### فهرست مطالب • Volume:42 Issue:3, 2016
• تاریخ انتشار: 1395/04/10
• تعداد عناوین: 20
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• H. Hosseinzadeh, N. Soltankhah* Pages 499-506
ýLet G=(V(G),E(G)) be a graphý, ýγ t (G) . Let ooir(G) be the total domination and OO-irredundance number of G ý, ýrespectivelyý. ýA total dominating set S of G is called a total perfect code if every vertex in V(G) is adjacent to exactly one vertex of S ý. ýIn this paperý, ýwe show that if G has a total perfect codeý, ýthen γ t (G)=ooir(G) ý. ýAs a consequence, we determine the value of ooir(G) for some classes of graphsý.
Keywords: Total domination number, OOý, ýirredundance numberý, total subdivision number
• PÝ. Ý Zhao*, C. Ýzhao Pages 507-519
• A. Ebadian, S. Rahrovi, S. Shams, J. Sokol* Pages 521-537
We determine theý ýform of polynomially bounded solutions to the Loewner differential ýequation that is satisfied by univalent subordination chains of theý ýform f(z,t)=e∫t0A(τ)dτz⋯ý, ýwhereý ýA:[0,∞]→L(Cn,Cn) is a locallyý ýLebesgue integrable mapping and satisfying the conditioný ý
sups≥0∫∞0∥∥∥exp{∫tsýý[A(τ)−2m(A(τ))In]dτ}∥∥∥dt0 for t≥0ý, ýwhereý ým(A)=min{Re⟨ýýA(z),z⟩:∥z∥=1}ý. ýWe also give sufficient conditionsý ýfor g(z,t)=M(f(z,t)) to be polynomially boundedý, ýwhere f(z,t) isý ýan A(t)-normalized polynomially bounded Loewner chain solution toý ýthe Loewner differential equation and M is an entire functioný. ýOn ýthe other handý, ýwe show that all A(t)
-normalized polynomiallyý ýbounded solutions to the Loewner differential equation are Loewnerý ýchains.ý
Keywords: Biholomorphic mappingý, ýLoewnerý ýdifferential equationý, ýpolynomially boundedý, ýsubordination chainý, ýparametric representation
• X. F. Qi* Pages 539-554
Let A and B be unital ringsý, ýand Mý ýbe an (Aý,ýB)-bimoduleý, ýwhich is faithful as aý ýleft A-module and also as a right B-moduleý. ýLet U=\rm Tri(Aý,ýMý,ýýýB) be the triangular ring and Z(U) itsý ýcenterý. ýAssume that f:U→U is a mapý ýsatisfying f(x)−f(x)−f(y)∈Z(U) for allý ýx, y∈U and k is a positive integerý. ýIt is showný ýthatý, ýunder some mild conditionsý, ýthe following statements areý ýequivalentý: ý(1) [f(x),xk]∈Z(U) for allý ýx∈U; (2) [f(x),xk]=0 for all x∈U;ý ý(3) [f(x),x]=0 for all x∈U; (4) there exist aý ýcentral element z∈Z(U) and an additiveý ýmodulo Z(U) map h:ýýU→Z(U) such that f(x)=zx(x)ý ýfor all x∈Uý. ýIt is also shown that there is noý ýnonzero additive k-skew-centralizing maps on triangular rings.
Keywords: Triangular ringsý, ýcentralizing mapsý, ýk, skew, centralizing mapsý, ýnest algebrasý
• R. Nekooei*, F. Mirzaei Pages 555-563
In this paper we characterize the radical of an arbitraryý ýsubmodule N of a finitely generated free module F over aý ýcommutatitve ring R with identityý. ýAlso we study submodules ofý ýF which satisfy the radical formulaý. ýFinally we deriveý ýnecessary and sufficient conditions for R to be aý ýPru¨fer domainý, ýin terms of the radical of aý ýcyclic submodule in R⨁R.
Keywords: ýPrime submodulesý, ýRadical of a submoduleý, ýRadical formulaý, ýPru¨fer domainsý, ýDedekindý ýdomains
• M. Zarei, S.M.B. Kashani*, H. Abedi Pages 565-584
In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo- topy groups of the orbits have been presented as well.
Keywords: ýPýositively curved manifoldý, ýirreducible representationý, ýcohomogeneity one action
• H. Daghigh*, S. Didari Pages 585-594
The Mordell-Weil theorem states that the group of rational pointsý ýon an elliptic curve over the rational numbers is a finitelyý ýgenerated abelian groupý. ýIn our previous paper, Hý. ýDaghighý, ýand Sý. ýDidariý, On the elliptic curves of the form y2=x3−3pxý, ýýBullý. ýIranian Mathý. ýSocý.ýý 40 (2014)ý, noý. ý5ý, ý1119--1133ý.ý, ýusing Selmer groupsý, ýwe have shown that for a prime p the rank of elliptic curve y2=x3−3px is at most twoý. ýIn thisý ýpaper we go furtherý, ýand using height functioný, ýwe will determine the Mordell-Weil group of aý ýfamily of elliptic curves of the form y2=x3−3nx
ý, ýand giveý ýa set of its generators under certain conditionsý. ýWe willý ýintroduce an infinite family of elliptic curves with rank at leastý ýtwoý. ýThe full Mordell-Weil group and the generators of aý ýfamily (which is expected to be infinite under the assumption of a standard conjecture) of elliptic curves with exact rank two will be describedý.
Keywords: ýElliptic Curve, Mordell, Weil Group, Generators, Height Function
• X. Liu, J. Benitez*, M. Zhang Pages 595-610
In this article, we characterize the involutiveness of the linear combination of the form a1A1 歠 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix, and A2 is arbitrary, under certain properties imposed on A1 and A2.
Keywords: Quadratic matrix, involutive matrix, linear combination
• Y. Jalilian* Pages 611-626
In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.
Keywords: Infinitely many solutions, Nehari manifold, sign, changing weight function, Bi, nonlocal equation
• S. Ebrahimi Atani, M. Khoramdel*, S. Dolati Pish Hesari Pages 627-642
We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) R-module is T-dual Rickart if and only if overlineZ2(R) is a direct summand of R and End(overlineZ2(R)) is a semisimple (resp. regular) ring. It is shown that, while a direct summand of a (strongly) T-dual Rickart module inherits the property, direct sums of T-dual Rickart modules do not. Moreover, when a direct sum of T-dual Rickart modules is T-dual Rickart, is included. Examples illustrating the results are presented.
Keywords: Dual Rickart modules, t, lifting modules, t, dual Baer modules, T, dual Rickart modules, strongly T, dual Rickart modules
• H. Tang*, C. Liu, Z. Zhao Pages 643-658
In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0
Keywords: Cahn, Hilliard, Allen, Cahn equationý, ýexistenceý, ýglobal attractorý
• F. Zhang*, X. Qi, J. Ýzhang Pages 659-678
Let mathcalM be a factor von Neumann algebra. It is shown that every nonlinear ∗-Lie higher derivation D=phinninmathbbN on mathcalM is additive. In particular, if mathcalM is infinite type I factor, a concrete characterization of D is given.
Keywords: von Neumann algebra, nonlinear ∗ Lie higher derivation, additive ∗ higher derivation
• M. R. Fander* Pages 679-685
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipartite or weakly chordal graph.
Keywords: Castelnuovo, Mumford regularity, Induced matching number, Cochordal cover number
• A. Shokri*, H. Saadat Pages 687-706
Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the radial Schrodinger equation is used frequently. In the present paper we will study a symmetric two-step Obrechkoff method, in which we will use of technique of VSDPL (vanished some of derivatives of phase-lag), for the numerical integration of the one-dimensional Schrodinger equation. We will show superiority of new method in stability, accuracy and efficiency. So we present a stability analysis and an error analysis based on the radial Schrodinger equation. Also we will apply the new proposed method to the resonance problem of the radial Schrodinger equation.
Keywords: P, stable, Phase, lag, Schr{o}dinger equation, trigonometrically fitted
• M. Soleimani, Damaneh*, M. Movahedi, D. Behmardi Pages 707-717
In this paper, we deal with the subdi erential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and nec- essary and sucient conditions are presented to prove that the subdif- ferential set in Hadamard spaces is nonempty. Proximal subdi erential in Hadamard spaces is addressed and some basic properties are high- lighted. Finally, a density theorem for subdi erential set is established.
Keywords: Subdiff erential, Hadamard Space, Flat space, Hilbert space, Convexity
• W. Zhu, S. Ling* Pages 719-730
Let C be a nonempty closed convex subset of a real Hilbert space H. Let Sn and Tn be sequences of nonexpansive self-mappings of C, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process xn=betanxn(1−betan)Sn(alphanu(1−alphan)Tnxn) for finding the common fixed point of Sn and Tn, where uinC is an arbitrarily (but fixed) element in C, x0inC
arbitrarily, alphan and betan are sequences in [0,1]. But in the case where unotinC, the iterative scheme above becomes invalid because xn may not belong to C. To overcome this weakness, a new iterative scheme based on the thought of boundary point method is proposed and the strong convergence theorem is proved. As a special case, we can find the minimum-norm common fixed point of Sn and Tn whether 0inC or 0notinC.
Keywords: minimum, norm common fixed point, strongly nonexpansive mappings, strong convergence, boundary point method, variational inequality
• E. Ghashghaei*, M. Namdari Pages 731-747
The submodules with the property of the title ( a submodule N of an R-module M is called strongly dense in M, denoted by N≤sdM, if for any index set I, ∏IN≤d∏IM) are introduced and fully investigated. It is shown that for each submodule N of M there exists the smallest subset D′⊆M such that N′ is a strongly dense submodule of M and D′⋂N=0. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module M, dense submodules in M are strongly dense if and only if M≤sdE~(M), where E~(M) is the rational hull of M. It is proved that R has no strongly dense left ideal if and only if no nonzero-element of every cyclic R-module M has a strongly dense annihilator in R. Finally, some appropriate properties and new concepts related to strong density are defined and studied.
Keywords: Strongly essential submodule, strongly dense submodule, singular submodule, special submodule, column submodule
• U. Ahmad*, SÝ. ÝmÝ. Ý Husnine Pages 749-759
A power digraph, denoted by G(n,k), is a directed graph with Zn=0,1,...,n−1 as the set of vertices and L=(x,y):xkequivy (bmod,n) as the edge set, where n and k are any positive integers. In this paper, the structure of G(2q,k), where q is a Sophie Germain prime is investigated. The primality tests for the integers of the form n=2q are established in terms of the structure of components of G(n,k). The digraphs in which all components look like directed star graphs are completely classified. This work generalizes the results of M. Krizekek, L. Somer, Sophie Germain Little Suns, Math. Slovaca 54(5) (2004), 433-442.
Keywords: Iteration digraph, Carmichael lambda function, Fixed point, Sophie Germain primes, Safe primes
• K. Sharma, V. Ravichandran* Pages 761-777
Let p be an analytic function defined on the open unit disc mathbbD with p(0)=1. The conditions on alpha and beta are derived for p(z) to be subordinate to 1泶=:varphiC(z) when (1−alpha)p(z)橚慪(z)淫嫎′(z)/p(z) is subordinate to ez. Similar problems were investigated for p(z) to lie in a region bounded by lemniscate of Bernoulli |w2−1|=1 when the functions (1−alpha)p(z)橚慪(z)淫嫎′(z) , (1−alpha)p(z)橚慪(z)淫嫎′(z)/p(z) or p(z)淫嫎′(z)/p2(z) is subordinate to varphiC(z). Related results for p to be in the parabolic region bounded by the REw=|w−1|
are investigated.
Keywords: convex, starlike functions, differential subordination, univalent functions
• N. A. Secelean* Pages 779-798
In this paper we define weak F-contractions on aý ýmetric space into itself by extending F-contractionsý ýintroduced by Dý. ýWardowski (2012) and provide some fixed pointý ýresults in complete metric spaces and in partially ordered complete ýgeneralized metric spacesý. ýSome relationships between weaký ýF-contractions and \Fi -contractions are highlightedý. ýWe also ýgive some applications on fractal theory improving the classicalý ýHutchinson-Barnsley's theory of iterated function systemsý. ýSomeý ýillustrative examples are providedý.
Keywords: F, contraction, partially ordered metric space, generalized metric, iterated function system, fixed point theorem