University of KashanMathematics Interdisciplinary Research2538-36391220160701Motion of Particles under Pseudo-Deformation2732773410810.22052/mir.2016.34108ENAkhilesh ChandraYadavM G Kashi Vidyapith VaranasiJournal Article20160401In this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{A}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{A}(t)) dt +mathbf{c}$. We also observe that the effective force $mathbf{F}_e$ on that particle due to pseudo-force $mathbf{A}(t)$, is given by $ mathbf{F}_e= mathbf{F} mathbf{A}(t)+ mathbf{L} dmathbf{A}(t)/dt$, where $mathbf{F}= m d^2mathbf{r}/dt^2 $ and $mathbf{L}= m dmathbf{r}/dt$. We have discussed stream lines under pseudo-force.http://mir.kashanu.ac.ir/article_34108_1020df1e5666b6a0fea4c5f804264b84.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36391220160701C-Class Functions and Remarks on Fixed Points of Weakly Compatible Mappings in G-Metric Spaces Satisfying Common Limit Range Property2792903410610.22052/mir.2016.34106ENArslanHojat AnsariDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran,DianaDolicanin-DekicFaculty of Technical Science, 38000 Kosovska Mitrovica,FengGuInstitute of Applied Mathematics and
Department of Mathematics,
Hangzhou Normal University, Hangzhou, Zhejiang 310036,BranislavPopovic4Faculty of Science, University of Kragujevac, Radoja Domanovica 12, 34000 Kragujevac, Serbia,Stojan NRadenovicFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, SerbiaJournal Article20160409In this paper, using the contexts of C-class functions and common limit<br />range property, common fixed point result for some operator are obtained.<br />Our results generalize several results in the existing literature. Some examples<br />are given to illustrate the usability of our approach.http://mir.kashanu.ac.ir/article_34106_f7148aa5b4661811ab50e7cd0cffd3d4.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36391220160701Unconditionally Stable Difference Scheme for the Numerical Solution of Nonlinear Rosenau-KdV Equation2913041551210.22052/mir.2016.15512ENAkbarMohebbiUniversity of KashanZahraFarazUniversity of KashanJournal Article20151010In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method. In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method. In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method.http://mir.kashanu.ac.ir/article_15512_124ceee6f307b4edb7a77d6025a2e5e1.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36391220160701Wiener Polarity Index of Tensor Product of Graphs3053163410910.22052/mir.2016.34109ENMojganMogharrabPersian Gulf UniversityRezaSharafdiniPersian Gulf UniversitySomayehMusaviMathematics House of BushehrJournal Article20160704Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index of a graph G is denoted by W_P (G) is the number of unordered pairs of vertices of distance 3. The Wiener polarity index is used to demonstrate quantitative structure-property relationships in a series of acyclic and cycle-containing hydrocarbons. Let G,H be two simple connected graphs. Then the tensor product of them is denoted by G⨂H whose vertex set is V(G⨂H)=V(G)×V(H) and edge set is E(G⨂H)={(a,b)(c,d)| ac∈E(G) ,bd∈E(H) }. In this paper, we aim to compute the Wiener polarity index of G⨂H which was computed wrongly in [J. Ma, Y. Shi and J. Yue, The Wiener Polarity Index of Graph Products, Ars Combin., 116 (2014) 235-244].http://mir.kashanu.ac.ir/article_34109_2979030b6f901a9245e59b804f53aab3.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36391220160701Diameter Two Graphs of Minimum Order with Given Degree Set3173233410710.22052/mir.2016.34107ENGholamrezaAbrishamiFerdowsi University of MashhadFreydoonRahbarniaFerdowsi University of MashhadIrandokhtRezaeeFerdowsi University of MashhadJournal Article20160502The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for a given set of natural numbers greater than one, we determine the minimum order of a 2-self-centered graph with that degree set.http://mir.kashanu.ac.ir/article_34107_f8c714c2b1ea6bcadfdfe4ef88683da2.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36391220160701Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions3253343385010.22052/mir.2016.33850ENSeyfollahMosazadehUniversity of KashanJournal Article20160507In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem. Finally, by the sequence of orthogonal eigenfunctions, we provide the eigenfunction expansions for twice continuously differentiable functions.http://mir.kashanu.ac.ir/article_33850_0af3a4d1236273501fd68bad66d189f3.pdf