Caspian Journal of Mathematical Sciences
Volume:13 Issue: 2, Summer Autumn 2024

Let $\pounds$ be a lattice with $1$ and $0$. The co-identity join graph of $\pounds$, denoted by $\mathbb{CG} (\pounds)$, is an undirected simple graph whose vertices are all nontrivial elements (i.e. different from $1$ and $0$) of $\pounds$ and two distinct elements $x$ and $y$ are adjacent if and only if $x \vee y \neq 1$. The basic properties and possible structures of this graph are studied and the interplay between the algebraic properties of $\pounds$ and the graph-theoretic structure of $\mathbb{CG} (\pounds)$ is investigated.\\

Exponential partial Bell polynomials are a main tool for computing explicit formula for a large family of numbers and polynomials. Using these polynomials, we review most of the polynomials already studied in the book of Djordjevic-Milovanovic (2014). This study allows to unify the writing of these polynomials and obtain other extensions. Consequently the obtained results find their application in Number Theory; notably for the arithmetical properties of power products, Fermat numbers, Mersenne numbers and Fermat Last Theorem.

The most important part of the hydrological cycle is precipitation. The study aimed to forecast rainfall with a time series model. Many studies have been done, but we want to predict annual rainfall in Kashan. Annual rainfall of 53 years was collected from Kashan (office of Meteorology) from spring 1967 to winter 2019. We predicted the amount of annual rainfall from 2020 to 2023. The method of data analysis is that the time series models are fitted to the data using statistical package for the social science (SPSS) statistical software (also, we used R and MINITAB software). The average annual rainfall is 133.70 mm with a standard deviation of 49.32 mm. The best model is ARIMA (0,0,1). In the selected model, AIC and BIC are equal to 564.64 and 570.55, respectively. Our prediction results show a significant drop in rainfall in these four years. Since Kashan is one of the arid and semi-arid regions, we will face the problem of water shortage, so water consumption must be saved.

The object of this article is to investigate some geometric conditions for an invariant submanifold of a hyperbolic Sasakian manifold. Additionally, we take into account a generalized quasiconformal curvature tensor on an invariant submanifold of a hyperbolic Sasakian manifold to be totally geodesic with certain geometric restrictions. Further we explore the characteristics of the conformal eta-Ricci-Yamabe soliton on such submanifold. In addition, we construct an example to verify our results.

‎This article examines the transmission of COVID-19 from a mathematical model perspective‎, ‎analyzing its spread pattern‎. ‎Given the virus's adherence to standard epidemic disease transmission principles and the effectiveness of vaccination in mitigating and controlling its spread‎, ‎we employ the SVIR model to demonstrate the disease's progression in Yazd‎. ‎The data used in this study was provided by the medical care monitoring center of Yazd Shahid Sadoughi University of Medical Sciences‎, ‎Yazd‎, ‎Iran‎, ‎for 770 days between September 27‎, ‎2020 to November 5‎, ‎2022‎. To establish thelparameters‎, ‎we utilized the genetic algorithm (GA) to minimize the cost function between the model's prediction and the real data‎.‎Additionally‎, ‎we conducted our simulations using Matlab software‎. ‎Identifying the factors that contribute to the spread of the virus through mathematical modeling can be a crucial step towards controlling the disease‎, ‎given its catastrophic impact on the economy‎, ‎society‎, ‎and health‎.

Given a discrete semi-group $S$, we define a topological action $\theta$ of S on a locally compact space $X$. Additionally, there is an action α of $S$ on the $C^∗$-algebra $C0(X)$, which is introduced in relation to $θ$. We explore the topological independence of $\theta$ and the impact of $\theta$ on α. Finally, we discuss the concept of a semi-partial dynamical system $(C0(X), S, \alpha)$ and examine some of its properties.

‎‎Our focus in this paper is on numerically solving fourthorder time-fractional integro-dierential equations with weakly  singular kernels. L1 and quadrature formulas are used to discretize  the temporal and memory terms. For spatial discretization, a highorder local discontinuous Galerkin method is employed. Finally, the numerical optimal convergence rate for the proposed scheme is demonstrated by the use of numerical results.

Our current investigation is primarily motivated by the application of special polynomials in Geometric Function Theory (GFT). This paper aims to utilize (M,N)-Lucas polynomials to estimate the initial coefficient bounds for a subclass of bi-univalent functions consisting of normalized analytic functions. We then derive the famous Fekete-Szegö inequality estimate. We also establish connections between our results and those examined in previous investigations.

In this paper, we introduce the definition of (σ, τ ) − e-reversible ring. Precisely, take R is a e-reversible ring such that σ and τ are automorphism mappings of R, we named R is (σ, τ ) − e-reversible ring if σ(x)τ (y) = 0 leads to τ (y)σ(x)e = 0, where x, y ∈ R. In fact, we seek and characterize the various properties of (σ, τ )-e-reversible rings.

Topological indices of graphs are numerical descriptors that determine the relationship between the properties of  molecules and their structures. In this paper, we introduce three novel vertex degree-based topological indices that show a good correlation with the Sombor index. We have also derived bounds for them, identified the relationship between them and other topological indices, and finally examined their ability to predict some physico-chemical properties of octane isomers.

We consider the existence of positive solutions of singular nonlinear semipositone problem of the form \[\left\{\begin{array}{ll} -div(|x|^{-\alpha p}|\nabla u|^{p-2}\nabla u)=|x|^{-(\alpha+1)p+\beta}(au^{p-1}-bu^{r}-f(u)-\frac{c}{u^{\gamma}}), & x\in\Omega, \\ u=0, & x\in\partial\Omega, \end{array}\right.\]where $\Omega$ is a bounded domain in ${\mathbb{R}}^{N}$ with smooth boundary $\partial\Omega$, $1p-1 $,$\gamma\in (0,1)$, $a,b,c,\beta$ are positive parameters, and $f:[0,+\infty)\to{\mathbb{R}}$ is a continuous function . This model arises in the studies of population biology of one specieswith u representing the concentration of the species. We obtain our results via the method of sub and supersolutions.