The prevalence of differential equations as a mathematical technique has refined the fields of control theory and constrained optimization due to the newfound ability to accurately model chaotic, unbalanced systems. However, in recent research, systems are increasingly more nonlinear and difficult to model using Differential Equations only. Thus, a newer technique is to use policy iteration and Reinforcement Learning, techniques that center around an action and reward sequence for a controller. Reinforcement Learning (RL) can be applied to control theory problems since a system can robustly apply RL in a dynamic environment such as the cartpole system (an inverted pendulum). This solution successfully avoids use of PID or other dynamics optimization systems, in favor of a more robust, reward-based control mechanism. This paper applies RL and Q-Learning to the classic cartpole problem, while also discussing the mathematical background and differential equations which are used to model the aforementioned system.

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

This work focuses on expressing the TSP with Time Windows (TSPTW for short) as a quadratic unconstrained binary optimization (QUBO) problem. The time windows impose time constraints that a feasible solution must satisfy. These take the form of inequality constraints, which are known to be particularly difficult to articulate within the QUBO framework. This is, we believe, the first time this major obstacle is overcome and the TSPTW is cast in the QUBO formulation. We have every reason to anticipate that this development will lead to the actual execution of small scale TSPTW instances on the D-Wave platform.

Due to a simple crane limited capacity; there is an urgent need to use high capacity cranes such as tower cranes. However, with regard to their high expense, we have to take into consideration selecting what type of cranes to be utilized which has been discussed by many researchers. In this research, a proposed technique was created to select the suitable type of crane and best place for crane erection, in addition to minimum radius for requested crane in order to minimize cost. To fulfill that target, a computer program is designed to numerate these problems, demonstrating an example explaining how to apply program and the result donated best place.

We applied a generalized SEIR epidemiological model to the recent SARS-CoV-2 outbreak in the world, with a focus on Italy and its Lombardia, Piemonte, and Veneto regions. We focus on the application of a stochastic approach in fitting the model numerous parameters using a Particle Swarm Optimization (PSO) solver, to improve the reliability of predictions in the medium term (30 days). We analyze the official data and the predicted evolution of the epidemic in the Italian regions, and we compare the results with data and predictions of Spain and South Korea. We link the model equations to the changes in people’s mobility, with reference to Google’s COVID-19 Community Mobility Reports. We discuss the effectiveness of policies taken by different regions and countries and how they have an impact on past and future infection scenarios.

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocation approximation based on trigonometric cubic B-splines for spatial discretization is followed by the linearization of the nonlinear term. The efficiency and accuracy of the present method are validated by measuring the error between the numerical and analytical solutions when exist. The conservation laws representing momentum and energy are also computed for all problems.

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. We find two classes of representation, the normal representation and exceptional one. The normal representation is a large class of representation which can only be expanded into $4m+1$ dimension, but the exceptional representation can be expanded as generators of the next period. In the cases $p+q=4m$, the representation is unique in equivalent sense. These results are helpful for both theoretical analysis and practical calculation. The generators of Clifford algebra are the faithful basis of $p+q$ dimensional Minkowski space-time or Riemann space, and Clifford algebra converts the complicated relations in geometry into simple and concise algebraic operations, so the Riemann geometry expressed in Clifford algebra will be much simple and clear.

In this paper we use the Mellin convolution theorem, which is related to Perron's formula. Also we introduce new explicit formulae for arithmetic function which generalize the explicit formulae of Weil for other arithmetic functions different from the Von-Mangoldt function.

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.

Topology optimization is a pioneering design method that can provide various candidates with high mechanical properties. However, the high-resolution for the optimum structures is highly desired, normally in turn leading to computationally intractable puzzle, especially for the famous Solid Isotropic Material with Penalization (SIMP) method. In this paper, an efficient and high-resolution topology optimization method is proposed based on the Super-Resolution Convolutional Neural Network (SRCNN) technique in the framework of SIMP. The SRCNN includes four processes, i.e. refining, path extraction & representation, non-linear mapping, and reconstruction. The high computational efficiency is achieved by a pooling strategy, which can balance the number of finite element analysis (FEA) and the output mesh in optimization process. To further reduce the high computational cost of 3D topology optimization problems, a combined treatment method using 2D SRCNN is built as another speeding-up strategy. A number of typical examples justify that the high-resolution topology optimization method adopting SRCNN has excellent applicability and high efficiency for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

Integration of multi-view datasets which are comprised of heterogeneous sources or different representations is challenging to understand the subtle and complex relationship in data. Such data integration methods attempt to combine efficiently the complementary information of multiple data types to construct a comprehensive view of underlying data. Nonnegative matrix factorization (NMF), an approach that can be used for signal compression and noise reduction, has aroused widespread attention in the last two decades. The Kullback–Leibler divergence (or relative entropy) information distance can be used to measure the loss function of NMF. In this article, we propose a fast and robust framework (RSNMF) based on symmetric nonnegative matrix factorization (SNMF) and similarity network fusion (SNF) for clustering human microbiome data including functional, metabolic and phylogenetic profiles. Many existing methods typically utilize all the information provided by each view to create a consensus representation, which often suffers a lot from noise in data and cannot provide a precise representation of the latent data structures. In contrast, RSNMF combines the strength of SNMF and the advantage of SNF to form a robust clustering indicator matrix thus can reduce the noise influence. We conduct experiments on one synthetic and two real dataset (microbiome data, text data) and the results show that the proposed RSNMF has better performance over the baseline and the state-of-art methods, which demonstrates the potential application of RSNMF for microbiome data analysis.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

In this paper we report a new development on the numerical model for aluminum-steam combustion. This model is based on diffusion flame of continuum regime and the thermal equilibrium between the particle and the flow field, which can be used to calculate the aluminum particle combustion model for two phase calculation conditions. The model prediction is in good agreement with the experimental data. A new type of vortex combustor was proposed for the combustion of aluminum and steam, and the mathematical model of the two phase reacting flow with in this combustor was established. The turbulence effects are modeled using the Reynolds Stress Model (RSM) with Linear Pressure-Strain approach, and the Eddy-Dissipation model is used to simulate the gas phase combustion. Aluminum particles are injected into the vortex combustor and form a swirling flow around the chamber and their trajectories are traced using the Discrete Phase Model (DPM). The simulation results show that the vortex combustor can achieve high efficient combustion of aluminum and steam. The influencing factors, such as the eccentric distance of the inlet of aluminum particles, particle size and steam inlet diameter, etc., are studied. The work described in this paper represents an attempt to the design of a vortex combustor in order to increase aluminum combustion efficiency.

This work deals with a numerical implementation of a fifth order CENTRAL WENO-TVD (\textit{Weighted Essentially Non-Oscillatory-Total Variation Dimimishing}) of Haschem (2006) scheme applied to the convective terms of some hyperbolic conservation laws problems, in a volume finite framework. The WENO-TVD scheme is used to solve the 1D advection and Burgers equations. For this case is implemented two different numerical fluxes: The Lax-Friedrichs and TVD fluxes. In the TVD fluxes the schemes applied are in flux-limiter form. The schemes implemented for this flux are: Van Albada-1 (van Albada et al.,1982), van Albada-2 (Kermani et al., 2003), van Leer (Hassanzadeh, 2009) and MINMOD (Hirsch, 2007). The WENO type schemes are characterized for their high order approximation, and do not produce spurious oscilations near discontinuities, shocks and higher gradients. A third order Runge-Kutta TVD for the temporal variable is used. Qualitative and quantitative comparison are presented. The numerical solutions are computed with an in-house computer code developed in MATLAB software. In future works, it will develope a paralelization of computer code for solving systems of conservation laws, e.g. Euler equations of gas dynamics.

In this short paper we study some properties of the lines associated with van Aubel’s theorem in the special case when squares are replaced with equilateral triangles constructed on the sides of an arbitrary quadrilateral.

This paper presents an approach to the Euler-Bernoulli beam theory (EBBT) using the finite difference method (FDM). The EBBT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally, the finite difference approximations are derived based on fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection curve; the FOPH is made for the fourth and third derivative of the deflection curve while the SOPH is made for its second and first derivative. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, the FOPH was made for all of the derivatives of the deflection curve, and additional points were introduced at the beam’s ends and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. First-order analysis, second-order analysis, and vibration analysis of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis). Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid. Further research will be needed to investigate polynomial refinements (higher-order polynomials such as fifth-order, sixth-order…) of the deflection curve; the polynomial refinements aimed to increase the accuracy, whereby non-centered finite difference approximations at beam’s ends and positions of discontinuity would be used.

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

The systematic sampling is used as a method to get the quantitative results from the tissues and the radiological images. Systematic sampling on real line (R) is a very attractive method within which the biomedical imaging is consulted by the practitioners. For the systematic sampling on R, the measurement function (MF) is occurred by slicing the three-dimensional object equidistant systematically. The currently used covariogram model in variance approximation proposed by [28,29] is tested for the different measurement functions in a class to see the performance on the variance estimation of systematically sampled R. This study is an extension of [17], and an exact calculation method is proposed to calculate the constant λ(q,N) of confidence interval in the systematic sampling. The exact value of constant λ(q,N) is examined for the different measurement functions as well. As a result, it is observed from the simulation that the proposed MF should be used to check the performances of the variance approximation and the constant λ(q,N). Synthetic data can support the results of real data.

In this paper, we consider the development of algorithms for the solution of first order initial value problems whose solution exhibits exponential behaviour. Method of interpolation and collocation of basis function to give system of nonlinear equations which is solved for the unknown parameters to give a continuous scheme. The discrete methods recovered from the continuous scheme are implemented in block form. The stability properties of the method is verified and numerical experiments show that our method is efficient in handling these problems

It is well known that the primes and prime powers have a deep relationship with the nontrivial zeros of Riemann’s zeta function. This is a reciprocal relationship. The zeros and the primes are encoded in each other and are reciprocally recoverable. Riemann’s zeta is an extended or continued version of Euler’s zeta function which in turn equates with Euler’s product formula over the primes. This paper shows that the zeros of the converging Dirichlet or Catalan beta function, which requires no continuation to be valid in the critical strip, can be easily determined. The imaginary parts of these zeros have a deep and reciprocal relationship with the odd primes and odd prime powers. This relationship separates the odd primes into those having either 1 or 3 as a remainder after division by 4. The vector pathway of the beta function is such that the real part of its zeros has to be a half.

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from improper selection of the parameter is resolved efficiently. Based on the framework of the VRP-GMRES(m) algorithm and the relevant properties of generalized inverse matrix, the projection of the error vector r_m+1 on r_m is deduced. The result proves that the proposed algorithm is not only rapidly convergent but also highly accurate. Numerical experiments further show that the new algorithm can significantly improve the computational efficiency and accuracy. Its superiorities will be much more remarkable when it is used to solve larger scale problems. Therefore, it has extensive prospects in the FM-BEM field and other scientific and engineering computing.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S₅³ (∆_mn⁽²⁾). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

This paper investigates existing mathematical morphology based techniques applied for performing malaria parasites detection and identification in both Giemsa and Leishman stained blood smears images. Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis; this kind of visual inspection is subjective, errorprone and time consuming. In order to cope with such issues, computer-aided methods have been increasingly evolved for abnormal erythrocyte and/or parasites detection, segmentation and semi/fully automated classification. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection.

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here we discuss the original motivation of the development of long memory and Mandelbrot's influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

Euler’s product formula over the primes and Euler’s zeta function equate to enshrine the Fundamental Theorem of Arithmetic that every integer > 1 is the product of a unique set of primes. The product formula has no zero, and with a domain ≤1 Euler’s zeta diverges. Dirichlet’s eta function η(s), negates alternate terms of zeta, permitting convergence when s∈C and Re(s) < 1, and its non-trivial zeros {ρ}, have a deep relationship with the distribution of the primes. The Riemann Hypothesis is that all the non-trivial zeros have Re(ρ) = 1/2. This work examines the symmetries in a partial Euler’s zeta series with a complex domain equating it to the difference between two finite vector series whose matched terms have mirror-image arguments, but whose magnitudes differ when Re(s) ≠ 1/2. Analytical continuation generates a modified eta series η_l(s), in which every l^th term is multiplied by (1-l). If the integer l is appropriately determined by the Im(s), similar paired finite vector series have a difference that closely follows η_l (s) and their terminal vectors intersect in a unique way permitting zeros only when Re(s) = 1/2. Furthermore, those vectors tracking the derivatives of the series, have a special relationship permitting zeros of the differential only when Re(s) > 1/2.

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

Linear mixed models are frequently used for analysing heterogeneous data in a broad range of applications. The restricted maximum likelihood method is often preferred to estimate co-variance parameters in such models due to its unbiased estimation of the underlying variance parameters. The restricted log-likelihood function involves log determinants of a complicated co-variance matrix. An efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the first derivatives and the second derivatives of the restricted log-likelihood function, i.e., the observed information. Standard approaches to compute the observed information and its expectation, the Fisher information, is computationally prohibitive for linear mixed models with thousands random and fixed effects. Customized algorithms are of highly demand to keep mixed models analysis scalable for increasing high-throughput heterogeneous data sets. In this paper, we explore how to leverage an averaged information splitting technique and dedicate matrix transform to significantly reduce computations and to accelerate computing. Together with a fill-in reducing multi-frontal sparse direct solver, the averaged information splitting approach improves the performance of the computation process.

This paper presents an extension for principles of Differential Geometry on Surfaces (re-hashed through the budding field of CMS, the Calculus of Moving Surfaces). It analyzes mostly 2D Hypersurfaces with Riemannian Geometry and proposes the construction of a 3D Static Frame combining the Surface Basis Vectors with the Orthogonal Normal Field as a 3D Orthogonal Vector Frame. The paper introduces conventions for manipulating Tensors defined using this 3D Orthogonal Vector Frame as well as Curvature Connections associated with this Vector Frame. It then finally introduces Symbols and Tensors to describe Inner Products and Variance within the 3D Vector Frame and then extends all the above concepts to a surface which is Dynamic utilizing principles from CMS. This formulation has potential to extend identities and concepts from CMS and from Differential Geometry in a compact Tensorial Framework, which agrees with the new Framework proposed by CMS.

In Functional Analysis as well as Topology, we frequently encounter sets, say $X$, that contain elements close to each other. These sets display a defining "finite-ness" property: for all open cover $\mathcal{O}$ of $X$, there exists a finite subcollection $\mathcal{U}\subseteq\mathcal{O}$ such that $\mathcal{U}$ covers $X$. Such spaces $X$ are called $\textbf{compact}$, and the above "finite-ness" property afford us great convenience, because we can always investigate $X$ by investigating its finite open cover $\mathcal{U}$Arzela-

This paper predict and effectively control the temperature distribution of the steady-state and transient states of anisotropic four-layer composite materials online, knowing the density, specific heat, heat conductivity and thickness of the composite materials. Based on the transfer function, a mathematical model was established to study the dynamic characteristics of heat transfer of the composite materials. First of all, the Fourier heat transfer law was used to establish a one-dimensional Fourier heat conduction differential equation for each composite layer, and the Laplace transformation was carried out to obtain the system function. Then the approximate second-order transfer function of the system was obtained by Taylor expansion, and the Laplace inverse transformation was carried out to obtain the transfer function of the whole system in the time domain. Finally, the accuracy of the simplified analytical solutions of the first, second and third order approximate transfer functions was compared with computer simulation. The results showed that the second order approximate transfer functions can describe the dynamic process of heat transfer better than others. The research on the dynamic characteristics of heat transfer in the composite layer and the dynamic model of heat transfer in composite layer proposed in this paper have a reference value for practical engineering application. It can effectively predict the temperature distribution of composite layer material and reduce the cost of experimental measurement of heat transfer performance of materials.

Most of existing fuzzy forecasting models partition historical training time series into fuzzy time series and build fuzzy-trend logical relationship groups to generate forecasting rules. The determination process of intervals is complex and uncertainty. In this paper, we present a novel fuzzy forecasting model based on high-order fuzzy-fluctuation trends and the fuzzy-fluctuation logical relationships of the training time series. Firstly, we compare each data with the data of its previous day in historical training time series to generate a new fluctuation trend time series(FTTS). Then, fuzzify the FTTS into fuzzy-fluctuation time series(FFTS) according to the up, equal or down range and orientation of the fluctuations. Since the relationship between historical FFTS and the fluctuation trend of future is nonlinear, Particle Swarm Optimization (PSO) algorithm is employed to estimate the required parameters. Finally, use the acquired parameters to forecast the future fluctuations. In order to compare the performance of the proposed model with that of the other models, we apply the proposed method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets. The experimental results and the comparison results show that the proposed method can be successfully applied in stock market forecasting or such kinds of time series. We also apply the proposed method to forecast Shanghai Stock Exchange Composite Index (SHSECI) to verify its effectiveness and universality.

This paper considers a two-way relay network, where two source nodes exchange messages through several relays in the presence of an eavesdropper, and the channel state information (CSI) of the eavesdropper is imperfectly known. The amplify-and-forward relay protocol is used and the relay beamforming weights are designed. The model is built up to minimize the total relay transmit power while guaranteeing the quality of service at users and preventing the eavesdropper from decoding the signals. Due to the imperfect CSI, a semi-infinite programming problem is obtained. An algorithm is proposed to solve the problem, and the iterative points are updated through the linesearch technique, where the feasibility are preserved during iterations. The optimality property is analyzed. The obtained subproblems are quadratic constrained quadratic programming problems, either with less than $4$ constraints or with only one variable, which are solved optimally. Simulation results demonstrate the importance of the proposed model, and imply that the proposed algorithm is efficient and converges very fast, where more than 85% of the problems are solved optimally.

We present a first formal analysis of specific and complete local integration. Complete local integration was previously proposed as a criterion for detecting entities or wholes in distributed dynamical systems. Such entities in turn were conceived to form the basis of a theory of emergence of agents within dynamical systems. Here, we give a more thorough account of the underlying formal measures. The main contribution is the disintegration theorem which reveals a special role of completely locally integrated patterns (what we call ι-entities) within the trajectories they occur in. Apart from proving this theorem we introduce the disintegration hierarchy and its refinement-free version as a way to structure the patterns in a trajectory. Furthermore we construct the least upper bound and provide a candidate for the greatest lower bound of specific local integration. Finally, we calculate the i-entities in small example systems as a first sanity check and find that ι-entities largely fulfil simple expectations.

In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.

In nonlinear self-consistent system, Lorenz system (Lorenz equations) is a classic case with chaos solutions which are sensitively dependent on the initial conditions. As it is difficult to get the analytical solution, the numerical methods and qualitative analytical methods are widely used in many studies. In these papers, Runge-Kutta method is the one most often used to solve these differential equations. However, this method is still a method based on explicit time scheme, which would be the main reason for the chaotic solutions to Lorenz system. In this work, numerical experiments based on implicit time scheme and explicit scheme are setup for comparison, the results show that: in implicit time scheme, the numerical solutions (counterexamples) are without chaos; for an original volume, the volume shrinks exponentially fast to 0 in common.

In this paper, we introduce a new generalization of the Hermite polynomials via (p, q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also de…ne a (p, q)-analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p, q)-hyperbolic representations of the (p, q)-Bernstein polynomials. In addition, we obtain a correlation between (p, q)-Hermite polynomials and (p, q)-Bernstein polynomials.

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets appear in the current literature. In the present paper we propose the score, accuracy functions for neutrosophic cubic sets and prove their basic properties. We firstly develop TODIM method to solve multi attribute group decision making in neutrosophic cubic set environment, which we call NC-TODIM. Also, we solve a MAGDM problem using the proposed NC-TODIM method to show the applicability and effectiveness of the developed method. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of attenuation factor of losses for multi-attribute group decision making problem.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

This paper presents a multi-swarm PSO algorithm for the Quadratic Assignment Problem (QAP) implemented on the OpenCL platform. Our work was motivated by results of time efficiency tests performed for single-swarm algorithm implementation that showed clearly that the benefits of a parallel execution platform can be fully exploited provided the processed population is large. The described algorithm can be executed in two modes: with independent swarms or with migration. We discuss the algorithm construction as well as we report results of tests performed on several problem instances from the QAPLIB library. During the experiments the algorithm was configured to process large populations. This allowed us to collect statistical data related to values of goal function reached by individual particles. We use them to demonstrate on two test cases that although single particles seem to behave chaotically during the optimization process, when the whole population is analyzed, the probability that a particle will select a near-optimal solution grows.

Complex and real valued exact solutions to some reaction-diffusion equations are suggested by using homogeneous balance and Sine-Gordon equation expansion method. The predicted solution of finite series of some hyperbolic functions are determined by using some relations between the hyperbolic functions and trigonometric functions based on Sine-Gordon equation and traveling wave transform. The Newel-Whitehead-Segel and Zeldovich equations are solved explicitly. Some real valued solutions are depicted for some particular choice of parameters.

New exact solutions to conformable time fractional EW and modified EW equations are constructed by using Sine-Gordon expansion approach. The fractional traveling wave transform and homogeneous balance have significant roles in the solution procedure. The predicted solution is of the form of some finite series of multiplication of powers of cos and sin functions. The relation among trigonometric and hyperbolic functions in sense of Sine-Gordon expansion gives opportunity to construct the solutions in terms of hyperbolic functions.

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

This research aims to analyse the sustainability of retirement system and relevant optimal path to achieve sustainable post-retirement livings in Malaysia context. Focus of this study is put on Employees Provident Fund (EPF) which is mainly constituted by employees from private sector. EPF is a fully funded defined-contribution by both employees and employers. In this research, main variables used are contribution rate and retirement age based on relevant indexation of pension. For a sustainable retirement living, retirement benefits are expected to be in a maximisation function. Attempts to find sustainable retirement fund are via step-by-step mathematical calculation using formulas in Microsoft Excel and verification of the result with Excel Solver via Generalised Reduced Gradient (GRG) algorithm. Eventually, two-third retirement decision model is used to justify the sustainability of retirement fund other than justification using monthly household expenditure.

This study developed a system dynamics model to understand the spread of coronavirus disease (COVID-19) in Japan. The model is built on the generic SEIR (Susceptible, Exposed, Infected, and Recovered) framework adopted by Ghaffarzadegan and Rahmandad (2020) to build a system dynamics model for the spread of COVID-19 in Iran. Japan seems to be successful in containing the spread compared with other countries, and its first peak has passed. However, because this also leaves a large population still susceptible to the virus, it could cause a second and potentially higher peak of infection after the state of emergency aimed at reducing contact rate is lifted. As the government has proposed the “New Lifestyle,” it is critical to behave cautiously so as not to be infected. While the model focuses on the SEIR structure, the reflection of other sub-structures such as economy and hospital capacity that have tradeoffs with reducing contact rate should be beneficial. However, before extending the model, it is also critical to conduct estimates using confidence intervals rather than point estimates to better reflect uncertainties.

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and π, and then it gives the proof of a new inequality for transcendental numbers. Also, in relationship with these topics, we study solutions to the Yang-Baxter equation from hyperbolic functions and from logical implication.

In this paper, by using the q-integer, we introduce a new generalization of Fibonacci and Lucas sedenions called q-Fibonacci and q-Lucas sedenions. We present some fundamental properties of these type of sedenions such as Binet formulas, exponential generating fuctions, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity.

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equation in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions.

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

In this paper, we use three different experimental methods (particle method, grid method and hybrid method) to model and simulate the smoke from the perspective of fluid dynamics. Through the comparison of different methods, we conclude: The particle method can avoid the numerical dissipation problem caused by grid calculation, but it also brings problems such as the distortion of the trajectory of the example. The grid method is accurate in calculation, but it is prone to numerical dissipation and loss of details. Finally, we choose the hybrid method to store the vorticity in the form of particles in vortex particles, avoiding the numerical dissipation problem caused by the use of grids, and including rich turbulence, which perfectly shows the simulation effect of smoke.

We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.

The class of A-stable symmetric one-step Hermite-Obrechkoff (HO) methods introduced in [1] for dealing with Initial Value Problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order schemes are conjugate symplectic which is a benefit when the methods have to be applied to Hamiltonian problems. Furthermore a new efficient approach for the computation of the spline extension is introduced, adopting the same strategy developed in [2] for the BS linear multistep methods. The performances of the schemes are tested in particular on some Hamiltonian benchmarks and compared with those of the Gauss Runge-Kutta schemes and Euler-Maclaurin formulas of the same order.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

The visualization of hyperspectral images in display devices, having RGB colour composition channels is quite difficult due to the high dimensionality of these images. Thus, principal component analysis has been used as a dimensionality reduction algorithm to reduce information loss, by creating uncorrelated features. To classify regions in the hyperspectral images, K-means clustering has been used to form clusters/regions. These two algorithms have been implemented on the three datasets imaged by AVIRIS and ROSIS sensors.

The current paper explores the potential interlink between names of individuals in a society and its collective social consciousness, particularly with reference to the pervasive occurrence of the ‘mathematical names’ in the current Hindu society in the Indian subcontinent and beyond. Initially, an attempt is made to put things into mathematical perspective by drawing a quick sketch of some of the stellar achievements of the Indian mathematicians. Under the six broad categories of geometry, trigonometry, numeration, arithmetic, algebra, and mathematics in the Vedic tradition, a concise simple description of these subdivisions is presented, underlining the names of the concepts and terms, sometimes by producing the textual references. Then, upon identification of such mathematical terms, an attempt is made to juxtapose these with the names current in the Indian Hindu society. By employing an extensive dataset of university student names in India and the directories of Facebook and LinkedIn, we produce both qualitative and quantitative evidence of the presence of such names in the Indian subcontinent. Evidently, these names reflect the impressions of the tremendously rich mathematical heritage left by the Hindu stalwart mathematicians. This hypothesis has also been examined by taking surveys of people bearing these mathematical names, as well as by documenting the ‘conscious procedures’ that go behind the naming of a Hindu Indian child. In trying to investigate if such a phenomenon is unique to the Indian tradition, a stark contrast with the ‘names in mathematics’ as prevalent in the European mathematical traditions is presented, as cultural roots of mathematics are explored. Further, we ascribe the presence of these names as the extant remains of the colossal impact of multifarious mathematical traditions existing in India. Interestingly, the present research also brings to the fore, certain unseen facets of the Indian Hindu society as regards the education of mathematics to women – through an indirect exploration of their names. We also show that the pervasive occurrence of these names is not merely the result of semantic chance events, but denotes the richness of the Indian mathematical legacy. Next, we also present cross-cultural comparisons to show the uniqueness of Indian mathematical and scientific traditions that led to the pervasiveness of ‘mathematical names’ in India. Finally, an attempt is made to clarify some subtle points on the associations between mathematics and religion in India and other cultures of the world. It is sincerely hoped that the present study may shed light on the cultural roots of mathematics and may furnish a new dimension in the study of mathematics, culture and civilizations across the world.

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

By unraveling a persistent misconception in the zeta Hadamard product expansion, and employing the zeta functional equation, a concise proof of the Riemann Hypothesis is presented, which conclusively demonstrate that the Riemann Hypothesis is true.

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δ_p, ϑ_p and the real norms η_r,p and θ_r,p are provided as well.

Software is playing the most important role in recent vehicle innovation, and consequently the amount of software has been rapidly growing last decades. Safety-critical nature of ships, one sort of vehicles, makes Software Quality Assurance (SQA) has gotten to be a fundamental prerequisite. Just-In-Time Software Defect Prediction (JIT-SDP) aims to conduct software defect prediction (SDP) on commit-level code changes to achieve effective SQA resource allocation. The first case study of SDP in maritime domain reported feasible prediction performance. However, we still consider that the prediction model has still rooms for improvement since the parameters of the model are not optimized yet. Harmony Search (HS) is a widely used music-inspired meta-heuristic optimization algorithm. In this article, we demonstrated that JIT-SDP can produce the better performance of prediction by applying HS-based parameter optimization with balanced fitness value. Using two real-world datasets from the maritime software project, we obtained an optimized model that meets the performance criterion beyond baseline of previous case study throughout various defect to non-defect class imbalance ratio of datasets. Experiments with open source software also showed better recall for all datasets despite we considered balance as performance index. HS-based parameter optimized JIT-SDP can be applied to the maritime domain software with high class imbalance ratio. Finally, we expect that our research can be extended to improve performance of JIT-SDP not only in maritime domain software but also in open source software.

A modified free-wake vortex ring model is proposed to compute the dynamics of a floating horizontal-axis wind turbine. The model is divided into two parts. The near wake model uses a blade bound vortex model and trailed vortex model, which is developed based on vortex filament method. By contrast, the far wake model is based on the vortex ring method. The proposed model is a good compromise between accuracy and computational cost, for example when compared with more complex vortex methods. The present model is used to assess the influence of floating platform motions on the performance of a horizontal-axis wind turbine rotor. The results are validated on the 5MW NREL rotor and compared with other aerodynamic models for the same rotor subjected to different platform motions. It was found that the results from the proposed method are more reliable than the results from BEM theory especially at small angles of attack in the region of low wind speeds, on the one hand, and high wind speeds with blade pitch motions, on the other hand. And also the proposed method is less time consuming and has similar accuracy when comparing with more advanced vortex based methods.

To solve the problem of energy constraint and spectrum scarcity for cognitive radio wireless sensor networks (CR-WSNs), an underlay decode-and-forward relaying scheme is considered, where the energy constrained secondary source and relay nodes are capable of harvesting energy from a multi-antenna power beacon (PB) and using that harvested energy to forward the source information to the destination. Based on the time switching receiver architecture, three relaying protocols, namely, hybrid partial relay selection (H-PRS), conventional opportunistic relay selection (C-ORS), and best opportunistic relay selection (B-ORS) protocols are considered to enhance the end-to-end performance under the joint impact of maximal interference constraint and transceiver hardware impairments. For performance evaluation and comparison, we derive exact and asymptotic closed-form expressions of outage probability (OP) and throughput (TP) to provide significant insights into the impact of our proposed protocols on the system performance over Rayleigh fading channel. Finally, simulation results validate the theoretical results.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

In this article, we set up some adequate conditions for analytic functions associated with cosine hyperbolic function. We determine conditions on α such that 1+α (ϰ^(2+P(j-1) ) g^' (ϰ))/(Pg^j (ϰ)),for each j=0,1,2,3 are subordinated by Janowski function, then (g(ϰ))/ϰ^P <cosℏ⁡(ϰ),(ϰ∈C). By choosing specific values of functions g we get some adequate conditions for multivalent starlike function related with cosine hyperbolic.

In this paper, some mixed type bounds on the spectral radius $\rho(A\circ B)$ for the Hadamard product of two nonnegative matrices ($A$ and $B$) and the minimum eigenvalue $\tau(C\star D)$ of the Fan product of two $M$-matrices ($C$ and $D$) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several $M$-matrices is also presented: $$ \tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq n}\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\}, $$ where $A_{1},\ldots, A_{k}$ are $n\times n$ $M$-matrices and $P_{1},\ldots, P_{k}>0$ satisfy $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$. Some special cases of the above result and numerical examples show that this new bound improves some existing results.

In this paper we introduce the hypo-q-operator norm and hypo-q-numerical radius on a Cartesian product of algebras of bounded linear operators on Banach spaces. A representation of these norms in terms of semi-inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given.

In the present study, a simple approximation expression is given for the relationship between the period and amplitude of a simple pendulum under magnetic action. The analytical solution presented for the given problem. Two numerical quadrature methods Simpson's and Boole's method were utilized to demonstrate a new approximation of the problem. The results of the numerical quadrature have been compared to the exact solution. Absolute and relative mistakes of the problem have been presented. The Matlab program 2013R has created a numerical method that is used to analyze the outcome, It has been determined that the comparison's outcomes attest to the method's suitability and correctness. Moreover, the results show that numerical solution is suitable for the problem.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

The collision avoidance mechanism adopted by the IEEE 802.11 standard is not optimal. The mechanism employs a binary exponential backoff (BEB) algorithm in the medium access control (MAC) layer. Such an algorithm increases the backoff interval whenever a collision is detected to minimize the probability of subsequent collisions. However, the expansion of the backoff interval causes degradation of the radio spectrum utilization (i.e., bandwidth wastage). That problem worsens when the network has to manage the channel access to a dense number of stations, leading to a dramatic decrease in network performance. Furthermore, a wrong backoff setting increases the probability of collisions such that the stations experience numerous collisions before achieving the optimal backoff value. Therefore, to mitigate bandwidth wastage and, consequently, maximize the network performance, this work proposes using reinforcement learning (RL) algorithms, namely Deep Q Learning (DQN) and Deep Deterministic Policy Gradient (DDPG), to tackle such an optimization problem. As for the simulations, the NS-3 network simulator is used along with a toolkit known as NS3-gym, which integrates a reinforcement-learning (RL) framework into NS-3. The results demonstrate that DQN and DDPG have much better performance than BEB for static and dynamic scenarios, regardless of the number of stations. Moreover, the performance difference is amplified as the number of stations increases, with DQN and DDPG showing a 27% increase in throughput with 50 stations compared to BEB. Furthermore, DQN and DDPG presented similar performances.

In this article, our main purpose is to establish a new extension of Mittag-Leffler function by using the known extended beta function $\mathbf{B}_{\omega}(a,b;p)$ introduced in [1]. It led to a novel extension of the applicability of Mittag-Leffler function that introduced them as distributions defined for a specific set of functions. We also, investigate some of its important properties, namely recursion relation, Mellin transform and differential formulas.

Many cryptographic systems require random numbers, and weak random numbers lead to insecure systems. In the modern world, there are several techniques for generating random numbers, of which the most fundamental and important methods are deterministic extractors proposed by von Neumann, Elias, and Peres. Elias’s extractor achieves the optimal rate (i.e., information theoretic upper bound) h(p) if the block size tends to infinity, where h(·) is the binary entropy function and p is probability that each bit of input sequences occurs. Peres’s extractor achieves the optimal rate h(p) if the length of input and the number of iterations tend to infinity. The previous researches related to both extractors did not mention practical aspects including running time and memory-size with finite input sequences. In this paper, based on some heuristics, we derive a lower bound on the maximum redundancy of Peres’s extractor, and we show that Elias’s extractor is better than Peres’s one in terms of the maximum redundancy (or the rates) if we do not pay attention to time complexity or space complexity. In addition, we perform numerical and non-asymptotic analysis of both extractors with a finite input sequence with any biased probability under the same environments. For doing it, we implemented both extractors on a general PC and simple environments. Our empirical results show that Peres’s extractor is much better than Elias’s one for given finite input sequences under the almost same running time. As a consequence, Peres’s extractor would be more suitable to generate uniformly random sequences in practice in applications such as cryptographic systems.

The properties of iterative splitting methods with serial versions have been analyzed since recent years, see [1] and [3]. We extend the iterative splitting methods to a class of parallel versions, which allow to reduce the computational time and keep the benet of the higher accuracy with each iterative step. Parallel splitting methods are nowadays important to solve large problems, which can be splitted in subproblems and computed independently with the dierent processors. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, see [2], [10] and [15]. Such a exibilisation with multisplitting methods allow to decompose large iterative splitting methods and recover the benet of their underlying waveform-relaxation (WR) methods. We discuss the convergence results of the parallel iterative splitting methods, while we could reformulate such an error to a summation of the individual WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods and present dierent numerical applications to validate the benet of the parallel versions.

The airport ground handling service (AGHS) equipment vendor selection (AGHSEVS) problem is critical for ramp work safety management, because AGHS equipment malfunctions affect airport ramp work safety. Appropriate vendor selection can prevent aircraft damage and delays in airlines schedules, and ensure reliable and high-quality ground handling service. The AGHSEVS problem is a time-consuming and complex process that requires professional knowledge and experience to make judgments. Specifically, AGHSEVS is a multi-criteria decision-making (MCDM) problem. Previous research has seldom integrated MCDM methods with linear and goal programming to solve the AGHSEVS problem. The objective of this study was to develop a new system evaluation model for AGHSEVS by considering both qualitative and quantitative methods. We test the proposed approach on an AGHS company in Taiwan.

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

In this research work, we present a mathematical model for novel coronavirus -19 (NCOVID-19) which is consisted on three different compartments susceptible, infected and recovered classes abbreviated as under convex incident rate involving and emigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by using various tools of nonlinear analysis. Then by mean of nonstandard finite difference scheme (NSFD), we simulate the results against the data of Wuhan city for the sixty days. By means of simulation, we show how protection, exposure, emigration, death and cure rates affect the susceptible, infected and recovered population with the passage of time involving emigration. On the basis of simulation, we observe the dynamical behavior due to emigration of susceptible and infected classes or one of these two.

Four methods in two different families have been constructed to derive the exact solutions to Benjamin-Bona-Mahony equation in two space dimensions. Simply defined hyperbolic tangent, hyperbolic secant and hyperbolic cosecant ansatzes and the expansion method based on the Sine-Gordon equation in two dimensions are directly substituted into the governing ODE reduced from the two dimensional BBM equation. Classical algebraic method is used to find the relations among the target parameters representing the nonzero coefficients in the predicted solutions and the wave transform parameters. Some complex and real solutions have been constructed in explicit forms.

The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses extensions of invariance alignment and Haberman linking concerning the choice of linking functions for comparisons of many groups. Robust linking functions are proposed for invariance alignment and robust Haberman linking that are particularly suited to item response data under partial invariance. In a simulation study, it is shown that both linking approaches have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment.

One of essential procedure nowadays to analyze a dynamic process in Science and Engineering is Computational modeling. Most of dynamic processes are distributed parameter systems, i.e., systems with state variables depend on the number of independent variables (such as space and time) which are expressed by a set of Partial Differential Equations (PDEs). Lateral method of lines is a method which used for solving PDEs numerically by solving a set of boundary value problems sequentially. The aim is to report the development of PDE toolbox based on SCILAB. This paper provides users with a method that is very easy to understand in the applications related to dynamic process. The method uses a SCILAB template to develop numerical simulations in the new field. In this paper, a model of tropical fruit heat treatment for decimating insect is presented. The illustration will be given to show how the lateral method of line template works to solve the problem.

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.

Limnologists often adhere to a discretized view of waterbodies—they classify them, divide them into zones, promote discrete management targets, and use research tools, experimental designs, and statistical analyses focused on discretization. This approach to limnology has profoundly benefited the way we understand, manage, and communicate about waterbodies. But the research questions and the research tools in limnology are changing rapidly with consequences for the relevance of our current discretization schemes. Here, I examine how and why we discretize and argue that selectively rethinking the extent to which we must discretize gives us an exceptional chance to advance limnology in new ways.

Various empirical models are available to evaluate the temperature effects on relative permeability of the different rock and fluid systems. However, the implementation of limited experimental data points may hinder the applicability of such models to other systems. This study aims to develop new predictive models for k_ro estimation based on multilayer perceptron artificial neural network (MLP-ANN), adaptive neuro-fuzzy inference system (ANFIS), and least squares support vector machine (LSSVM) approaches. A database comprising of 626 data points applied to the model development. The independent variables are temperature, oil viscosity, water viscosity, water saturation ( ), and the absolute permeability. Each variable covers a wide range of variations which increases models’ potential to be applied in various systems with different characteristics. The doubtful experimental data points excluded using a leverage value approach and a sensitivity analysis carried out to determine the quantitative impact of every individual independent variable on the k_ro. Statistical error analyses demonstrated the coefficient of determination (R²) values of 0.985, 0.975, and 0.999 for MLP-ANN, ANFIS, and LSSVM, respectively. The comparative study indicated that the LSSVM had the best performance regarding both graphical and statistical error analyses among the newly proposed models and previously reported models in the literature.

Susceptible, infective, recovered, and hospitalized/isolated individuals are placed on the cells of a nxn square lattice, where each cell is occupied by a single individual or is vacant. At discrete time units (typically one day each) all susceptibles and infectives execute a random movement and when a coincidence of the two types occurs the susceptible is converted to infective status according to some probability. Infectives are labelled by the number of days since originally infected. At each time increment the age label of the infectives is increased by one unit. When the label reaches a number like 15 or 20 days the susceptibles recover with some probability or become isolated/hospitalized. Upon reaching some age the latter types either recover or die. Probabilities for the movements and conversions from one status to another are implemented by random numbergeneration. Simulations were carried out to investigate the effect of several probability and age parameters, the size of population (proportional to nxn) and density (related to fraction of occupied cells), and the size of the movements. Mid-term gradual conversion of susceptibles to isolated was explored as intervention policy.

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

Integrating artificial intelligence (AI) and natural language processing (NLP) technologies with project-based learning experiences in Science,Technology, Reading, Engineering, Arts, and Mathematics (STREAM) education offers the potential to enhance student engagement, critical thinking,problem-solving, and interdisciplinary learning. This paper presents a comprehensive approach to implementing AI and NLP technologies, such as ChatGPT, in STREAM project-based learning experiences, highlighting the potential advantages and challenges of this innovative educational approach. The proposed method encompasses personalized learning pathways, AI-powered research assistance, collaborative AI tools, real-time feedback, virtual mentoring, advanced simulation, and objective assessment. We also discuss the implications of this integration for educators, institutions, and students, along with recommendations for future research and development in this emerging field.

In tracking-by-detection paradigm for multi-target tracking, target association is modeled as an optimization problem that is usually solved through network flow formulation. In this paper, we proposed combinatorial optimization formulation and used a bipartite graph matching for associating the targets in the consecutive frames. Usually, the target of interest is represented in a bounding box and track the whole box as a single entity. However, in the case of humans, the body goes through complex articulation and occlusion that severely deteriorate the tracking performance. To partially tackle the problem of occlusion, we argue that tracking the rigid body organ could lead to better tracking performance compared to the whole body tracking. Based on this assumption, we generated the target hypothesis of only the spatial locations of person’s heads in every frame. After the localization of head location, a constant velocity motion model is used for the temporal evolution of the targets in the visual scene. Qualitative results are evaluated on four challenging video surveillance dataset and promising results has been achieved.

Voronoi entropy for the random patterns and patterns demonstrating various elements of symmetry are calculated. The symmetric patterns are characterized by the values of the Voronoi entropy very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points, constituting the pattern. The extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables revealing of the elements of symmetry of the pattern.

In the era of sustainable development, green supplier selection has become a key component of supply chain management, as it considers criteria such as carbon footprint, water usage, energy usage and recycling capacity. Since the green supplier selection problem involves subjective criteria and uncertainty in preferences, it is well suited to using multi-criteria decision-making methods (MCDM). Although few researchers have investigated MCDM for green supplier selection under uncertainty using intuitionistic and Pythagorean fuzzy sets. Still, the newly developed fermatean fuzzy can handle greater data uncertainty than intuitionistic and Pythagorean fuzzy sets. Since interval extension of fuzzy theory provides more accurate modeling, in this paper, we propose an interval extension of fermatean fuzzy set and discuss its fundamental set operations, arithmetic operations and related properties. We propose the Hamming distance function and the score function of the interval-valued fermatean fuzzy numbers. The recently developed Multi-attribute Border Approximation Area Comparison (MABAC) method is also considered due to its stable and simple computation compared to other conventional MCDM methods. Therefore, an interval-valued fermatean fuzzy MABAC method is proposed and solved to select a green supplier based on multiple criteria. The proposed method's comparative analysis and sensitivity analysis validate the proposed method's effectiveness and robustness.

This paper puts forward an alteration for Tensor Calculus utliized in a coordinate system which is under a dynamic distortion drawing inspiration from similar fields such as the Calculus of Moving Surfaces (CMS). The paper establishes transformation laws for Tensors within these regions and establishes Operators such as the Tensorial Field Derivative which enforce a Tensorial Transformation on Tensors defined within a Dynamically Moving coordinate system. This variation of Tensor Calculus can be utilized to observe how disciplines such as QFT and Continuum Mechanics would change to accomodate for a distorting coordinate system and can be utliized to develop new theoretical models which account for this temporal distortion particularly within Biological Settings.

In standard construction of hyperrational numbers using ultra-power we assume that the ultralter is selective. It makes possible toassign real value to any nite hyperrational number. So, we can consider hyperrational numbers with selective ultralter as extension of traditional real numbers. Also proved the existence of strictly monotonic or stationary representing sequence for any hyperrational number.

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivative, second-order pseudoinvexity functions and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of \textit{"Higgs Boson like"} potentials among others.

Ultrasonic imaging & NDE applications can greatly improve their signal-to-noise ratios (SNR) by driving each transducer (composing piezoelectric arrays) with a spike giving pulsed power of k-Watts, repetitively at a PRF = 5000 spikes/s, by using a HV capacitive-discharge generator. However very-high levels, of pulsed intensities (3-10 A) and voltages (300-700 V) must be considered for a rigorous spike modeling. Even though the consumed "average" power will be small, the intensity through each transducer achieves several amperes, so the pulsed powers delivered by each HV generator can attain levels higher than in CW high-power ultrasonic applications: e.g., up to 5 kW / spike. This is concluded here from a transient modeling of the loaded generator. Then, unforeseen phenomena rise: intense brief pulses of driving power & emitted force in transducers, and non-linearities in driver semiconductors, because their characteristic curves only include linear ranges. But fortunately, piezoelectric devices working in this intense regime do not show serious heating problems, because the average power remains being moderate. Intensity, power and voltage, driving a broadband transducer from a HV capacitive pulser, are calculated to drastically improve (in ≅ 40 dB) the ultrasonic net dynamic range available, with emitted forces ≅ 250 Newtons pp and E/R received pulses of 70 V pp.

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

Has anyone ever missed an event because he was confused in days and dates? Do we remember the date of any day without looking at a calendar? Is the current Gregorian Calendar efficient enough for use, and does it facilitate our life or make it more complicated? Have you ever thought about a much simpler way to calculate days and dates in a year? All these questions are answered in this paper, in which the author proposes original optimization algorithm that creates optimal perennial calendars. Results show that there is more than one way to create a perennial calendar, in which the number of days in each month does not change, neither the dates. Hence, all months have the same sequence of days and dates. In other meaning, Monday becomes the first day of every month, and Sunday becomes the last day. Consequently, the calendars become much easier to memorize and very simple to predict the days and dates in any year.

The purpose of this paper is to prove strong convergent theorems for Browder's type iterations and Halpern's type iterations of a family of nonexpansive mappings in a complete geodesic space with curvature bounded above by a positive number. Moudafi's viscosity type methods are also discussed without the nice projection property.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

In this paper, we study the dynamics of following system of nonlinear difference equations x_n+1 = x_n-1y_n - 1, y_n+1 = y_n-1z_n - 1, z_n+1 = z_n-1x_n - 1. Especially we investigate the periodicity, boundedness and stability of related system of difference equations.