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In this paper, we introduce the notion of ♭, ℓ-neutrosophic subsemigroup (NSS), neutrosophic left ideal(NLI), neutrosophic right ideal(NRI), neutrosophic ideal (NI), neutrosophic bi-ideal(NBI), (ϵ, ϵ ∨ q)-neutrosophic ideal, neutrosophic bi-ideal of an ordered Γ-semigroups and discuss some of their properties. The concept of ♭, ℓ-neutrosophic ideal is a new extension of neutrosophic ideal over ordered Γ-semigroups Z. A non-empty subset ξ♭ is a (♭, ℓ)-NSS (NLI, NRI, NBI, (1,2)-ideal) of Z. Then the lower level set Δ♭ is an subsemigroup (LI, RI, BI, (1, 2) - ideal) of Z, where Δ♭ = {ρ ∈ Z|Δ(ρ) > ♭}, Ψ♭ = {ρ ∈ Z|Δ(ρ) > ♭} and 0♭ = {ρ ∈ Z|Δ(ρ) < ♭}. A subset ξ = [Δ,Ψ,0] is a (♭, ℓ) - NSS[NLI, NRI, NBI, (1, 2) - ideal] of Z if and only if each non-empty level subset ξt is a subsemigroup [LI, RI, BI, (1, 2) - ideal] of Z for all t ∈ (♭, ℓ]. Every (ϵ, ϵ ∨ q)NBI of Z is a (♭, ℓ)NBI of Z, but converse need not be true and examples are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

Quality control (QC) charts are essential for ensuring industry process stability, but imprecise data make traditional methods unuseful in such a case. Neutrosophic control charts are available to handle the imprecise data. This article learns fuzzy logic as an approach of handling uncertainty more suitably than neutrosophic approaches. Fuzzy QC charts make use of fuzzy numbers, membership functions and fuzzy control limits and as such are more realistic compared to conventional charts. The study introduces a Fuzzy Adaptive Exponentially Weighted Moving Average (FAEWMA) chart, specifically designed for univariate data in a fuzzy atmosphere. The FAEWMA chart, incorporating α-cuts, is engineered to detect shifts in process means, showcasing its effectiveness through both theoretical development and practical applications. This approach improves decision-making in process control and represents a significant advancement over traditional QC methods. [ABSTRACT FROM AUTHOR]

A neutrosophic is a strong framework to characterize novel mathematical structures. This framework is more suitable and flexible set side by side to fuzzy sets and intuitionistic fuzzy sets. In this work, we focus on some famous mathematical spaces like Lδ,p(U) when we work on displaying a feature the immediate and contrary theorems of unrestrained functions in the space Lδ,p(U) are considered. Also, some characteristics of modification symmetric and modulus of neutrosophic smoothness have been discussed. Moreover, the identical among approximate tools such as the neutrosophic K-functional and neutrosophic modulus of softness. [ABSTRACT FROM AUTHOR]

In this study, a broader class of rational functions r(u(z)) of degree mn, where u(z) is a polynomial of degree m is taken into consideration and obtain certain sharp compact generalization of well-known inequalities for rational functions. [ABSTRACT FROM AUTHOR]

Background: While protein-protein docking is fundamental to our understanding of how proteins interact, scoring protein-protein complex conformations is a critical component of successful docking programs. Without accurate and efficient scoring functions to differentiate between native and non-native binding complexes, the accuracy of current docking tools cannot be guaranteed. Although many innovative scoring functions have been proposed, a good scoring function for docking remains elusive. Deep learning models offer alternatives to using explicit empirical or mathematical functions for scoring protein-protein complexes. Results: In this study, we perform a comprehensive survey of the state-of-the-art scoring functions by considering the most popular and highly performant approaches, both classical and deep learning-based, for scoring protein-protein complexes. The methods were also compared based on their runtime as it directly impacts their use in large-scale docking applications. Conclusions: We evaluate the strengths and weaknesses of classical and deep learning-based approaches across seven public and popular datasets to aid researchers in understanding the progress made in this field. [ABSTRACT FROM AUTHOR]

In this paper, we develop a stochastic multi-molecule chemical reaction model with reaction rate perturbed by log-normal O r n s t e i n - U h l e n b e c k process in order to consider the effects of random factors on chemical reaction dynamics. Firstly, we prove the existence and uniqueness of the global positive solution for the stochastic model. In addition, we obtain the conditions under which the corresponding stochastic system exist a stationary distribution. Then, we derive a sufficient condition to end the reaction. Furthermore, the stochastic system has been transformed into a linearized system, by solving F o k k e r - P l a n c k equation, we obtain the exact expression of the density function around the quasi-equilibrium of this system. Finally, we draw a conclusion that the dynamical behaviors of the stochastic system will be affected by random factor, O r n s t e i n - U h l e n b e c k process respectively [ABSTRACT FROM AUTHOR]

Based on the theory of hyperelliptic curves, the algebraic curve method is extended to construct algebro-geometric quasiperiodic solutions of nonlocal reverse space–time soliton equations. The nonlocal reverse space–time sine-Gordon equation is chosen as an example to illustrate our method. Given the Lax matrix of the nonlocal reverse space–time sine-Gordon equation, we introduce an algebraic hyperelliptic curve of genus , from which the Dubrovin-type equations, a meromorphic function , and a Baker–Akhiezer function are found. Using the theory of algebraic curves, the nonlocal reverse space–time sine-Gordon flows are straightened by using the Abel–Jacobi coordinates. In accordance with the asymptotic properties of the Baker–Akhiezer function, we construct explicit theta-function representations of the Baker–Akhiezer function and the meromorphic function, including that for solutions of the nonlocal reverse space–time sine-Gordon equation. [ABSTRACT FROM AUTHOR]

With increasing remote work and online learning, there is a growing demand for image encryption algorithms with sufficient capacity and efficiency. In this paper, we propose an effective multiimage encryption algorithm. By coupling the Sine map and some useful mathematical functions, we design a two-dimensional hyperchaotic system (2D SFCM). After evaluating different chaos indicators, it is found that the Lyapunov exponent and the permutation entropy of 2D SFCM are significantly higher than those of other chaotic mappings. Additionally, its sample entropy has an average value of 1.916. These results indicate that the chaotic sequences generated by 2D SFCM exhibit a high level of randomness. The pseudo-random sequences generated by this chaotic system are combined with image encryption algorithms to shuffle 3D images by accessing pixels from different planes. Using randomly determined pixel points, cyclic diffusion is performed on each plane to ensure that the pixel information at any point extends to the whole 3D image. Experimental results demonstrate that the proposed algorithm exhibits good key sensitivity and robustness. Numerical results show that the algorithm has considerable capabilities in resisting common attacks. Compared to related algorithms, our algorithm shows certain advantages in terms of information entropy and resistance to differential attacks. [ABSTRACT FROM AUTHOR]

A non-polynomial spline is a technique that utilizes information from symmetric functions to solve mathematical or physical models numerically. This paper introduces a novel non-polynomial spline construct incorporating a rational function term to develop an efficient numerical scheme for solving time-fractional differential equations. The proposed method is specifically applied to the time-fractional KdV–Burgers (TFKdV) equation. and time-fractional differential equations are crucial in physics as they provide a more accurate description of various complex processes, such as anomalous diffusion and wave propagation, by capturing memory effects and non-local interactions. Using Taylor expansion and truncation error analysis, the convergence order of the numerical scheme is derived. Stability is analyzed through the Fourier stability criterion, confirming its conditional stability. The accuracy and efficiency of the rational non-polynomial spline (RNPS) method are validated by comparing numerical results from a test example with analytical and previous solutions, using norm errors. Results are presented in 2 D and 3 D graphical formats, accompanied by tables highlighting performance metrics. Furthermore, the influences of time and the fractional derivative are examined through graphical analysis. Overall, the RNPS method has demonstrated to be a reliable and effective approach for solving time-fractional differential equations. [ABSTRACT FROM AUTHOR]

We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve convex optimization problems. In particular, we consider (i) classes of optimization problems of finite-sum form with (possibly strongly) convex and possibly smooth functional components, (ii) first-order methods that can be written as a linear system on state-space form in feedback interconnection with the subdifferentials of the functional components of the objective function, and (iii) quadratic Lyapunov inequalities that can be used to draw convergence conclusions. We present a necessary and sufficient condition for the existence of a quadratic Lyapunov inequality within a predefined class of Lyapunov inequalities, which amounts to solving a small-sized semidefinite program. We showcase our methodology on several first-order methods that fit the framework. Most notably, our methodology allows us to significantly extend the region of parameter choices that allow for duality gap convergence in the Chambolle–Pock method when the linear operator is the identity mapping. [ABSTRACT FROM AUTHOR]

In this paper, we have discussed an innovative method for crafting a one-dimensional photonic crystal (1D PhC) based Optical Band Pass Filter (OBPF) using a Differential Evolution (DE) algorithm. 1D PhC-based OBPF plays a vital role in optical communication systems due to its ability to control light propagation. The proposed technique optimizes the photonic crystal structure to achieve the desired optical bandpass characteristics efficiently. The DE algorithm streamlines the design process and enables fast exploration of the design space. The effectiveness of this approach is validated through simulations and comparisons with the existing well-known methods. The OBPF comprises multiple dielectric layers with varying thicknesses and refractive indices to enable high transmission at specific wavelengths and low transmission elsewhere. The Optimization techniques are employed to adjust the parameters like thickness, refractive index, and number of layers. The DE method, thus, enhances the performance of OBPF. MATLAB implementation showcases significant outcomes with high transmittance (99.9727%), low reflectance (0.0273%), and a narrow Full Width at Half Maximum of 0.5 nm that affirms its efficacy. [ABSTRACT FROM AUTHOR]

Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. In general, ML models employ generic mathematical functions and attempt to learn essential physics and chemistry from large amounts of data. The reliability of predictions, however, is often not guaranteed, particularly for out-of-distribution data, due to the limited physical or chemical principles in the functional form. Therefore, it is critical to quantify the uncertainty in ML predictions and understand its propagation to downstream chemical and materials applications. This review examines existing uncertainty quantification (UQ) and uncertainty propagation (UP) methods for atomistic ML under the framework of probabilistic modeling. We first categorize the UQ methods and explain the similarities and differences among them. Following this, performance metrics for evaluating their accuracy, precision, calibration, and efficiency are presented, along with techniques for recalibration. These metrics are then applied to survey existing UQ benchmark studies that use molecular and materials datasets. Furthermore, we discuss UP methods to propagate uncertainty in widely used materials and chemical simulation techniques, such as molecular dynamics and microkinetic modeling. We conclude with remarks on the challenges and opportunities of UQ and UP in atomistic ML. [ABSTRACT FROM AUTHOR]

Copyright of Food & Fermentation Industries is the property of Food & Fermentation Industries and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An enhanced whale optimization algorithm (WOA) through the implementation of a generalized type-2 fuzzy logic system (GT2FLS) is outlined. The initial idea is to improve the efficacy of the original WOA using a GT2FLS to find the optimal values of the r → 1 and r → 2 parameters of the WOA, for the case of optimizing mathematical functions. In the WOA algorithm, r → 1 is a variable that affects the new position of the whale in the search space, in this case, affecting the exploration, and r → 2 is a variable that has an effect on finding the local optima, which is an important factor for the exploration. The efficiency of a fuzzy WOA with a GT2FLS (FWOA-GT2FLS) is highlighted by presenting the excellent results of the case study of the benchmark function optimization. A relevant analysis and comparison with a bio-inspired algorithm based on artificial bees is also presented. Statistical tests and comparisons with other bio-inspired algorithms and the initial WOA, with type-1 FLS (FWOA-T1FLS) and interval type-2 FLS (FWOA-IT2FLS), are presented. For each of the methodologies, the metric for evaluation is the average of the minimum squared errors. [ABSTRACT FROM AUTHOR]

Prompt injection is a type of attack that induces violent or discriminatory responses via the input of a prompt containing illegal instructions to the large language model (LLM). Most early injection attacks used simple text prompts; however, recently, injection attacks employing elaborately designed prompts to overcome the strong security policies of modern LLMs have been applied to input prompts. This study proposed a method to perform injection attacks that can bypass existing security policies via the replacement of sensitive words that may be rejected by a language model in the text prompt with mathematical functions. By hiding the contents of the prompt so that the LLM cannot easily detect the contents of the illegal instructions, we achieved a considerably higher success rate than existing injection attacks, even for the latest securely aligned LLMs. As the proposed method employed only text prompts, it was capable of attacking most LLMs. Moreover, it exhibited a higher attack success rate than multimodal attacks using images despite using only text. An understanding of the newly proposed injection attack is expected to aid in the development of methods to further strengthen the security of current LLMs. [ABSTRACT FROM AUTHOR]

This paper honors Thomas J. Fararo by highlighting his foundational contributions to two chief theoretical methods – generativity and unification – noting the footsoldiers episode, surprise, and beauty along with other elements of his legacy that accelerate progress in generativity and unification, such as mathematical functions and probability distributions. Generativity and unification enable progress toward the goal of understanding more and more by less and less, generativity by linking theoretical elements to observables in testable propositions, unification by unifying elements from two or more theories. Though deductive strategies are classical in origin, generativity – both the word and its expanded meaning that covers not only deductive strategies but also the Toulmin-type nondeductive strategies and computer simulation strategies – was Fararo’s invention. U nification, too, was classical in origin, but Fararo expanded it from a purely theoretical operation to a spirit of unification with the potential to make peace between warring intellectual factions. Fararo’s guiding hand is discernible in both the substance and methods of wide swaths of theoretical work in sociology, and this paper illustrates that aspect of his legacy by discussing his contributions to the author’s early work on justice theory, including strategies of generativity later used also in status theory, and the more recent proposed unification of justice, status, and power. All of Fararo’s work, not only writing and teaching but also guiding others, exemplified, in Toulmin’s words: “the personal attitudes needed for effective work in science – adventurous skepticism and critical open-mindedness.” [ABSTRACT FROM AUTHOR]

We construct integral representations and asymptotic estimates for remainder terms arising in the summation of the Appell hypergeometric series and the related series , which are included in Horn's list of hypergeometric series of two variables. The obtained formulas can be used to develop algorithms for calculating with the help of analytic continuation formulas to the entire space . The results can find application in problems of mathematical physics and computational function theory, including in the construction of conformal mappings of complicated polygons based on the Schwarz–Christoffel integral. [ABSTRACT FROM AUTHOR]

As aircraft electrification advances, permanent magnet synchronous motors (PMSMs) require higher power density and efficiency, but optimisation is hindered by high computational costs and resource consumption. To address this, the paper proposes a multi‐objective optimisation method based on adaptive sampling radial basis function (ASRBF). The ASRBF algorithm adaptively adds sample points by estimating expected improvements at prediction points, enabling the surrogate model to rapidly approximate the global optimum while significantly reducing function evaluations. It integrates optimisation objectives and constraints using probabilistic improvement techniques, enhancing robustness and convergence speed by avoiding excessive exploration of invalid regions. Mathematical test functions validate ASRBF's excellent performance in handling complex objective domains. Applied to high‐speed PMSM with hollow conductors, it aims to minimise AC losses while maximising slot fill factor and heat dissipation, resulting in a 15% reduction in losses and an increase in conductor heat dissipation area and slot fill factor, at one‐thousandth of the cost of the full factorial optimisation method. The ASRBF algorithm efficiently constructs surrogate models for multi‐dimensional, multi‐objective, non‐linear, and constrained problems, providing a powerful tool for comprehensive performance optimisation of complex systems such as motors. [ABSTRACT FROM AUTHOR]

When excavating tunnels in urban areas with shallow overburden in poor rock mass, the deformations are very pronounced, which can result in serious potential risks to the safety, costs and time of tunnel construction. In the Kobilja Glava tunnel, which will be part of the project connecting Vogošća with Sarajevo and connecting the city center of Sarajevo with the A1 motorway on Corridor Vc, monitoring of displacements was conducted in a specific section of the left tunnel tube over a length of 80 m, in terms of various distances between the top heading excavation and the primary invert in poorer rock mass with a defined RMR ranging from 27 to 32. The results indicate that displacements can be effectively controlled by defining the optimal distance between the excavation phases of the top heading and the primary invert. A detailed analysis of the collected data yielded a mathematical function relating displacement to the distance between the excavation of the top heading and the primary invert, which can serve as a tool for quick and straightforward correlation of displacements during tunnel excavation, considering the geological conditions present in the Kobilja Glava tunnel. [ABSTRACT FROM AUTHOR]

This article discusses the role of gestures in enhancing inhibition, working memory, and cognitive flexibility as the three components of executive functions during the processing of mathematical concepts that are metaphorically described in terms of motion events. Gestures can contribute to the process of inhibition by highlighting the relevant information and keeping the irrelevant information out of focus of attention. Gestures contribute to working memory in two ways during mathematical processing. They increase activity in the motor areas of the brain. Therefore, they may facilitate the process of understanding those mathematical concepts that are described in terms of motion event, as the motor system could play a role in the grounding and the processing of these concepts. Also, gestures can function as an external working memory and keep the visual representation of some parts of information for a short period of time in order to manipulate that information in later stages of processing. Gestures enhance cognitive flexibility by allowing us to have a spatial representation of that concept or idea for a period of time. During this time, we can shift our perspective and process that concept or idea from a variety of perspectives. [ABSTRACT FROM AUTHOR]

The modified version of quasi-SMILES is studied. Unlike the previous ones, the new version allows building codes of experimental conditions in a user-friendly (easily interpreted) form. The quasi-SMILES can be a convenient basis for discussion between experimentalists and developers of models. The optimal descriptors for regression one-parameter models were calculated with the Monte Carlo method, using the vector of ideality of correlation. The vector of the ideality of correlation has two components: (i) the index of ideality of correlation (IIC) and (ii) the correlation intensity index (CII). Both the indices are components of the stochastic Monte Carlo process. The contribution of these indices is paradoxical: they improve the statistical quality of a model on the external validation set but to the detriment of the statistical quality of the model for the training set. Taking into account IIC and CII values for the Monte Carlo optimization gives an improvement of models of zeta potential of considered nanoparticles. The described approach is convenient for modelling the zeta potential of the considered nanoparticles. No less important is the universality of the use of quasi-SMILES as a means for studying the values of endpoints in the form of mathematical functions of not only the structures of the simulated objects (nanoparticles) but also the experimental conditions. [ABSTRACT FROM AUTHOR]

When there are some restrictions on the random variables of insurance risk model, it is impossible to calculate the exact value of ruin probabilities. For these cases, even finding a suitable approximation, is very important from a practical point of view. In the present paper, we consider the renewal insurance surplus model with light-tailed claim amount distributions and try to find some inequalities on the infinite time ruin probability depending on the amount of initial reserve using statistical and mathematical approaches if the assumption of net profit does not hold but there exist some other restrictions on the mathematical functions of random variables of model. The assertions depend on the amount of initial reserve, distribution of nonnegative claim occurrences times and successive claim amounts are obtained. Finally, to show the application and effectiveness of given theorems two examples are presented. Through these examples, the infinite time ruin probabilities are estimated using Monte Carlo simulation and give an intuitive way to understand the nature of ruin. [ABSTRACT FROM AUTHOR]

Growing items like chicken broilers play a critical role in consumption baskets; however, their real characteristics have been neglected in the research focusing on inventory models such as economic order quantity (EOQ). Mainstream research conducted in this field considers an approximation of the edible rate of chicken broilers in cost analysis. On the other hand, this subject was the objective of other research, and the function that represents the relationship between the weight and age of broilers was derived through extensive research. This study proposes an EOQ model that considers a realistic function for extracting the exact value of edible parts of broilers and the correct form of feeding function that is dependent on their age. In other words, this study not only addresses the challenge arising in the estimation of the edible part of broilers but also introduces another function to obtain the correct amount of feeding and nurturing cost of broilers. Solution methodology encompasses these mathematical functions and then provides a straightforward framework to find the optimal solution. An exact heuristic solution is obtained that considers the real factors, and then the approach is applied to case studies, and insights are derived to manage real situations for corporations. [ABSTRACT FROM AUTHOR]

This research work introduces a connection of adjoint Bernoulli's polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various functional spaces with the aid of the Korovkin theorem, Voronovskaja-type theorem, first order of modulus of continuity, second order of modulus of continuity, Peetre's K-functional, Lipschitz condition, etc. In the last section, we extend our research to a bivariate case of these sequences of operators, and their uniform rate of approximation and order of approximation are investigated in different functional spaces. Moreover, we construct a numerical example to demonstrate the applicability of our results. [ABSTRACT FROM AUTHOR]

Summary: This note offers a natural geometric proof for the length-curvature identity for a C2 function of two variables. [ABSTRACT FROM AUTHOR]

The Virtual Calculator project is a Python-based application that allows users to perform mathematical calculations through an intuitive graphical user interface (GUI). Designed to support basic operations such as addition, subtraction, multiplication, and division, the calculator offers a simple yet powerful tool for solving everyday mathematical problems. The application leverages Python's Tkinter library to create an easy-to-use interface, ensuring that users can interact with the tool effortlessly, regardless of their technical background. This project demonstrates the versatility of Python in developing practical applications. The backend logic, powered by Python's built-in mathematical functions, ensures accurate and efficient computations. With a focus on accessibility and ease of use, the Virtual Calculator provides a seamless experience for students, professionals, and anyone needing a reliable tool for quick calculations. The project also serves as an example of how Python can be utilized to build interactive software applications for real-world problems. [ABSTRACT FROM AUTHOR]

Copyright of Revista Foco (Interdisciplinary Studies Journal) is the property of Revista Foco and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Radial Basis Function Neural Network (RBFNN) is a type of artificial neural networks used for supervised learning. They rely on radial basis functions (RBFs), nonlinear mathematical functions employed to approximate complex nonlinear data. Determining the architecture of the network is challenging, impacting the achievement of optimal learning and generalization capacities. This paper presents a multi–objective model for optimizing and training RBFNN architecture. The model aims to fulfill three objectives: the first is the summation of distances between the input vector and the corresponding center for the neurons in the hidden layer. The second objective is the global error of the RBFNN, defined as the discrepancy between the calculated output and the desired output. The third objective is the complexity of the RBFNN, quantified by the number of neurons in the hidden layer. This innovative approach utilizes multiple objective simulated annealing to identify optimal parameters and hyperparameters for neural networks. The numerical results provide accuracy and reliability of the theoretical results discussed in this paper, as well as advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

We study for each fixed integer $g \ge 2$ , for all primes $\ell $ and p with $\ell \neq p$ , finite regular directed graphs associated with the set of equivalence classes of $\ell $ -marked principally polarized superspecial abelian varieties of dimension g in characteristic p , and show that the adjacency matrices have real eigenvalues with spectral gaps independent of p. This implies a rapid mixing property of natural random walks on the family of isogeny graphs beyond the elliptic curve case and suggests a potential construction of the Charles–Goren–Lauter-type cryptographic hash functions for abelian varieties. We give explicit lower bounds for the gaps in terms of the Kazhdan constant for the symplectic group when $g \ge 2$. As a byproduct, we also show that the finite regular directed graphs constructed by Jordan and Zaytman also has the same property. [ABSTRACT FROM AUTHOR]

This paper focuses on a comprehensive study of a four-axle vehicle, including dynamics analysis, equivalent modeling methods, and their comparison. Firstly, a linear two-degree lateral dynamic model is established, which has four drive axles and two steer axles. Secondly, the mathematical transfer function expressions for the yaw rate and the centroid sideslip angle were derived on the basis of the model. The steady-state parameters, such as yaw rate gain Gγss, centroid sideslip angle gain Gβss, stability factor Kn, equivalent axial distance ln, and equivalent centroid sideslip angle coefficient Kn' were obtained by using the transfer functions. Then, the steady-state and transient characteristics are roundly discussed, including steady-state parameters, system root trajectory, frequency domain, and time domain. Some recommendations for the four-axle vehicle's parameter design are also given. Finally, for a more simple and efficient analysis of response characteristics of four-axle vehicles and even n (n > 4) axle vehicles, the equivalent model is developed for the four-axle vehicle, and comprehensive analyses are presented with four equalization methods, which are based on the inner heart of the approximation triangle, the outer heart of the approximation triangle, the center of gravity of the approximation triangle and the compensation point. Following a thorough analysis of the four, it is determined that the inner approximation triangle solution approach is most suited for four-axle vehicles. [ABSTRACT FROM AUTHOR]

River infiltration is important to groundwater recharge. The vertical infiltration volume of rivers is an important index for studying the mutual recharge of surface water and groundwater. In this study, the factors influencing the vertical infiltration of heterogeneous sediments were identified, and a vertical infiltration model of heterogeneous sediments was constructed via mathematical functions and machine learning. This study also applied a calculation method to the calculation of tributaries in the upper reaches of the Wenyu River. The effective grain size d10 and the inhomogeneity coefficient Cu are the main controlling factors of the infiltration coefficient, and a genetic algorithm was introduced to fit a functional formula for the vertical infiltration volume based on the main controlling factors. It was found that the gradient boosting decision tree (GDBT) vertical infiltration model with the Lad function as the loss function was more effective than the back propagation neural network (BP) vertical infiltration model created with the Adam optimiser and ReLU activation function. The results of this study provide technical support for the quantitative calculation of natural sediment infiltration coefficients and principal support for the formulation of relevant standards for river ecological safety and management, which are of great theoretical significance and far‐reaching application value. [ABSTRACT FROM AUTHOR]

The use of spherical modes offers an efficient solution for storing embedded element patterns with significant angular structure for large scale arrays, such as the Square Kilometer Array (SKA)‐Low radio telescope. These patterns are required for calibration of the numerous stations comprising the telescope, each containing several hundred elements, and operating over a 7:1 bandwidth. However, implementation is significantly complicated by the many differences in the notation used in the literature for the Legendre special functions. The differing phasor conventions used in electrical engineering and physics further complicate this. This paper synthesizes much of the existing literature on this topic, paying special attention to these issues. Mathematical implementation issues are also addressed. A number of suitable tests using canonical dipole radiators to verify correct implementation are outlined. The paper concludes with tests on an individual SKALA4 antenna and a full‐scale SKA‐Low prototype station comprising 256 of these antennas. The storage saving afforded is some three orders of magnitude; this is very significant for a full SKA‐Low station. Supporting material summarizes differing formulations and conventions encountered in the literature. Plain Language Summary: The Square Kilometer Array Observatory aims to significantly advance our understanding of the Universe and the laws of fundamental physics by providing two telescopes of unprecedented capability, located in South Africa and Western Australia (WA). The "low" frequency telescope (in WA), covering radio frequencies from 50 to 350 MHz, comprises a large number of stations, which are groups of antennas. These antennas interact strongly with each other within the station; this interaction is captured via a set of elemental radiation patterns which describe the sensitivity of each antenna as a function of angle on the sky. These patterns are pre‐calculated and used for calibrating the station, which is essential for optimal performance. Storing these patterns by finely sampling them in angle results in very large data sets. Using a special mathematical function known as an associated Legendre function, which captures angular variation over a sphere very efficiently, it is possible to greatly reduce the size of these sets — typically by a factor of around one thousand. However, there are a number of different conventions in use for these functions which makes this difficult to implement. This paper provides a consistent development of the method, supported by a software implementation in MATLAB. Key Points: Embedded element patterns for large arrays can be efficiently stored using spherical modesReconstructing the fields from the stored modes is challenging due to many differences in the notation used in the literatureThis work provides a consistent development of the method, supported by a software implementation in MATLAB [ABSTRACT FROM AUTHOR]

A soft set functions as a mathematical instrument crafted to handle uncertainties. Semigraph, a broader form of graph distinct from hypergraph, saw the integration of soft set principles to give rise to soft semigraph. Utilizing parameterization, soft semigraph delineates various representations of a semigraph’s relationships. The pivotal role of graph isomorphism lies in its ability to discern patterns across diverse domains such as image processing, computer systems, social network analysis, chemical bonding exploration, and protein structure analysis. Different types of isomorphisms are present within soft semigraphs, including s-isomorphism, sev-isomorphism, se-isomorphism, and sa-isomorphism. This paper focuses on elucidating certain characteristics associated with these isomorphisms. Additionally, we investigate the complement of a soft semigraph. [ABSTRACT FROM AUTHOR]

The known nonlinear kinetic equations, in particular, the wave kinetic equation and the quantum Nordheim–Uehling–Uhlenbeck equations are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this goal we introduce the general Boltzmann-type kinetic equation that depends on a function of four real variables F(x, y; v, w). The function F is assumed to satisfy certain simple relations. The main properties of this kinetic equation are studied. It is shown that the above mentioned specific kinetic equations correspond to different polynomial forms of the function F. Then the problem of discretization of the general Boltzmann-type kinetic equation is considered on the basis of ideas similar to those used for construction of discrete velocity models of the Boltzmann equation. The main attention is paid to discrete models of the wave kinetic equation. It is shown that such models have a monotone functional similarly to the Boltzmann H-function. The theorem of existence, uniqueness and convergence to equilibrium of solutions to the Cauchy problem with any positive initial conditions is formulated and discussed. The differences in long time behaviour between solutions of the wave kinetic equation and solutions of its discrete models are also briefly discussed. [ABSTRACT FROM AUTHOR]

This work presents a general framework that innovates and explores different mathematical aspects associated with special functions by utilizing the mathematical physics-based idea of monomiality. This study presents a unique family of multivariable Hermite polynomials that are closely related to Frobenius–Genocchi polynomials of Apostol type. The study’s deductions address the differential equation, generating expression, operational formalism, and other characteristics that define these polynomials. The affirmation of the controlling monomiality principle further confirms their mathematical foundations. In addition, the work proves recurrence relations, fractional operators, summation formulae, series representations, operational and symmetric identities, and so on, all of which contribute to our knowledge of these complex polynomials. [ABSTRACT FROM AUTHOR]

The development of new algorithms can aid researchers and professionals in resolving problems that were once unsolvable or discovering superior solutions to problems that were already settled. By recognizing the importance of continuous research on creating novel algorithms, this paper introduced a hybrid metaheuristic algorithm-h-PSOGNDO, which is a combination of Particle Swarm Optimization (PSO) and Generalized Normal Distribution Optimization (GNDO). The proposed algorithm utilizes the Particle Swarm Optimization's strategy for exploitation and the Generalized Normal Distribution Optimization's global search strategy for exploration. Through this combination, h-PSOGNDO is believed to be an effective algorithm that can promote the advantages of its parents' algorithms. Different assessment methods are used to assess the proposed novel algorithm. First, the h-PSOGNDO is set to conduct experiments on two sets of mathematical functions, including twenty-eight IEEE CEC2017 and ten IEEE CEC2019 benchmark test functions, respectively. Then, the h-PSOGNDO algorithm is applied to a case study on the prediction of antimicrobial peptides' toxicity to evaluate its performance on real-life problems. The statistical findings collected from both the test function sets and the case study show that the h-PSOGNDO algorithm works effectively, proving its astonishing ability to yield highly competitive outcomes for complex problems. [ABSTRACT FROM AUTHOR]

Mathematical education requires innovative didactic strategies to enhance the understanding and application of mathematical concepts, as traditional teaching methods often lack relevance. This methodology aims to develop a problem-solving scientific approach called design thinking as a strategy for learning mathematics functions. The study was applied to a sample of 138 students of biochemical, biological, and industrial engineering careers attending the first academic cycle at the Faculty of Natural and Exact Sciences of the Particular Technical University of Loja-Ecuador. The methodology uses a quasi-experimental design with a convenience sampling method. All participants were divided into a control group (C, D, K) and an experimental group (P, Q, R). Knowledge, skills, perceptions, and engagement were measured through pretest, posttest, workshop, rubric, project, and survey instruments. The pretest results indicate that both groups had similar knowledge of mathematical functions (pretest mean experimental group: 1.42/2 and mean control group: 1.55/2). Moreover, after applying design thinking strategy to the experimental group, variables questionnaire , project , and workshop show statistical differences (p < 0.001) between groups related to the traditional learning strategy, increasing the experimental group's score in the project (posttest mean experimental group: 1.62/2 points, and mean control group: 1.65/2). The survey opinion indicates that 53.5% of the experimental group highlighted the project's development as positively impacting their academic training. In conclusion, problem-solving design thinking using scientific projects as a mathematical function learning strategy contributes to improving the comprehension of polynomial functions and developing mathematical competencies, abilities, and skills to generate tangible solutions for real problems. [ABSTRACT FROM AUTHOR]

In a mathematical program with generalized complementarity constraints (MPGCC), complementarity relation is imposed between each pair of variable blocks. MPGCC includes the traditional mathematical program with complementarity constraints (MPCC) as a special case. On account of the disjunctive feasible region, MPCC and MPGCC are generally difficult to handle. The ℓ1 penalty method, often adopted in computation, opens a way of circumventing the difficulty. Yet it remains unclear about the exactness of the ℓ1 penalty function, namely, whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original one. In this paper, we consider a class of MPGCCs that are of multi-affine objective functions. This problem class finds applications in various fields, e.g., the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network transportation. We first provide an instance from this class, the exactness of whose ℓ1 penalty function cannot be derived by existing tools. We then establish the exactness results under rather mild conditions. Our results cover those existing ones for MPCC and apply to multi-block contexts. [ABSTRACT FROM AUTHOR]

As technology rapidly advances and internet reliance grows for daily activities, the demand for robust and efficient cryptographic protocols is undeniable. Cryptography, the art of secret writing, uses symmetric mathematical functions to secure data in transit or at rest. Stream ciphers, unlike block ciphers, encrypt data sequentially, eliminating the need for padding with extra bits to complete a block. Rivest Cipher 4 (RC‐4) has been one of the most widely used stream ciphers. However, vulnerabilities exploited by attackers in 2014 led to its widespread replacement. In this paper, we introduce a modified version of RC‐4 designed to address and mitigate the security threats of traditional RC‐4. By incorporating negative numbers into the key generation schedule, our preliminary analysis shows promising results. This adaptation not only enhances RC‐4's security features but also revitalizes its applicability in modern cryptographic scenarios, potentially restoring its viability as a secure cryptographic tool. [ABSTRACT FROM AUTHOR]

Purpose: The application of 3D printing technology in drug delivery is often limited by the challenges of achieving precise control over drug release profiles. The goal of this study was to apply surface equations to construct 3D printed tablet models, adjust the functional parameters to obtain multiple tablet models and to correlate the model parameters with the in vitro drug release behavior. Methods: This study reports the development of 3D-printed tablets using surface geometries controlled by mathematical functions to modulate drug release. Utilizing fused deposition modeling (FDM) coupled with hot-melt extrusion (HME) technology, personalized drug delivery systems were produced using thermoplastic polymers. Different tablet shapes (T1-T5) were produced by varying the depth of the parabolic surface (b = 4, 2, 0, -2, -4 mm) to assess the impact of surface curvature on drug dissolution. Results: The T5 formulation, with the greatest surface curvature, demonstrated the fastest drug release, achieving complete release within 4 h. In contrast, T1 and T2 tablets exhibited a slower release over approximately 6 h. The correlation between surface area and drug release rate was confirmed, supporting the predictions of the Noyes-Whitney equation. Differential Scanning Calorimetry (DSC) and Scanning Electron Microscope (SEM) analyses verified the uniform dispersion of acetaminophen and the consistency of the internal structures, respectively. Conclusions: The precise control of tablet surface geometry effectively tailored drug release profiles, enhancing patient compliance and treatment efficacy. This novel approach offers significant advancements in personalized medicine by providing a highly reproducible and adaptable platform for optimizing drug delivery. [ABSTRACT FROM AUTHOR]

First-principles calculations were performed to investigate the electronic and optical properties of small clusters of CH3NH3SnBr3. The reactive sites of the CH3NH3SnBr3 clusters were identified. The minimum values of electrostatic potential decreases monotonically with increasing cluster size from monomer to tetramer. The density of states (DOS) spectrum was obtained by convoluting molecular orbitals (MOs) with mathematical functions. The LUMO consists of Sn(5p), Br(4s), and Br(4p) orbitals, while the HOMO consists of Sn(5s), Sn(5p), and Br(4p) orbitals. The HOMO was observed to be more delocalized than the LUMO, likely due to the repulsion between the lone pair and the bonding pair. As "n" increases from 1 to 4, the HOMO–LUMO gap decreases. The HOMO–LUMO gap, optical gap, and wavelength corresponding to the absorption band maximum for the (CH3NH3SnBr3)n cluster (n → ∞) were modeled and found to be 3.622 eV, 3.091 eV, and 346.03 nm (3.5830 eV), respectively. The HOMO–LUMO gap of CH3NH3SnBr3 obtained from DOS was approximated to be 2.19 eV. [ABSTRACT FROM AUTHOR]

Functions are an essential concept in mathematics. The studies that have examined functions in advanced contexts have primarily focused on students' reasoning about specific types of functions (such as binary operations and isomorphisms) but not on the core characteristics of well-definedness and everywhere-definedness. Here, we report on a study in which we conducted task-based clinical interviews to gain insight into students' techniques for addressing "is the given relation a function?" tasks. We found that the techniques students employed necessarily extended far beyond those reported in the literature (such as the vertical line test) and relied on the previously undocumented notions of sameness, convention, and ambiguity (for well-defined) and notions of containment, existence, and set operations (for everywhere-defined). These techniques coordinated the domain, codomain, and rule, which previous research has highlighted the importance of but stopped short of directly investigating. Two contributions of this work include identifying successful techniques (as the landscape of functions literature predominantly focuses on challenges and difficulties) and identifying techniques for everywhere-definedness (which had not previously received any direct attention in the literature). [ABSTRACT FROM AUTHOR]

The document is a special issue on nonlinear analysis and its applications in symmetry, featuring ten papers by experts in the field. Topics covered include solving convex constrained equations, unconstrained optimization methods based on symmetry, existence of positive solutions for perturbations of eigenvalue problems, and stability analysis of time-delay differential systems. The papers explore various mathematical frameworks and offer valuable insights into complex mathematical problems. [Extracted from the article]

Metaheuristic algorithms are stochastic-based search techniques widely used for solving different types of optimization problems. These methods mostly adjust their search behavior using pre-defined search pattern(s) regardless of the current problem specifications. Therefore, integrating them with logical auxiliary modules can significantly enhance their search efficiency by enabling them to dynamically adapt their search behavior. The present study introduces a novel decision-making approach that employs interval type-2 fuzzy logic to balance the search behavior during optimization process. The proposed approach, designed as a stand-alone module with the flexibility to be integrated into various algorithms, is incorporated into the Interactive Search Algorithm. The developed reinforced technique is named Type-2 Fuzzy Interactive Search Algorithm. Performance of the proposed method is tested on different unconstrained mathematical functions and constrained structural and mechanical optimization problems. The attained results are compared with standard ISA method and seven other metaheuristic techniques through a suite of numerical and statistical evaluations. Drawing from the obtained results, the integration of the type-2 fuzzy decision module significantly enhances the algorithm's search capability. This improvement is evident in terms of stability, accuracy, and computational cost. It is worth noting that the employed comparative performance index for the proposed method indicates improvements of 3.38, 13.09, 16.61, and 27.23 percent compared to the best solution found by the selected methods for engineering problems. [ABSTRACT FROM AUTHOR]

Wireless sensor networks are composed of many nodes distributed in a region of interest to monitor different environments and physical variables. In many cases, access to nodes is not easy or feasible. As such, the system lifetime is a primary design parameter to consider in the design of these networks. In this regard, for some applications, it is preferable to extend the system lifetime by actively reducing the number of packet transmissions and, thus, the number of reports. The system administrator can be aware of such reporting reduction to distinguish this final phase from a malfunction of the system or even an attack. Given this, we explore different mathematical functions that drastically reduce the number of packet transmissions when the residual energy in the system is low but still allow for an adequate number of transmissions. Indeed, in previous works, where the negative exponential distribution is used, the system reaches the point of zero transmissions extremely fast. Hence, we propose different dampening functions with different decreasing rates that present oscillations to allow for packet transmissions even at the end of the system lifetime. We compare the system performance under these mathematical functions, which, to the best of our knowledge, have never been used before, to find the most adequate transmission scheme for packet transmissions and system lifetime. We develop an analytical model based on a discrete-time Markov chain to show that a moderately decreasing function provides the best results. We also develop a discrete event simulator to validate the analytical results. [ABSTRACT FROM AUTHOR]