Journals: Abdelhafid Boussouf University Center of Mila, Algeria
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Some integral properties in the theory of generalized Bessel matrix functions
Full text linkThe main purpose of this article is to define some original properties in the theory of the generalized modified Bessel matrix functions. These special functions, defined in terms of Wright matrix functions, are generalized and their properties studied in depth. Moreover, it is shown their application to the analysis of certain generalized integral formulas involving the generalized modified Bessel matrix function
On numerical and analytical solutions of the generalized Burgers-Fisher equation
No full textIn this paper, the semi-analytic iterative and modified simple equation methods have been implemented to obtain solutions to the generalized Burgers-Fisher equation. To demonstrate the accuracy, efficacy as well as reliability of the methods in finding the exact solution of the equation, a selection of numerical examples was given and a comparison was made with other well-known methods from the literature such as variational iteration method, homotopy perturbation method and diagonally implicit Runge-Kutta method. The results have shown that between the proposed methods, the modified simple equation method is much faster, easier, more concise and straightforward for solving nonlinear partial differential equations, as it does not require the use of any symbolic computation software such as Maple or Mathematica. Additionally, the iterative procedure of the semi-analytic iterative method has merit in that each solution is an improvement of the previous iterate and as more and more iterations are taken, the solution converges to the exact solution of the equation
Variance exchange process: overcoming the problem of singular information matrices in quadratic three−variable response designs
Full text linkMany a time, in a variance exchange process looking for D-optimal designs, the initial designs of all quadratic components of three-variable response polynomials produce non-invertible information matrices. For such matrices, the variances of predicted responses at variance points cannot be evaluated, and the variance exchange process, not possible. D-optimality is a design criterion that seeks to maximize the determinant of the information matrix, or equivalently minimize the determinant of the inverse information matrix of the design. This work seeks to address the challenges posed by initial quadratic designs with zero-determinant information matrices for three-variable response polynomials to allow for the possibility of the variance exchange.The singular value decomposition (SUV) method was adopted and an algorithm was constructed for a variance exchange process involving quadratic designs of threevariable response functions. The study considered generated data for quadratic threevariable designs of sizes 12 and 13 for the analysis. MATLAB 7.5.0 (R2007b) was used to obtain the Penrose inverses.The results show that a variance exchange process was possible, evaluating the variances of the predicted responses at the design points, thereby overcoming the problem of singular information matrices on the initial quadratic designs.The D-optimal designs, computer-generated optimal designs, provide ready alternatives for finding optimum conditions for factors in engineering optimization problems with response surface functions that require structured data collection using experimental design when the experimental design space is constrained owing to zero determinant of the information matrices of the initial designs
A new concept of q-calculus with respect to another function
Full text linkIn this paper, we present an approach to quantum calculus and its applications through a functional method. This approach enables the exploration of the number-theoretic properties of q-calculus in a functional framework, facilitating the modification of variable-order q-differential equations and their solutions. The paper primarily focuses on the functional aspects of quantum number theory, functional-order q-derivatives, and their applications
Existence of solutions for a class of kirchhoff-type problem with triple regime logarithmic nonlinearity
No full textIn this paper, we use variational methods to study the existence of nontrivial solutions for a class of Kirchhoff-type elliptic problems driven by the p(x)-Laplacian with triple regime and sign-changing nonlinearity.
The main novelty of this paper is our ability to establish an existence result for a class of Kirchhoff-type problems in which the reaction term is sign-changing and exhibits a triple regime (subcritical, critical, and supercritical)
A distance metric for ordinal data based on misclassification
No full textDistances between data sets are used for analyses such as classification and clustering analyses. Some existing distance metrics, such as the Manhattan (City Block or L1 ) distance, are suitable for use with categorical data, where the data subtype is numeric, or more specifically, integers. However, ordinality of categories imposes additional constraints on data distributions, and the ordering of categories should be considered in the calculation of distances. A new distance metric is presented here that is based on the number of misclassifications that must have occurred within one data set if it were in fact identical to another data set. This "misclassification distance" is equivalent to the number of reclassifications necessary to transform one data set into another. This metric takes account not only of the numbers of observations in corresponding ordinal categories, but also of the number of categories across which observations must be moved to correct all misclassifications. Each stepwise movement of an observation across one or more categories that is required to equalize the distributions increases the distance metric, thus this method is referred to as a stepwise ordinal misclassification distance (SOMD). An algorithm is provided for the calculation of this metric
A biparameterized analysis of integral inequalities for bounded and holderian mappings
Full text linkIn this study, we introduce a new parameterized identity that generates a series of Newton-Cotes formulas for one, two, three, and four points. We then derive several novel Newton-Cotes-type inequalities for functions with bounded and rr-LL-H\"{o}lderian derivatives. The research is finalized with numerical examples and graphical illustrations that validate the precision of our findings
Collaboration and authority in the collective action problem
Full text linkDirect reciprocity and contingent collaboration deter opportunistic behavior in social predicaments. However, in large collectives, these mechanisms may lose efficacy as they rely on individuals\u27 influence. Zero-Determinant (ZD) strategies in the collective action problem reshape our understanding of individual influence. Our study introduces a theoretical framework extending these strategies to multiplayer dilemmas, offering insights into lone participants\u27 impact. We delineate intriguing sub-classes of strategies: fair, extortionate (advantageous), and generous (disadvantageous). We explore models showcasing strategic enhancement through alignment with others. The present study elucidates the significance of individual decision-making and collective coordination as essential components contributing to favorable outcomes within expansive group settings
Periodic solutions of third order differential equations
No full textIn this paper, we study the existence of periodic solutions for the following piecewise third-order differential equation:with a real parameter sufficiently small, and real numbers. By applying new results from the averaging theory for continuous differential systems, we prove the existence of at most one periodic solution for the differential equation. An example is given to illustrate the established result.
 
Analyzing the fractional order T. Regge problem using the Laplace transformation method
Full text linkThis study uses the Laplace transformation method to solve the fractional-order T. Regge problem. In this paper, we develop formulations for the fractional Laplace transform applied to fractional integrals and derivatives, and we use this method to solve the T. Regge problem. Moreover, several examples are presented to demonstrate the method\u27s value and effectiveness. Examples prove that the Laplace transformation method significantly advances the fractional computation field and can potentially solve fractional differential equations (FDEs). On the other hand, the advantages and disadvantages of the method are provided