eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2016-07-01
1
2
273
277
10.22052/mir.2016.34108
34108
Motion of Particles under Pseudo-Deformation
Akhilesh Yadav
akhileshyadav538@gmail.com
1
M G Kashi Vidyapith Varanasi
In 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.pdf
Right loops
right transversals
gyrotransversals
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2016-07-01
1
2
279
290
10.22052/mir.2016.34106
34106
C-Class Functions and Remarks on Fixed Points of Weakly Compatible Mappings in G-Metric Spaces Satisfying Common Limit Range Property
Arslan Hojat Ansari
analsisamirmath2@gmail.com
1
Diana Dolicanin-Dekic
dolicanin_d@yahoo.com
2
Feng Gu
gufeng99@sohu.com
3
Branislav Popovic
bpopovic@kg.ac.rs
4
Stojan Radenovic
radens@beotel.rs
5
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran,
Faculty of Technical Science, 38000 Kosovska Mitrovica,
Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036,
4Faculty of Science, University of Kragujevac, Radoja Domanovica 12, 34000 Kragujevac, Serbia,
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia
In 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.pdf
Generalized metric space
common fixed point
generalized weakly G-contraction
weakly compatible mappings
common (CLRST ) property
C-class functions
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2016-07-01
1
2
291
304
10.22052/mir.2016.15512
15512
Unconditionally Stable Difference Scheme for the Numerical Solution of Nonlinear Rosenau-KdV Equation
Akbar Mohebbi
a_mohebbi@kashanu.ac.ir
1
Zahra Faraz
zahrafaraz44@yahoo.com
2
University of Kashan
University of Kashan
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. 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.pdf
Finite difference scheme
solvability
unconditional stability
Convergence
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2016-07-01
1
2
305
316
10.22052/mir.2016.34109
34109
Wiener Polarity Index of Tensor Product of Graphs
Mojgan Mogharrab
mmogharab@gmail.com
1
Reza Sharafdini
sharafdini@gmail.com
2
Somayeh Musavi
smusavi92@gmail.com
3
Persian Gulf University
Persian Gulf University
Mathematics House of Bushehr
Mathematical 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.pdf
topological index
Wiener polarity index
tensor product
Graph
Distance
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2016-07-01
1
2
317
323
10.22052/mir.2016.34107
34107
Diameter Two Graphs of Minimum Order with Given Degree Set
Gholamreza Abrishami
gh.abrishamimoghadam@stu.um.ac.ir
1
Freydoon Rahbarnia
rahbarnia@um.ac.ir
2
Irandokht Rezaee
iran_re899@yahoo.com
3
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
The 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.pdf
Degree set
self-centered graph
radius
diameter
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2016-07-01
1
2
325
334
10.22052/mir.2016.33850
33850
Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
Seyfollah Mosazadeh
s.mosazadeh@kashanu.ac.ir
1
University of Kashan
In 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
Boundary value problem
Eigenvalue
eigenfunction
completeness
eigenfunction expansion