Mathematics Interdisciplinary Research
https://mir.kashanu.ac.ir/
Mathematics Interdisciplinary Researchendaily1Fri, 01 Mar 2024 00:00:00 +0330Fri, 01 Mar 2024 00:00:00 +0330Virtual Element Method for Numerical Simulation of Burgers-Fisher Equation on Convex and Non-Convex Meshes
https://mir.kashanu.ac.ir/article_114194.html
&lrm;We present an enhanced approach to solving the combined non-linear time-dependent Burgers-Fisher equation&lrm;, &lrm;which is widely used in mathematical biology and has a broad range of applications&lrm;. &lrm;Our proposed method employs a modified version of the finite element method&lrm;, &lrm;specifically the virtual element method&lrm;, &lrm;which is a robust numerical approach&lrm;. &lrm;We introduce a virtual process and an Euler-backward scheme for discretization in the spatial and time directions&lrm;, &lrm;respectively&lrm;. &lrm;Our numerical scheme achieves optimal error rates based on the degree of our virtual space&lrm;, &lrm;ensuring high accuracy&lrm;. &lrm;We evaluate the efficiency and flexibility of our approach by providing numerical results on both convex and non-convex polygonal meshes&lrm;. &lrm;Our findings indicate that the proposed method is a promising tool for solving non-linear time-dependent equations in mathematical biology&lrm;.&nbsp;Gorenstein Homological Dimension of Groups Through Flat-Cotorsion Modules
https://mir.kashanu.ac.ir/article_114195.html
&lrm;The representation theory of groups is one of the most interesting examples of the interaction between physics and pure mathematics&lrm;, &lrm;where group rings play the main role&lrm;. &lrm;The group ring $\rga$ is actually an associative ring that inherits the properties of the group $\ga$ and the ring of coefficients $R$&lrm;. &lrm;In addition to the fact that the theory of group rings is clearly the meeting point of group theory and ring theory&lrm;, &lrm;it also has applications in algebraic topology&lrm;, &lrm;homological algebra&lrm;, &lrm;algebraic K-theory and algebraic coding theory&lrm;.&lrm;In this article&lrm;, &lrm;we provide a complete description of Gorenstein flat-cotorsion modules over the group ring $\rga$&lrm;,&lrm;where $\ga$ is a group and $R$ is a commutative ring&lrm;. &lrm;It will be shown that if $\ga'\leqslant \ga$ is a finite-index subgroup&lrm;, &lrm;then the restriction of scalars along the ring homomorphism $\rga'\rt\rga$ as well as its right adjoint $\rga\otimes_{\rga'}-$&lrm;, &lrm;preserve the class of Gorenstein flat-cotorsion modules&lrm;. &lrm;Then&lrm;, &lrm;as a result&lrm;, &lrm;Serre's Theorem is proved for the invariant $\Ghcd_{R}\ga$&lrm;, &lrm;which refines the Gorenstein homological dimension of $\ga$ over $R$&lrm;, &lrm;$\Ghd_{R}\ga$&lrm;, &lrm;and is defined using flat-cotorsion modules&lrm;. &lrm;Moreover&lrm;, &lrm;we show that the inequality $\GF (\rga)\leqslant \GF (R)+{\cd_{R}\ga}$ holds for the group ring $\rga$&lrm;, &lrm;where $\GF (R)$ denotes the supremum of Gorenstein flat-cotorsion dimensions of all $R$-modules and $\cd_{R}\ga$ is the cohomological dimension of $\ga$&lrm; over $R$&lrm;.&nbsp;Ricci Bi-Conformal Vector Fields on Siklos Spacetimes
https://mir.kashanu.ac.ir/article_114196.html
&lrm;Ricci bi-conformal vector fields have find their place in geometry as well as in physical applications&lrm;. &lrm;In this paper&lrm;, &lrm;we consider the Siklos spacetimes and we determine all the Ricci bi-conformal vector fields on these spaces&lrm;.A Gauge Theory for Extra Dimension Detecting by Point Particle
https://mir.kashanu.ac.ir/article_114197.html
&lrm;From the viewpoint of&lrm; "&lrm;extra dimension detecting,&lrm;" &lrm;the phenomenon of the transition of the free point particle into 3d space is investigated&lrm;. &lrm;In this way&lrm;, &lrm;we formulate the problem using the second-class constrained system&lrm;. &lrm;To investigate it using a gauge theoretical approach&lrm;, &lrm;we use two methods to convert its two second-class constraints to first-class ones&lrm;. &lrm;In symplectic embedding&lrm;, &lrm;we construct a pair of scaler and vector gauge potentials&lrm;, &lrm;which can be interpreted as interactions for detecting extra dimensions&lrm;. &lrm;A Wess-Zumino variable appears as a new coordinate in potentials&lrm;, &lrm;and the particle's mass plays the role of a globally conserved charge related to the constructed gauge theory for extra dimensions&lrm;.A Hidden Markov Model Based Extended Case-Based Reasoning Algorithm for Relief Materials Demand Forecasting
https://mir.kashanu.ac.ir/article_114202.html
&lrm;In emergency situations&lrm;, &lrm;accurate demand forecasting for relief materials such as food&lrm;, &lrm;water&lrm;, &lrm;and medicine is crucial for effective disaster response&lrm;. &lrm;This research is presented a novel algorithm to demand forecasting for relief materials using extended Case-Based Reasoning (CBR) with the best-worst method (BWM) and Hidden Markov Models (HMMs)&lrm;. &lrm;The proposed algorithm involves training an HMM on historical data to obtain a set of state sequences representing the temporal fluctuations in demand for different relief materials&lrm;. &lrm;When a new disaster occurs&lrm;, &lrm;the algorithm first determines the current state sequence using the available data and searches the case library for past disasters with similar state sequences&lrm;. &lrm;The effectiveness of the proposed algorithm is demonstrated through experiments on real-world disaster data of Iran&lrm;. &lrm;Based on the results&lrm;, &lrm;the forecasting error index for four relief materials is less than 10\%; therefore&lrm;, &lrm;the proposed CBR-BWM-HMM is a strong and robust algorithm&lrm;.&nbsp;Some Remarks on the Annihilating-Ideal Graph of Commutative Ring with Respect to an Ideal
https://mir.kashanu.ac.ir/article_114213.html
&lrm;The graph $ AG ( R ) $ {of} a commutative ring $R$ with identity has an edge linking two unique vertices when the product of the vertices equals {the} zero ideal and its vertices are the nonzero annihilating ideals of $R$&lrm;.&lrm;The annihilating-ideal graph with {respect to} an ideal $ ( I ) $, &lrm;which is {denoted} by $ AG_I ( R ) $&lrm;, &lrm;has distinct vertices $ K $ and $ J $ that are adjacent if and only if $ KJ\subseteq I $&lrm;. &lrm;Its vertices are $ \{K\mid KJ\subseteq I\ \text{for some ideal}\ J \ \text{and}\ K$&lrm;, &lrm;$J \nsubseteq I&lrm;, &lrm;K\ \text{is a ideal of}\ R\} $&lrm;. &lrm;The study of the two graphs $ AG_I ( R ) $ and $ AG(R/I) $ and {extending certain} prior findings are two main objectives of this research&lrm;. &lrm;This studys {among other things&lrm;, &lrm;the} findings {of this study reveal}&lrm;&lrm;that $ AG_I ( R ) $ is bipartite if and only if $ AG_I ( R ) $ is triangle-free&lrm;.