فهرست مطالب
Iranian Journal of Mathematical Sciences and Informatics
Volume:15 Issue: 1, May 2020
- تاریخ انتشار: 1399/03/17
- تعداد عناوین: 13
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Pages 1-13
Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength of graph G and denoted by tes(G). In this paper, we determine the exact value of total edge irregularity strength for staircase graphs, double staircase graphs and mirror-staircase graphs.
Keywords: Total edge irregularity strength, Staircase graphs, Double staircase graphs, Mirror-staircase graphs -
Pages 15-21
Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is not greater than 500. We exhibit a collection of (probably infinitely many) rational numbers k for which this Diophantine equation is satisfied. Finally, appealing these observations, we conjecture that the above result is true for all rational numbers k.
Keywords: Diophantine equation, Elliptic curve -
Pages 23-34
It is well-known that the sum of two $z$-ideals in $C(X)$ is either $C(X)$ or a $z$-ideal. The main aim of this paper is to study the sum of strongly $z$-ideals in ${mathcal{R}} L$, the ring of real-valued continuous functions on a frame $L$. For every ideal $I$ in ${mathcal{R}} L$, we introduce the biggest strongly $z$-ideal included in $I$ and the smallest strongly $z$-ideal containing $I$, denoted by $I^{sz}$ and $I_{sz}$, respectively. We study some properties of $I^{sz}$ and $I_{sz}$. Also, it is observed that the sum of any family of minimal prime ideals in the ring ${mathcal{R}} L$ is either ${mathcal{R}} L$ or a prime strongly $z$-ideal in ${mathcal{R}} L$. In particular, we show that the sum of two prime ideals in ${mathcal{R}} L$ such that are not a chain, is a prime strongly $z$-ideal.the formula is not displayed correctly!
Keywords: Frame, Ring of real-valued continuous functions, z-Ideal, Strongly z-ideal -
Pages 35-40
Let $p=(q^4+q^3+q^2+q+1)/(5,q-1)$ be a prime number, where $q$ is a prime power. In this paper, we will show $Gcong mathrm{PSL}(5,q)$ if and only if $|G|=|mathrm{PSL}(5,q)|$, and $G$ has a conjugacy class size $frac{| mathrm{PSL}(5,q)|}{p}$. Further, the validity of a conjecture of J. G. Thompson is generalized to the groups under consideration by a new way. the formula is not displayed correctly!
Keywords: Conjugacy class size, Prime graph, Thompson's conjecture -
Pages 41-52
In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a Banach contractive type mapping in algebraic cone metric spaces associated with an algebraic distance and endowed with a graph.
Keywords: Algebraic cone metric space, Algebraic distance, Banach contraction, Orbitally G-continuous mapping -
Pages 53-63
The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.
Keywords: Torsion modules, Artinian module, Prime submodules -
Pages 65-78
We consider four-dimensional lie groups equipped with left-invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields defining harmonic maps, and calculate explicitly the energy of these vector fields. Then we study the minimality of critical points for the energy functional.
Keywords: Harmonic vector fields, Harmonic maps, Einstein metrics, Lie group, Pseudo-Riemannian homogeneous spaces -
Pages 79-83
In this note, we give some estimates of the generalized quadratureformula of Gauss-Jacobi type for phi-preinvex functions.
Keywords: Integral inequality, $varphi $-preinvex function, H ̈older inequality, powermean inequality -
Pages 85-97
In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups .Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.
Keywords: n-ary Semihypergroup, G-system, Greens relations -
Pages 99-109
In some fields, there is an interest in distinguishing different geometrical objects from each other. A field of research that studies the objects from a statistical point of view, provided they are invariant under translation, rotation and scaling effects, is known as the statistical shape analysis. Having some objects that are registered using key points on the outline of the objects, the main purpose of this paper is to compare two popular clustering procedures to cluster objects. We also use some indexes to evaluate our clustering application. The proposed methods are applied to the real life data.
Keywords: Shape, Clustering, K-means, Model-based, Landmark -
Pages 111-124
The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.
Keywords: Fixed point, Weak contraction, Partially ordered space, Modular metric space -
Pages 125-133
begin If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems.the formula is not displayed correctly!
Keywords: Prime (Semiprime) ring, Additive mappings, Generalized (Jordan) left derivations, Generalized (Jordan) derivations, (Jordan)Centralizers -
Pages 135-159
A mathematical model describing the dynamics of a delayed stage structure prey - predator system with prey refuge is considered. The existence, uniqueness and bounded- ness of the solution are discussed. All the feasibl e equilibrium points are determined. The stability analysis of them are investigated. By employ ing the time delay as the bifurcation parameter, we observed the existence of Hopf bifurcation at the positive equilibrium. The stability and direction of the Hopf bifurcation are determined by utilizing the normal form method and the center manifold reduction. Numerical simulations are given to support the analytic results.
Keywords: Delayed Prey - Predator System_Stage- Structure_Refuge_Stability_Hop f Bifurcation