Iranian Journal of Mathematical Sciences and InformaticsIranian Journal of Mathematical Sciences and Informatics
http://iranjournals.nlai.ir/1315/
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http://iranjournals.nlai.ir/1315/
Feed provided by Iranian Journal of Mathematical Sciences and Informatics. Click to visit.Graded r-Ideals
http://iranjournals.nlai.ir/1315/article_601576_48438.html
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
divisor or a unit. In fact, we proved that $R$ is a $huz$-ring if and only
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 $R$.Hereditarily Homogeneous Generalized Topological Spaces
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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 $X$.Common Fixed Point Theorems for Weakly Compatible Mappings by (CLR) Property on Partial Metric Space
http://iranjournals.nlai.ir/1315/article_601578_48438.html
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.Solving A Fractional Program with Second Order Cone Constraint
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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.Approximation by $(p,q)$-Lupac{s} Stancu Operators
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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.On a Metric on Translation Invariant Spaces
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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.The Study of Some Boundary Value Problems Including Fractional Partial ...
http://iranjournals.nlai.ir/1315/article_601582_48438.html
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.Labeling Subgraph Embeddings and Cordiality of Graphs
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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.Local Symmetry of Unit Tangent Sphere Bundle With g- Natural Almost Contact B-Metric Structure
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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.On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs
http://iranjournals.nlai.ir/1315/article_601585_48438.html
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.}Bounds on $m_r(2,29)$
http://iranjournals.nlai.ir/1315/article_601586_48438.html
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.Copresented Dimension of Modules
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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 $Hom_{R}(S,M)$.A Bound for the Nilpotency Class of a Lie Algebra
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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.Arithmetic Teichmuller Theory
http://iranjournals.nlai.ir/1315/article_601589_48438.html
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.Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs
http://iranjournals.nlai.ir/1315/article_601590_48438.html
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.