximum value of the inverse magnetocaloric effect in a field of 10 T was observed ∆Tad = –2.7 K in the vicinity of the 1st order magnetostructural phase transition at T0 = 117 K. The ab initio and Monte Carlo calculations were performed to discuss the effect Cu doping into Ni-Mn-Sn compound on the ground state structural and magnetic properties. It is shown that with increasing Cu content the martensitic transition temperature decreases and the Curie temperature of austenite slightly increases. In general, calculated transition temperatures, magnetization values are correlated well with the experimental ones.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Giant plasmonic surface enhancement has been observed in gold coated micron sized inverse pyramids entrapping a gold nanoparticle. The amplification of both surface enhanced Raman and photoluminescence signals was found to be dependent on the diameter of trapped gold nanoparticle and around 50-fold enhancement was detected for 250nm diameter sample relatively to the 50nm one. Finite differential time domain simulations, performed to determine the near-field distribution in the structure, showed that when the nanoparticle protrudes into the hotspot zone of the void, coupling of electromagnetic field occurs and the plasmon-related near-field enhancement is concentrated into the close vicinity of the nanoparticle, mainly into the close gaps around the tangential points of the curved sphere and the flat pyramid surface. This results in a more than 15 times increase of the near-field intensity, compared to the empty void.

This paper describes a new approach that can be used to determine the mechanical properties of unknown materials and complex material systems. The approach uses inverse finite element modelling (FEM) accompanied with a designed algorithm to obtain the modulus of elasticity, yield stress and strain hardening material constants of an isotropic hardening material model, as well as the material constants of the Drucker-Prager material model (modulus of elasticity, cap yield stress and angle of friction). The algorithm automatically feeds the input material properties data to finite element software and automatically runs simulations to establish a convergence between the numerical loading-unloading curve and the target data obtained from continuous indentation tests using common indenter geometries. A further module was developed to optimise convergence using an inverse FEM analysis interfaced with a non-linear MATLAB algorithm. A sensitivity analysis determined that the dual Spherical and Berkovich (S&B) approach delivered better results than other dual indentation methods such as Berkovich and Vickers (B&V) and Vickers and Spherical (V&S). It was found that better convergence values can be achieved despite a large variation in the starting parameter values and / or material constitutive model and such behaviour reflects the uniqueness of the dual S&B indentation in predicting complex material systems. The study has shown that a robust optimization method based on a non-linear least-squares curve fitting function (LSQNONLIN) within MATLAB and ABAQUS can be used to accurately predict a unique set of elastic plastic material properties and Drucker-Prager material properties. This is of benefit to the scientific investigation of properties of new materials or obtaining the material properties at different location of a part which might be not be similar due to manufacturing processes (e.g. different heating and cooling rates at different locations).

In laser-assisted milling, higher temperature in shear zone softens the material potentially resulting in a shift of mean residual stress, which significantly affects the damage tolerance and fatigue performance of product. In order to guide the selection of laser and cutting parameters based on the preferred mean residual stress, inverse analysis is conducted by predicting residual stress based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. An analytical inverse analysis is therefore proposed for the mean residual stress in laser-assisted milling. The forward problem is solved by analytical prediction of mean residual stress after laser-assisted milling. The residual stress profile is predicted through the calculation of thermal stress, by treating laser beam as heat source, and plastic stress by first assuming pure elastic stress in loading process, then obtaining true stress with kinematic hardening followed by the stress relaxation. The variance-based recursive method is applied to solve inverse problem by updating process parameters to match the measured mean residual stress. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power, are updated with respected to the minimization of resulting residual stress and measurement in each iteration. Experimental measurements are referred on the laser-assisted milling of Ti-6Al-4V grade 5 and ELI. The percentage difference between experiments and predictions is less than 5% for both materials, and the selection is completed within 50 loops.

Before calcification begins, the early embryonic and fetal skeletal development of both mammalian Homo sapiens and the chondrichthyan fish Raja asterias consists exclusively of cartilage. This cartilage is formed and shaped through processes involving tissue segmentation and the frequency, distribution, and orientation of chondrocyte mitoses. In the subsequent developmental phase, mineral deposition in the cartilage matrix conditions the development further. The stiffness and structural layout of the mineralized cartilage have a significant impact on the shape of the anlagen (early formative structures of organs or tissues) and the mechanical properties of the skeletal segments. The fundamental difference between the two studied species lies in how calcified cartilage serves as a scaffold for osteoblasts to deposit bone matrix, which is then remodeled. In contrast, chondrichthyans retain the calcified cartilage as the definitive skeletal structure. This study documents the distinct mineral deposition pattern in the cartilage of the chondrichthyan R. asterias, in which calcification progresses with the formation of focal calcification nuclei or “tesserae”. These are arranged on the flat surface of the endo-skeleton (crustal pattern) or aligned in columns (catenated pattern) in the radials of the appendicular skeleton. This anatomical structure is well adapted to meet the mechanical requirements of locomotion in the water column. Conversely, in terrestrial mammals, endochondral ossification (associated with the remodeling of the calcified matrix) provides limb bones with the necessary stiffness to withstand the strong bending and twisting stresses of terrestrial locomotion. In this study, X-rays of marine mammals (reproduced from previously published studies) document how the endochondral ossification in dolphin’s flipper adapts to the mechanical demands of aquatic locomotion. This adaptation includes the reduction in the length of the stylopodium and zeugopodium and an increase in the number of elements in the autopodium’s central rays.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

The paper deals with the Compound Inverse Rayleigh distribution, shown to constitute a proper model for the characterization of the probability distribution of extreme values of wind-speed, a topic which is gaining growing interest in the field of renewable generation assessment, both in view of wind power production evaluation and the wind-tower mechanical reliability and safety. The first part of the paper illustrates such model starting from its origin as a generalization of the Inverse Rayleigh model - already proven to be a valid model for extreme wind-speeds - by means of a continuous mixture generated by a Gamma distribution on the scale parameter, which gives rise to its name. Moreover, its validity to interpret different field data is illustrated, also by means of numerous numerical examples based upon real wind speed measurements. Then, a novel Bayes approach for the estimation of such extreme wind-speed model is proposed. The method relies upon the assessment of prior information in a practical way, that should be easily available to system engineers. In practice, the method allows to express one’s prior beliefs both in terms of parameters, as customary, and/or in terms of probabilities. The results of a large set of numerical simulations – using typical values of wind-speed parameters - are reported to illustrate the efficiency and the accuracy of the proposed method. The validity of the approach is also verified in terms of its robustness with respect to significant differences compared to the assumed prior information.

Our work uses Iterative Boltzmann Inversion (IBI) to study the coarse-grained interaction between 20 amino acids and the representative carbon nanotube CNT55L3. IBI is a multi-scale simulation method that has attracted the attention of many researchers in recent years. It can effectively modify the coarse-grained model derived from the Potential of Mean Force (PMF). IBI is based on the distribution result obtained by All-Atom molecular dynamics simulation, that is, the target distribution function, the PMF potential energy is extracted, and then the initial potential energy extracted by the PMF is used to perform simulation iterations using IBI. Our research results have gone through more than 100 iterations, and finally, the distribution obtained by coarse-grained molecular simulation (CGMD) can effectively overlap with the results of all-atom molecular dynamics simulation (AAMD). In addition, our work lays the foundation for the study of force fields for the simulation of the coarse-graining of super-large proteins and other important nanoparticles.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

Novel tetragonal matrix Ba0.5Gd0.5-xNaxF2.5-x, where x = 0.05, doped by Yb3+, Ho3+, Er3+, was synthesized by molten salt synthesis (MSS) from nitrate flux. XRD data show that tetragonal phase with a = 4.122(1) Å, c = 17.672(1) Å is stable in argon atmosphere up to 960 °C. Luminescence spectra recorded in 500-900 nm and 1050-1700 nm upon 974 nm pumping demonstrated the characteristic luminescence at 1550 nm (4I13/2 → 4I15/2) for Er3+ and 1150 nm (5I6 → 5I8) for Ho3+. The relative thermal sensitivity (Sr) at 296-316 K were 0.3 %*K-1 and 5.5%*К-1 in shortwave infrared (SWIR) and visible range, respectively. Synthesized luminophores can be used as dual-range optical temperature sensors, which simultaneously operating in visible and SWIR ranges.

It is shown that a Mueller quaternion can be formulated as a quaternion with matrix coefficients, and this Mueller quaternion transforms the Stokes quaternion for depolarizing process as well as for nondepolarizing process. Mueller quaternion keeps track of the phase acquired by the Stokes quaternion and, in general, quaternion states of optical media comprises all properties of Jones, Mueller-Jones and Mueller matrices.

To deal with the uncertainties in modeling offshore wind turbines, we proposed a parameter inversion method for the pile-soil interaction model based on structural health monitoring results and the numerical model. The proposed parameter inversion method has a numerical model, an objective function selected using both the numerical and identified results, and an inverse optimization using a random search algorithm in the assumed parameter space. The parameter results in the minimum optimization objective function are identified as the in-situ parameter. The proposed method is confirmed to converge after some iterations, whatever the initial parameter values are. However, different initial parameter cases may converge to slightly different optimal parameters, implying the pile results are sensitive to geological parameters. Moreover, a comparison with the original design results shows design redundancy or risks. Though the proposed method has several flaws, it can shed some light on the influence of uncertainties in offshore wind turbines, such as soil parameters in geological surveys.

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

An inverse aeroacoustic problem for a helicopter rotor combined with aerodynamic constraint is proposed based on Ffowcs Williams and Hawkings equation in subsonic. The rotor noise includes thickness noise and loading noise when quadrupole noise is neglected. Thickness noise is related to geometry and motion conditions. Loading noise is related to the pressure on the wall. Therefore, the equation between pressure on the wall and far-field noise can be established, thus the pressure on the wall can be obtained by solving this equation. Since this equation is an ill-posed, the singular value decomposition combined with the regulation method is applied and the aerodynamic constraint is taken into account. The direct noise prediction is verify firstly and then the inverse problem is solved. The reconstruction pressure is compared to the input data. The result is in good agreement with the input value. At the same time, the influence of interference noise is also considered. Under low signal-to-noise ratio, the reconstruction result is also reasonable.

Iyer Markoulakis Helmholtz Hamiltonian mechanics formalisms mathematically modeled physics with vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields. Here, Helmholtz metrics have been gaged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields out of the mechanical fields from Helmholtz Hamiltonian mechanics. This ansatz general gaging helps to properly isolate field effects – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gage metrics, having the power to analyze dark energy superluminal phase, dark matter luminal phase, and light matter subluminal phase. Interpreting particle physics gage matrix pointing to Dirac seas electrons, monopoles with positrons, electron-positron annihilation leading to energy production, relativistic energy generating matter, and both monopoles – vacuum and compressed out of vortex Helmholtz decomposition fields have been interpolated. Quantum ASTROPHYSICS gage metrix posits superluminal profile of signals velocity generating electron-positron chain like “curdling” action that is consistent with physics literature reporting nature electron photon observed oscillatory fields configurations. This helps proposing creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon. These aspects will explain receding or fast expanding universe with dark matter in terms of flavor metrics versus gage associating metrics flavor. Additional interpretations of virtual gravitational dipoles that have gravitational charge of opposite signs, reported per physics literature at Planck dimensions, that may originate at the center of supermassive blackhole. On the other hands, vacuum monopoles occur probably at infinity with cosmos extent.

We work with reference to a well-known semiclassical model, in which quantum degrees of freedom interact with classical ones. We show that, in the classical limit, it is possible to represent classical results (e.g., classical chaos) by means a pure-state density matrix.

Portfolio weights solely based on risk avoid estimation error from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation and the Exponential Weighted Moving Average target matrices. By an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance, Inverse Volatility, Equal-risk-contribution and Maximum Diversification portfolios. We find out that the Identity and Variance Identity have very good statistical properties, being well-conditioned also in high-dimensional dataset. In addition, the these two models are the best target towards to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps reducing weights misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification, hence they benefit less from shrinkage.

Today, mechanical tracking systems have been downsized to allow them to be used in the field of airborne laser communications and in the military domain. Risley systems are used for this purpose, which work by directing a beam of light to a given target point, this procedure is commonly known as the inverse problem. In this paper, an analytical method, the geometric method, has been designed and developed to determine the beam steering in a Risley system and solve the inverse problem. The method focuses on different geometric shapes, like circumference or ellipse, that are described when the beam passes through the second prism. The accuracy and efficiency of the geometric method has been analysed and found to be faster than the two-step method. Furthermore, the geometric method has been implemented in an iterative process and an accuracy of up to 1 pm has been achieved. This high accuracy would allow the geometric method to be applied in fields such as lithography, stereolithography or 3D printers.

Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The problem is reduced to a linear algebraic system with a nondegerate matrix.

The application of instrumented indentation to assess material properties like Young’s modulus and micro-hardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e. kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress-strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress-strain-curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-non-destructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

This article is devoted to the results of in-depth analysis of the system of binary-oppositional structures in DNA n-plet alphabets and their algebraic-matrix representations. These results show that the molecular complementary replication of DNA strands is accompanied by the presence of an algebraic version of the principle "like begets like" in matrix representations of DNA alphabets having internal structures. This algebraic version is based on binary-oppositional structures in the genetic molecular system, which can be represented by binary numbers and corresponding matrices of DNA alphabets. The received results allow thinking that the phenomenon "like begets like" (or a complementary replication in a wide sense) is systemic in the genetic organization and is connected with algebraic features of biological organization. Correspondingly, the biological principle "like begets like" can be additionally modeled by algebraic-matrix methods and approaches. Such algebra-matrix modeling of the genetic coding system gives new ways for studying and understanding the key role of the named principle in genetic and other inherited physiological complexes. On this way, the author discovered general rules of stochastic organization of information binary sequences of genomic DNAs of eukaryotes and prokaryotes. The presented rules are connected with information dichotomies of probabilities and corresponding fractal-like trees of probabilities, which fundamentally differ from constructional dichotomies in biological bodies. The received phenomenological data and rules lead to new biological ideas.

The extracellular matrix (ECM) is a ubiquitous member of the body and is key to the maintenance of tissues and organs integrity. Initially thought to be a by-stander in many cellular processes, the extracellular matrix has been shown to have diverse components that regulate and activate many cellular processes and ultimately influence cell phenotype. Importantly, the ECM composition, architecture, and stiffness/elasticity influence cellular phenotypes. Under normal conditions and during development, the synthesized ECM is constantly undergoing degradation and remodeling processes via the action of matrix proteases that maintain tissue homeostasis. In many pathological conditions including fibrosis and cancer, the ECM synthesis, remodeling, and degradation is dysregulated causing its integrity to be altered. Both physical and chemical cues from the ECM are sensed via receptors including integrins and play key roles in driving cellular proliferation and differentiation and in various disease progression such as cancers. Advances in ‘omics’ technologies have seen an increase in studies focussing on bi-directional cell-matrix interactions and here we highlight emerging knowledge on the role played by the ECM during normal development and in pathological conditions. This review summarizes current ECM-targeted-therapies that can modify tumor ECM to overcome drug resistance and better cancer treatment.

By constructing a static map, the library robot can navigate and access documents autonomously, which greatly improves efficiency; however, for libraries where shelves can be moved, map changes do not allow for direct navigation, and also sensors such as radar and camera are relatively expensive, so we propose a low-cost navigation algorithm based on real-time ranging data and map matrices, and designed a mobile archive access robot. In order to obtain real-time distance data, nine near/long range sensors were mounted on the chassis and a composite digital filtering algorithm was designed based on different moving area characteristics; then the access task matrix and map matrix were designed based on the archive access task and the location characteristics of the archive shelf placement, the robot can rely on the range data to update the map matrix during the moving process, complete its own positioning, and use the task matrix The robot can use the task matrix to complete autonomous navigation and access to multiple files. Experiments show that the filtered positioning accuracy can reach 1cm, while the robot can move to the target shelf autonomously, which is more practical and less costly.

The paper summarizes in a step by step ‘recipe’ format a model of developing new ideas (Ideation) that can be used to form a new venture or develop a new product. The proposed ‘recipes’ are widely used and can be applied in tandem with other prevalently available models or tools. The intention of the paper is also to serve as a resource for entrepreneurs and innovators, and the links and references munificently used in the paper are serving this purpose. The author has used the outline and the tools described here in numerous Ideation classes taught for over a decade in several countries around the world. The paper’s intention is not to conduct a systematic review on the subject of new venture creation or propose new research agenda (for that, see for example Shepherd et al., 2021). The purpose is to provide an effective and efficient set of tools, models and techniques that can assist the entrepreneur in her journey to create and achieve her dreams. One such tool is the matrix of Reasonings-Outcomes introduced here for the first time.

The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.

Abstract: Congenital cytomegalovirus (cCMV) infection poses significant risks to fetal development, particularly affecting the nervous system. This study reports a fetal autopsy case, examining cCMV infection and focusing on CMV DNA measurements in various fetal organs before formalin fixation, a novel approach for comprehensive CMV DNA evaluations in fetal organs affected by cCMV. A 20-week-old male fetus was diagnosed with cCMV following the detection of CMV DNA in ascites obtained via abdominocentesis in utero. After termination of pregnancy, multiple organs of the fetus, including the cerebrum, thyroid gland, heart, lungs, liver, spleen, kidneys, and adrenal glands, were extracted and examined for CMV DNA loads using real-time polymerase chain reaction. Histopathological examination involved hematoxylin-eosin and CMV-specific immunostaining. A correlation was found between CMV DNA loads and pathology, with higher CMV-infected cell numbers observed in organs positively identified with both staining methods, exhibiting CMV DNA levels of ≥1.0 × 104 copies/mL, compared to those detected solely by CMV-specific immunostaining, where CMV DNA levels ranged from 1.0 x 103 to 1.0 x 104 copies/mL. These results highlight a quantifiable relationship between organ infection extent and CMV DNA concentration, providing insights into cCMV pathogenesis and potentially informing future diagnostic and therapeutic strategies for cCMV infection.

Modeling the reaction time required for the removal of chemical oxygen demand (COD) from wastewater is important because can be an indicator of harmful pollutants that may pose risks to human health.. Here, we evaluate the use of an inverse artificial neural network (ANNi) to optimize the removal of COD from aqueous herbicide solutions using sonophotocatalysis as the treatment process.. This algorithm takes the operating conditions as input and estimates the optimal reaction time to reach the required effluent COD. This model was validated by comparison with both experimental measurements and simulated analysis, resulting in low error (0.5%), high Pearson correlation (R2 = 0.9956), and short computing time (less than one minute). The results for the proposed methodology (ANNi-GAs) were efficient and attractive in a reasonable way providing a satisfactory picture of the relationships between the optimal input parameters. Such parameters control the degradation process of herbicides online and can be used to predict the behavior of COD removal, thus taking actions to reduce the impact of aqueous treatment with alazine and gesaprim herbicides on aquatic, soil biota, and human health. Therefore, this technique constitutes a promising framework for predicting the environmental impact of herbicides within a tolerable degree of error.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U_0/(2r^2) is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying the angular momentum, with the orbital and magnetic quantum numbers, l and m. They exist above a threshold value of the potential's strength, U_0 > l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an approximate analytical form for relatively small values of U_0 - l(l + 1). Explicit results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.