فهرست مطالب

  • Volume:14 Issue: 2, 2019
  • تاریخ انتشار: 1398/07/09
  • تعداد عناوین: 15
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  • M. Bataineh*, R. Abu, Dawwas Pages 1-8

    Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce  several results. We introduced several characterizations for graded $r$-ideals;  we proved that $P$ is a graded $r$-ideal of $R$ if and only if $aP=aRbigcap P$  for all $ain h(R)$ with $Ann(a)={0}$. Also, $P$ is a graded $r$-ideal of $R$  if and only if $P=(P:a)$ for all $ain h(R)$ with $Ann(a)={0}$. Moreover,  $P$ is a graded $r$-ideal of $R$ if and only if whenever $A, B$ are graded ideals of   $R$ such that $ABsubseteq P$ and $Abigcap r(h(R))neqphi$, then $Bsubseteq P$.    In this article, we introduce the concept of $huz$-rings. A graded ring $R$    is said to be $huz$-ring if every homogeneous element of $R$ is either a zero       if every graded ideal of $R$ is a graded $r$-ideal. Moreover, assuming that  $R$ is a graded domain, we proved that ${0}$ is the only graded $r$-ideal of $R$.

    Keywords: Graded prime ideals, Graded r-ideals
  • S. P.* Pages 9-18

    In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

    Keywords: $mu$-Open, $mu$-Closed, Generalized topology, Homogeneous, Hereditarily homogeneous GTS, Highly transitive permutation groups, Bihomogeneous
  • F. Nikbakhtsarvestani, S. M. Vaezpour, M. Asadi* Pages 19-32

    The purpose of this paper is to obtain the common fixed point results for two pair of weakly compatible mapping by using common (CLR) property in partial metric space. Also we extend the very recent results which are presented in [17,  Muhammad Sarwar, Mian Bahadur Zada and Inci M. Erhan, Common Fixed Point Theorems of Integral type on Metric Spaces and application to system of functional equations, Fixed point theory and applications, 2015, 2015:217] with proofing a new version of the continuity of partial
    metric.

    Keywords: Fixed point, Partial metric space, (CLR)-Property
  • M. Saraj*, A. Sadeghi, N. Mahdavi Pages 33-42

    We consider a fractional program with both linear and quadratic equation in numerator and denominator  having second order cone (SOC) constraints. With a suitable change of variable, we transform the problem into a  second order cone programming (SOCP)  problem.
     For the quadratic fractional case, using a relaxation, the problem is reduced to a semi-definite optimization (SDO) program. The problem is solved with SDO relaxation and the obtained results are compared with the interior point method (IPM), a sequential quadratic programming (SQP) approach, an active set strategy and a genetic algorithm. It is observed that the SDO relaxation method is much more accurate and faster than the other methods. Finally,a few numerical examples are worked through to demonstrate the applicability of the procedure.

    Keywords: Fractional Programming, Second Order Cone, SDP Relaxation
  • A. Khan*, V. Sharma Pages 43-60

    In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated.

    Keywords: $(p, q)$-Integers, Lupac{s} $(p, q)$-Bernstein Stancu operators, Statistical approximation, Korovkin's type approximation
  • M. Mortazavizadeh, R. Raisi Tousi*, R. A. Kamyabi Gol Pages 61-67

    In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

    Keywords: Locally compact abelian group, Translation invariant space, Translation metric
  • R. Hossinikomlaei*, M. ‎Jahanshahi, A. Pashavand, N. Aliev Pages 69-77

    In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional derivative. The peresented solutions for these problems are as infinite series. ‎Convergence‎ of series solutions and uniqueness of them are stablished by general theory of mathematical analysis and theory of ODEs.

    Keywords: Mittag-Lefller function‎, Fractional partial differential equation‎, Non local boundary condition
  • Zhen, Bin Gaoa, Ruo, Yuan Hana, Sin, Min Leeb, Hong, Nan Rena, Gee, Choon Lauc* Pages 79-92

    Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G$ is said to be friendly if $| v_{f}(1)-v_{f}(0) | leq 1$. The friendly index set of the graph $G$, denoted by $FI(G)$, is defined as  ${|e_{f^+}(1) - e_{f^+}(0)|$ : the vertex labeling $f$ is friendly$}$. The full friendly index set of the graph $G$, denoted by $FFI(G)$, is defined as ${e_{f^+}(1) - e_{f^+}(0)$ : the vertex labeling $f$ is friendly$}$. A graph $G$ is cordial if $-1, 0$ or $1in FFI(G)$. In this paper, by introducing labeling subgraph embeddings method, we determine the cordiality of a family of cubic graphs which are double-edge blow-up of $P_2times P_n, nge 2$. Consequently, we completely determined friendly index and full product cordial index sets of this family of graphs.

    Keywords: Vertex labeling, Full friendly index set, Cordiality, $P, 2$-embeddings, $C, 4$-embeddings
  • E. Peyghan*, F. Firuzi, Y. Alipour Pages 93-104

    We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficient for the g-natural metric G̃ to
    be locally symmetric.

    Keywords: Almost contact structure, B-metrics, g-natural metrics, Local symmetry, Sphere bundle
  • H. Ramane, G. Gudodagi, V. Manjalapur*, A. Alhevaz Pages 105-125

    Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in V(G)}[1+D-d_G(u, v)]$. Let $CT(G)=diag[CT_G(v_1), CT_G(v_2), ldots, CT_G(v_n)]$. The complementary distance signless Laplacian matrix of $G$ is $CDL^+(G)=CT(G)+CD(G)$.

    If $rho_1, rho_2, ldots, rho_n$ are the eigenvalues of $CDL^+(G)$ then the complementary distance signless Laplacian energy of $G$ is defined as $E_{CDL^+}(G)=sum_{i=1}^{n}left| rho_i-frac{1}{n}sum_{j=1}^{n}CT_G(v_j)right|$.
    noindent In this paper we obtain the bounds for the largest eigenvalue of $CDL^+(G)$. Further we determine Nordhaus-Gaddum type results for the largest eigenvalue. In the sequel we establish the bounds for the complementary distance signless Laplacian energy.}

    Keywords: Complementary distance matrix, Complementary distance signless Laplacian eigenvalues, Complementary distance signless Laplacian energy, Diameter
  • R. Daskalov*, E. Metodieva Pages 127-138

    An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  PG(2, q) is denoted by $m_r(2,q)$. In this paper thirteen new $(n, r)$-arc in  PG(2,,29) and a table with the best known lower and upper bounds on $m_r(2,29)$ are presented. The results are obtained by non-exhaustive local computer search.

    Keywords: Finite projective plane, $(n, r)$-Arc in a projective plane, $(l, t)$-Blocking set in a projective plane, Maximum size of an $(n, r)$-arc
  • M. Amini*, F. Hassani Pages 139-151

    In this paper, a new homological dimension of modules, copresented dimension, is defined. We study some basic properties of this homological dimension. Some ring extensions are considered, too. For instance, we prove that if $Sgeq R$ is a finite normalizing extension and $S_R$ is a projective module, then for each right $S$-module $M_S$, the copresented dimension of $M_S$ does not exceed the copresented dimension of $Hom_{R}(S,M)$.

    Keywords: Coherent ring‎, ‎Copresented‎, ‎Dimension‎, ‎Projective module
  • H. Safa* Pages 153-156

    In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.

    Keywords: Minimal number of generators, Nilpotency class, Nilpotent Lie algebra
  • A. Rastegar* Pages 157-171

    By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number fields. We also introduce Hecke-Teichmuller Lie algebra which plays the role of Hecke algebra in the anabelian framework.

    Keywords: Anabelian geometry, Grothendieck conjectures, Huperbolic curves, Outer automorphism, Galois representation
  • J. Kok*, K.A. Germina Pages 173-184

    In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and certain derivative split graphs.

    Keywords: Chromatic harmonic index, Chromatic harmonic polynomial, Split graph, Derivative split graph