Applied Mathematics and Modelling in Finance, Marketing and Economics

This paper presents the space-time fractional Klein-Gordon equations (FKGEs) for the spinless particle in potential field. It defines to describe the Higgs boson and the propagation of a boson in vacuum in Standard Model (SM). Besides, in this paper, the sine method is employed to construct exact solutions of the space-time fractional Klein-Gordon equations. Many new families of exact traveling wave solutions of the space-time fractional Klein-Gordon equations are successfully obtained. It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

In this study, we employ a blossoming technique and smoothness criteria to devise a two-step method for creating a \(C^2\) septic spline quasi-interpolant on any given triangulation. This approach ensures an optimal approximation order without the need for coefficient masks associated with smoothness or B-spline basis. To demonstrate the validity of our theoretical findings, we provide numerical experiments.

The linear programming tool covers a wide range of subject areas including Mathematics, Physics, Financial Management and Digital Economic. Particularly when solving financial planning problems with a goal using linear programming, the presence of fuzziness with the ranking or weighting of goals leads to some technical difficulties. Although significant research works which have been established on fuzzy linear programming, only the membership’s aspect or algebraic form are considered. The purpose of this paper is to deal with a kind of linear programming problem involving triangular fuzzy numbers given in the parametric form. In order to demonstrate and to test the proposed methodology, we give an illustrated example. This approach of parametric form will be extended and investigated for solving intuitionistic fuzzy linear programming and neutrosophic linear programming in the future perspective.

This paper deals with the optimisation of the Multi-Objectif k-Minimum Spanning Tree (MO k-MST) problem. A wide varieties of decision making problems in the real world can be formulated as a MO k-MST, which is known to be NP-complete. In order to solve a such problem, we propose two approximate approaches based on simulated annealing method: the first one will integrates the static weighted sum method while the second one uses the dynamic weighted sum method. Computational experiments were carried out in order to compare the performance of each method.

In this paper, the Kantorovich method for the numerical solution of nonlinear Urysohn equations with a smooth kernel is considered. The approximating operator is chosen to be either the orthogonal projection or an interpolatory projection onto a space of piecewise polynomials of degree \(\le r-1\). This method have asymptotic series expansions and the orders of convergence can be further improved by the Richardson extrapolation, assuming the calculation to be repeated with each subinterval halved. We show that these orders of convergence are preserved in the corresponding discrete methods obtained by calculating the integrals with a numerical quadrature formula. Numerical examples are given to illustrate the theoretical estimates.

Let n be a positive integer and let \(M_n (\mathbb {C})\) denote the algebra of all complex n-by-n matrices. A matrix \(A\in M_n (\mathbb {C})\) is called quadratic if it satisfies some non-trivial quadratic equation \((A-\alpha I)(A-\beta I) = 0\), where I denotes the \(n\times n\) identity matrix. In this paper, we give an explicit formula for the maximal numerical range of quadratic matrices.

In this present work, the micromechanical cochlea model has developed in order to describe mathematically the displacement of cochlear partition using finite difference method and Cramer’s rule, Then, we have studied the effect of basilar membrane (BM) stiffness on the displacements of the BM and tectorial membrane (TM). Results showed that the augmentation of the BM stiffness reduce the maximum amplitude displacement of the BM and TM. These findings contribute to understand that the loss of hearing at low frequencies may be the result of altered cochlear micromechanics.

In this paper we propose a new variant of GOST R 34.10-2012 digital signature algorithm. We modified the signature equation to make it more secure against current attacks. We analyze security and complexity of the proposed protocol.

This paper is devoted to considering the local existence and uniqueness of fuzzy fractional integration-differential problem under Caputo-type fuzzy fractional derivative employing the contraction principle. Some patterns are presented to describe these results.

Social dilemmas in economics characterize situations of social interaction in which the contradiction between individual and collective rationality occur in the classical game theory. In the case of financing public good, analyzed from the viewpoint of the Prisoner’s Dilemma to many players, this study highlights how social preferences determine the emergence of cooperation in accordance with the different results of experimental studies. The current study contributes to the literature with the aim of broadening our sight of the emergence of collaborative behaviors by taking into account the question of the nature of individual preferences and seeking to integrate the intentions and emotions of the players when seeking a conditionally efficient equilibrium which could be qualitatively greater than the Pareto optimal allocation. This paper provides a comprehensive analysis and discussion of the importance of adopting a collaborative behavior for providing an efficient solution to the problem of financing public goods when social dilemmas arise.

Let \(q_1\equiv q_2\equiv 3\pmod 8\) be two different prime integers, d a positive odd square-free integer relatively prime to \(q_1\) and \(q_2\). The main aim of this paper is to investigate the unit groups of some number fields of the form \(\mathbb {L}=\mathbb {Q}(\sqrt{2}, \sqrt{q_1}, \sqrt{q_2}, \sqrt{-d})\).

We extend a meshless method of fundamental solutions to the one-dimensional inverse Stefan problem for the heat equation, where the boundary data is to be reconstructed on the fixed boundary. The inverse problem is ill-posed for small errors in the input measured data can cause high deviations in solution. Therefore, we incorporate Tikhonov regularization to obtain a stable solution. Numerical results are presented.

In this work, we aim to solve the inverse problem of diffuse optical tomography by using enhanced gradient descent methods. The light propagation throughout the medium is described by the diffusion approximation in frequency domain. For comparison purpose we use the gradient descent method. We have studied the convergence of the objective functional. Our simulation results, in all cases we have tested, show the robustness and the quick convergence of Adam algorithm compared to the gradient descent algorithm.

This study introduces a new stochastic diffusion process that is based on the generalized Goel-Okumoto curve. By analyzing the corresponding stochastic differential equation (SDE), we can accurately determine the probabilistic characteristics of the process, including its solution, transition density probability function, and distribution. To estimate the model parameters, we employ the maximum likelihood method and utilize discrete sampling. This allows us to formulate a nonlinear equation that can be efficiently solved using metaheuristic optimization algorithms like simulated annealing. The proposed model is then applied to fit and forecast data on Individuals using the Internet (% of population) in Morocco.

The study described in this work focuses on the dam-break problem over a sandy bed. The goal is to analyze the effects and reactions of various parameters involved in the problem. The problem is mathematically modeled using a coupled model and a non-capacity model. To solve the mathematical model numerically, an unstructured finite volume method is employed. This method allows for the discretization of the problem domain into a mesh of cells, where the conservation equations are solved at the cell level. In order to achieve second-order accuracy in both space and time, the MUSCL method is used for spatial discretization, while the Runge–Kutta method is used for time integration. One particular aspect of the numerical implementation is the treatment of the source term, which is handled using an original approach. This treatment ensures the accurate representation of the physical phenomena involved in the dam-break problem. To enhance the accuracy of the results and reduce computational time, an adaptive mesh is employed. This means that the mesh is dynamically refined or coarsened in regions of interest based on certain criteria, allowing for a higher level of accuracy in those areas while saving computational resources in less critical regions. The study considers several cases, likely involving different initial conditions, boundary conditions, or parameter values. The results obtained from these simulations are presented and analyzed, highlighting the differences observed for different computational times.

In this research study, we derive a closed-form pricing formula for European options with analytical solution under the Heston model with the interest rate; in order to follow two-factor model by using the short-term interest rate and the volatility of the short term rate as the two factors. Heston-Longsraff-Schwartz hybrid model is proposed. Therefore, the numerical results in this paper represented different situations of computing European call option prices than can be more close to reality.

In the current generation of cellular networks, energy efficiency is considered as an important issue due to their high-energy consumption. To meet the rising traffic resulting from the growing mobile stations requests and covering the entire transmission area, base stations must be increasingly deployed. However, increasing the number of these stations increases the cost and energy consumption, which leads to conflicting goals. In this paper, we introduce a multi-objective mathematical model on cellular networks that aimed to minimize the expected total cost of base stations and maximize total coverage. This optimization must take into account the traffic demand profile. Given that the studied model corresponds to an NP-hard multi-objective problem, we use a meta-heuristic algorithm to solve it. The simulation results show the effectiveness of our approach to cover the grid while reducing costs and energy consumption.

Electrical impedance tomography is a technique that allows to image the distribution of the conductivity of a domain from impedance measurements made at several points on its surface. The method was initially developed by geophysicists for mineral prospecting (Maillet, 1947). However, its biomedical applications were quickly recognized (Brown and Barber, 1984). Electrical Impedance Tomography (EIT) is a non-invasive imaging technology that estimates the electrical conductivity distribution in a domain. In this study, the conductivity is reconstructed from boundary voltage measurements by using a reconstructing algorithm known as the forward problem. Simultaneously, the image reconstruction can be obtained using the inverse problem to detect regional lung ventilation.

The finite element method (FEM) is a numerical method of resolution of many problems modeled in terms of partial differential equations. It is a powerful and widely used method in science and engineering. Its simulation requires in a first phase the construction of a mesh of the computational domain. In our paper, we present an efficient approach for local and global mesh refinements of triangular and quadrilateral two-dimensional meshes in C programming language. The proposed refinement algorithms are based on a bisection-type method which produces nested refinements of the triangulation. The algorithms are short, easy to understand and modify, moreover they can be easily integrated in a FEM C program.