Mathematics Interdisciplinary Research
https://mir.kashanu.ac.ir/
Mathematics Interdisciplinary Researchendaily1Tue, 01 Aug 2023 00:00:00 +0430Tue, 01 Aug 2023 00:00:00 +0430Chaotic Time Series Prediction Using Rough-Neural Networks
https://mir.kashanu.ac.ir/article_113906.html
&lrm;Artificial neural networks with amazing properties&lrm;, &lrm;such as universal approximation&lrm;, &lrm;have been utilized to approximate the nonlinear processes in many fields of applied sciences&lrm;. &lrm;This work proposes the rough-neural networks (R-NNs) for the one-step ahead prediction of chaotic time series&lrm;. &lrm;We adjust the parameters of R-NNs using a continuous-time Lyapunov-based training algorithm&lrm;, &lrm;and prove its stability using the continuous form of Lyapunov stability theory&lrm;. &lrm;Then&lrm;, &lrm;we utilize the R-NNs to predict the well-known Mackey-Glass time series&lrm;, &lrm;and Henon map&lrm;, &lrm;and compare the simulation results with some well-known neural models&lrm;.Exact Solution of Schrödinger Equation for Pentaquark Systems
https://mir.kashanu.ac.ir/article_112796.html
&lrm;In this paper&lrm;, &lrm;we present an exact analytical solution for five interacting quarks&lrm;. &lrm;We solve the Schr\"{o}dinger equation for pentaquarks in the framework of five-body and two-body problems&lrm;. &lrm;For this purpose&lrm;, &lrm;we utilize Yukawa potential in Jacobi coordinates&lrm;. &lrm;Also finding the relation between the reduced masses and coupling constants of pentaquarks&lrm;, &lrm;we obtain the coupling constant of Yukawa potential for pentaquark systems&lrm;. &lrm;We calculate the energy of these systems in their ground state&lrm;. &lrm;The results are well consistent with the theoretical results&lrm;. &lrm;Our procedure to obtain these results is appropriate for other potentials and $n$-body systems&lrm;.On the Maximal Graph of a Commutative Ring
https://mir.kashanu.ac.ir/article_111486.html
Let R be a commutative ring with nonzero identity. Throughout this paper we explore some properties of two subgraphs of the maximal graph of R.The Effect of the Caputo Fractional Derivative on Polynomiography
https://mir.kashanu.ac.ir/article_112883.html
This paper presents the visualization process of finding the roots of a complex polynomial - which is called polynomiography - by the Caputo fractional derivative. In this work, we substitute the variable-order Caputo fractional derivative for classic derivative in Newton&rsquo;s iterative method. To investigate the proposed root-finding method, we apply it for two polynomials p(z) = z5 &minus;1 and p(z) = &minus;2z4 + z3 + z2 &minus;2z&minus;1 on the complex plan and compute the MNI and CAI parameters. Presented examples show that through the expressed process, we can obtain very interesting fractal patterns. The obtained patterns show that the proposed method has potential artistic application.Barnes−Godunova−Levin Type Inequalities for Generalized Sugeno Integral
https://mir.kashanu.ac.ir/article_113907.html
&lrm;This article will prove the Barnes&ndash;Godunova&ndash;Levin (B-G-L) type inequalities for generalized Sugeno integrals&lrm;. &lrm;Also&lrm;, &lrm;we use some techniques and properties of concave functions to prove theorems and to obtain new results&lrm;. &lrm;We will present a more robust version of the B-G-L type inequality for the operator $\star$&lrm;.Topics on $(H,Poly(P))$-Hypergroups
https://mir.kashanu.ac.ir/article_113908.html
&lrm;In this paper&lrm;, &lrm;we construct a hypergroup by using a hypergroup&lrm;
&lrm;$(H,\circ)$ and a polygroup $(P,\cdot)$&lrm;, &lrm;and call it&lrm;
&lrm;$(H,Poly(P))$-hypergroup&lrm;. &lrm;The method of constructing hypergroups in this paper is not present in the established techniques of group theory&lrm;. &lrm;Moreover&lrm;, &lrm;we compare&lrm;
&lrm;$(H,Poly(P))$-hypergroups with $K_H$-hypergroups&lrm;, &lrm;complete&lrm;
&lrm;hypergroups and extensions of polygroups by polygroups&lrm;.Coupling Chebyshev Collocation with TLBO to Optimal Control Problem of Reservoir Sedimentation: A Case Study on Golestan Dam, Gonbad Kavous City, Iran
https://mir.kashanu.ac.ir/article_113909.html
&lrm;In this paper&lrm;, &lrm;an efficient and robust approach based on the Chebyshev collocation method and Teaching-Learning-Based Optimization (TLBO) is utilized to solve the Optimal Control Problem (OCP) of reservoir sedimentation on Golestan dam in Gonbad Kavous City&lrm;, &lrm;Iran&lrm;. &lrm;The discretized method employs Mth degree of Lagrange polynomial approximation for an unknown variable and Gauss-Legendre integration&lrm;. &lrm;The OCP yields a nonlinear programming problem (NLP)&lrm;, &lrm;and then this NLP is solved by TLBO&lrm;. &lrm;Numerical implementations are given to demonstrate this approach yields more acceptable and the accurate results&lrm;. &lrm;Furthermore&lrm;, &lrm;it is found that filling the dam with sediment decreases the water storage&lrm;, &lrm;increases dam maintenance costs&lrm;, &lrm;and also decreases the stability of the dam over a period of 40 years&lrm;. &lrm;Our results show that the Golestan dam will gain development with the construction of the new reservoir&lrm;.On Power Graph of Some Finite Rings
https://mir.kashanu.ac.ir/article_113913.html
&lrm;Consider a ring $R$ with order $p$ or $p^2$&lrm;, &lrm;and let $\mathcal{P}(R)$ represent its multiplicative power graph&lrm;. &lrm;For two distinct rings $R_1$ and $R_2$ that possess identity element 1&lrm;, &lrm;we define a new structure called the unit semi-cartesian product of their multiplicative power graphs&lrm;. &lrm;This combined structure&lrm;, &lrm;denoted as $G.H$&lrm;, &lrm;is constructed by taking the Cartesian product of the vertex sets $V(G) \times V(H)$&lrm;, &lrm;where $G = \mathcal{P}(R1)$ and $H = \mathcal{P}(R2)$&lrm;. &lrm;The edges in $G.H$ are formed based on specific conditions&lrm;: &lrm;for vertices $(g,h)$ and $(g^\prime,h^\prime)$&lrm;, &lrm;an edge exists between them if $g = g^\prime$&lrm;, &lrm;$g$ is a vertex in $G$&lrm;, &lrm;and the product $hh^\prime$ forms a vertex in $H$&lrm;.
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&lrm;Our exploration focuses on understanding the characteristics of the multiplicative power graph resulting from the unit semi-cartesian product $\mathcal{P}(R1).\mathcal{P}(R2)$&lrm;, &lrm;where $R_1$ and $R_2$ represent distinct rings&lrm;. &lrm;Additionally&lrm;, &lrm;we offer insights into the properties of the multiplicative power graphs inherent in rings of order $p$ or $p^2$&lrm;.