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Bulletin of Iranian Mathematical Society - Volume:43 Issue: 5, 2017

Bulletin of Iranian Mathematical Society
Volume:43 Issue: 5, 2017

  • تاریخ انتشار: 1396/09/10
  • تعداد عناوین: 40
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  • N. Shafiei * Pages 975-994
    ýIn this paperý, ýwe propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraintsý. ýWe use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functionsý. ýWe also formulate an infinitive approximation set of the (weakly) nondominated points of biobjective optimization problemsý. ýMoreoverý, ýwe provide some numerical examples to illustrate the advantage of our algorithm.
    Keywords: Multiobjective optimization?, ?a?pproximation algorithm?, efficient solution?, ?nondominated point?
  • A. Ben Amar *, A. Tlili Pages 995-1015
    In this paper, we establish some new critical fixed point theorems for the sum AB in a Banach algebra relative to the weak topology, where I−CA allows to be noninvertible. In addition, a special class of Banach algebras will be considered.
    Keywords: Banach algebras, sequentially weakly continuous operators, weakly compact operators, fixed point theorems
  • M. Zahiri, A. Moussavi *, R. Mohammadi Pages 1017-1036
    This article examines annihilators in the skew polynomial ring R[x;alpha,delta]. A ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by P.P. Nielsen. We assume that R is an (alpha,delta )-compatible ring, and prove that, if R is nil-reversible then the skew polynomial ring R[x;alpha,delta] is strongly right AB. It is also shown that, every right duo ring with an automorphism alpha is skew McCoy. Moreover, if R is strongly right AB and skew McCoy, then R[x;alpha] and R[x;delta] have right Property (A).
    Keywords: McCoy ring, strongly right AB ring, nil-reversible ring, rings with Property(A)
  • H. Rahmatan, Sh. Najafzadeh *, A. Ebadian Pages 1037-1043
    ýIn the present investigationý, ýwe give the best estimates for the norm of the pre-Schwarzian derivative Tf(z)=f′′(z)f′(z) for bi-starlike functions and a new subclass of bi-univalent functions of order αý, ýwhereý ý∥Tf∥=sup|z|
    Keywords: Bi-Univalent Functions, bi-starlike functions, subordina- tion, pre-Schwarzian derivatives
  • F. Wang*, S. Zhang Pages 1045-1055
    ýThis paper gives an abstract order-type existence theorem for second order nonlocal boundary value problems at resonance and obtain existence criteria for at least two positive solutionsý, ýwhere f is a continuous functioný. ýOur results generalize or extend related results in the literature and give a positive answer to the question raised in the literatureý. ýAn example is given to illustrate the new results.
    Keywords: Order-type existence theoremý, ýnonlocal problemsý, ýat resonanceý
  • Y. Wang * Pages 1057-1071
    ýIn this paperý, ýwe consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equationý. ýMoreoverý, ýthe finite-time blow-up of the solution for the equation is investigated by the concavity methodý.
    Keywords: Boussinesq equation?, ?Cauchy problem?, ?global solution?, ?blow-up
  • A. Karimi, S. Salehi * Pages 1073-1088
    ýA universal schema for diagonalization was popularized by N.Sý. ýYanofsky (2003)ý, ýbased on a pioneering work of F.Wý. ýLawvere (1969)ý, ýin which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain functioný. ýIt was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schemaý. ýHereý, ýwe fit more theorems in the universalý ýschema of diagonalizationý, ýsuch as Euclid's proof for the infinitude of the primes and new proofs of G.~Boolos (1997) for Cantor's theorem on the non-equinumerosity of a set with its powersetý. ýThený, ýin Linear Temporal Logicý, ýwe show the non-existence of a fixed-point in this logic whose proof resembles the argument of Yablo's paradox (1985ý, ý1993)ý. ýThusý, ýYablo's paradox turns for the first time into a genuine mathematico-logical theorem in the framework of Linear Temporal Logicý. ýAgain the diagonal schema of the paper is used in this proof; and it is also shown that G.~Priest's inclosure schema (1997) can fit in our universal diagonal/fixed-point schemaý. ýWe also show the existence of dominating (Ackermann-like) functions (which dominate a given countable set of functionsý, ýsuch as primitive recursive functions) in the schema.
    Keywords: Diagonal argument?, ?self-reference?, ?fixed-points?, ?Yablo's paradox?, ?(linear) temporal logic?
  • J.J. Ao * Pages 1089-1099
    ýThe spectral analysis of two classes of third order boundary value problems is investigatedý. ýFor every positive integer m we construct two classes of regular third order boundary value problems with at most 2mý ýeigenvaluesý, ýcounting multiplicityý. ýThese kinds of finite spectrum results are previously known only for even order boundary value problemsý.
    Keywords: Eigenvalues?, ?finite spectrum?, ?third order boundary value? ?problems?
  • K. Petelczyc *, M. , Ynel Pages 1101-1126
    Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated. The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given.
    An affine covering for the Segre product of Veblenian gamma spaces is established. A general construction that produces non-degenerate hyperplanes in the Segre product of partial linear spaces embeddable into projective space is introduced.
    Keywords: Segre product?, ?hyperplane?, ?hyperplane complement
  • S. Suantai, B. Panyanak, W. Phuengrattana * Pages 1127-1141
    ýIn this paperý, ýwe propose a new one-step iterative process for aý ýcountable family of quasi-nonexpansive multi-valued mappings in aý ýCAT(0) spaceý. ýWe also prove strong and Delta-convergence theoremsý ýof the proposed iterative process under some control conditionsý. ýOurý ýmain results extend and generalize many results in the literature.
    Keywords: Fixed point?, ?quasi-nonexpansive multi-valued mappings?, ?CAT(0) spaces?
  • Q.H. Jiang, c.G. Shao, W.J. Shi *, q.L. Zhang Pages 1143-1151
    We characterize the finite simple groups L2(q) by the group orders and the largestý ýelement ordersý, ýwhere q is a prime or q=2aý, ýwith 2a or 2a−1
    a primeý.
    Keywords: ?Finite groups?, ?group orders?, ?largest element orders?, ?characterization
  • M. Haddadi *, M.M. Ebrahimi Pages 1153-1163
    Let S-Set be the category of S-sets, sets together with the actions of a semigroup S on them. And, let S-Pos be the category of S-posets, posets together with the actions compatible with the orders on them. In this paper we show that the category S-Pos is a radical extension of S-Set; that is there is a radical on the category S-Pos, the order desolator radical, whose torsion-free class is S-Set.
    To do this, first we give a precise definition of a radical on the category S-Posand construct some functors between the above mentioned categories and finally we show that S-Pos is a radical extension of S-Set.
    Keywords: Radical?, ?S-set?, ?S-poset?
  • M. Zeinadini, M. Namjoo* Pages 1165-1182
    ýIn this paperý, ýthe fractional--order form of three dimensional chemostat model with variable yields is introducedý. ýThe stability analysis of this fractional system is discussed in detailý. ýIn order to study the dynamic behaviours of the mentioned fractional systemý, ýthe well known nonstandard (NSFD) scheme is implementedý. ýThe proposed NSFD scheme is compared with the forward Euler and fourth order Runge--Kutta methodsý. ýNumerical results show that the NSFD approach is easy and accurate when applied to fractional--order chemostat model.
    Keywords: Chemostat modelý, ýfractional--order differential equationý, ýstabilityý, ýnonstandard finite difference scheme
  • X. Fu * Pages 1183-1194
    ýWe define hyperbolic harmonic ω-α-Bloch spaceý ýBαω in the unit ball B of Rn andý ýcharacterize it in terms ofý ý ω((1−|x|2)β(1−|y|2)α−β)|f(x)−f(y)|[x,y]γ|x−y|1−γý, where 0≤γ≤1ý. ýSimilar results are extended toý ýlittle ω-α-Bloch and Besov spacesý. ýThese obtainedý ýcharacterizations generalize the corresponding ones which were obtained by Gý. ýRený ýand Uý. ýK\"{a}hler in 2002 and 2005ý.
    Keywords: Hyperbolic harmonic function?, ?Bloch space?, ?Besov? ?space?, ?majorant
  • M. Abtahi * Pages 1195-1207
    ýGiven a compact space X and a commutative Banach algebraý ýAý, ýthe character spaces of A-valued function algebras on X areý ýinvestigatedý. ýThe class of natural A-valued function algebrasý, ýthose whose characters can be described by means of characters of A andý ýpoint evaluation homomorphismsý, ýis introduced and studiedý. ýFor aný ýadmissible Banach A-valued function algebra A on Xý, ýconditions under which the character space M(A)ý ýis homeomorphic to M(A)×M(A) are presentedý, ýwhere A=C(X)∩Aý ýis the subalgebra of A consisting of scalar-valued functionsý. ýAn illustration of the results is given by some examples.
    Keywords: Commutative Banach algebras?, ?Banach function algebras?, ?vector-valued function algebras?, ?vector-valued characters?
  • A.A. Shaikh *, I. Roy, H. Kundu Pages 1209-1225
    ýThe object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifoldsý, ýcalledý, ýsuper generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [ýA.Aý. ýShaikh and Aý. ýPatraý, On a generalized class of recurrent manifoldsý, Archý. ýMathý. ý(Brno) 46 (2010) 71--78ý.] and weakly generalized recurrent manifolds [ýA.Aý. ýShaikh and Iý. ýRoyý, On weakly generalized recurrent manifoldsý, Anný. ýUnivý. ýSciý. ýBudapest Rolando Eotvosý, ýSectý. ýMath. ý54 (2011) 35--45ý.]ý. ýThe nature of associated 1-forms of a super generalized recurrent manifold is determined and it is proved that on a Roter type manifold [ýRý. ýDeszczý, On Roter type manifoldsý,ý iný: ý5th Conference on Geometry and Topology of Manifoldsý, ýKrynicaý, ýPolandý, ý2003ý.] such a notion is equivalent to the notion of generalized Ricci-recurrent manifold [ýU.Cý. ýDeý, ýNý. ýGuha and Dý. ýKamilyaý, On generalized Ricci-recurrent manifoldsý, Tensor (N.S.) 56 (1995)ý, ýnoý. ý3ý, ý312--317ý.]ý. ýWe also obtain a sufficient condition for a super generalized recurrent manifold to be a semisymmetric one and the existence of such notion is ensured by a proper example.
    Keywords: Recurrent manifold?, ?hyper generalized recurrent manifold?, ?weakly generalized recurrent manifold?, ?super generalized recurrent manifold?, ?semisymmetric manifold?, ?Roter type manifold
  • E. Momtahan *, M. Motamedi Pages 1227-1235
    In this article we study relations between some algebraicý ýoperations such as tensor product and localization from one handý ýand some well-known dimensions such as uniform dimensioný, ýhollowý ýdimension and type dimension from the other handý. ýSome minorý ýapplications to the ring C(X) are observed.
    Keywords: Type dimension?, ?uniform dimension?, ?hollow dimension?
  • M. Tamekkante, E.M. Bouba* Pages 1237-1244
    Let f:A→B and g:A→C be two ring homomorphisms and let J and J′ be two ideals of B and Cý, ýrespectivelyý, ýsuch that f−1(J)=g−1(J′)ý. ýThe bi-amalgamation of A with (B,C) along (J,J′) with respect of (f,g) is the subring of B×C given byý ýA⋈f,g(J,J′)={(f(a),g(a ′)ý/ýa∈Aý,ý(j,j′)∈J×J′}.ý ýIn this paperý, ýwe study the transference of pmý, ýpm and finite character ring-properties in the bi-amalgamation.
    Keywords: Bi-amalgamated algebrasý, ýpm+ringsý, ýpm ringsý, ýrings with finite characterý
  • H. Majidian* Pages 1245-1258
    ýA natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equationsý. ýThe equations of this class appear in heat conduction problems with mixed boundary conditionsý. ýThe algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshesý. ýA comparative study is carried outý, ýwhich points out that the proposed method is the most efficient one among other existing methodsý. ýIn factý, ýthe results of this paper introduce a most-efficient decisive-choice for computing the solution of the heat conduction modelý.
    Keywords: Cordial Volterra integral equationý, ýheat conduction problemý, ýmixed-type boundaryý ýconditioný, ýcompound quadrature ruleý, ýgraded meshý
  • R. Mohammadpour * Pages 1259-1264
    ýWe present streamlined proofs of certain maximality principles studied by Hamkinsý ýand Woodiný. ýMoreoverý, ýwe formulate an intermediate maximality principleý, ýwhich isý ýshown here to be equiconsistent with the existence of a weakly compact cardinal κ such that Vκ≺V.
    Keywords: Hamkin's maximality principle?, ?weakly compact cardinal?, ?consistency result?
  • H. Jamali *, E. Afroomand Pages 1265-1279
    ýGiven a frame of a separable Hilbert space Hý, ýwe present someý ýiterative methods for solving an operator equation Lu=fý, ýwhere L is a boundedý, ýinvertible and symmetricý ýoperator on H ý. ýWe present some algorithmsý ýbased on the knowledge of frame boundsý, ýChebyshev method and conjugate gradient methodý, ýin order to give someý ýapproximated solutions to the problemý. ýThen we investigate theý ýconvergence and optimality of them.
    Keywords: Hilbert spaces?, ?dual space?, ?frame?, ?Chebyshev polynomials?, ?iterative method?
  • M. Sattari * Pages 1281-1285
    We present some inequalities for operator space numerical radius of 2×2 block matrices on the matrix space Mn(X)ý, ýwhen X is a numerical radius operator spaceý. ýThese inequalities contain some upper and lower bounds for operator space numerical radius.
    Keywords: Operator space?, ?numerical radius operator space?, ?operator space numerical radius?, ?block matrix?
  • E. Salavati *, B.Z. Zangeneh Pages 1287-1299
    Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are consideredý. ýThe coefficients are assumed to have linear growthý. ýWe do not impose coercivity conditions on coefficientsý. ýA novel method of proof for establishing existence and uniqueness of the mild solution is proposedý. ýExamples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developedý.
    Keywords: Stochastic evolution equation?, ?monotone operator?, ?Levy noise?, ?Ito type inequality?, ?stochastic convolution integral?
  • M. Khosravi, A. Sheikh Hosseini * Pages 1301-1311
    Some improvements of Young inequality and its reverse for positiveý ýnumbers with Kantorovich constant K(tý,ý2)=(1)24tý ýare givený. ýUsing these inequalities some operator inequalities andý ýHilbert-Schmidt norm versions for matrices are provedý. ýIný ýparticularý, ýit is shown that if aý,ýb are positive numbers andý ý0⩽ν⩽1, then for all integers k⩾ýý1ý:ýý ýK(h12n,2)rna♯νb⩽a∇νbý−ý∑n−1k=0rk((a♯mk2kbýý)12ý−ý(a♯mk흩ýý)12)2⩽K(h12n,2 Rna♯νb, ýwhere mk=[2kν] is the largest integer not greater thaný ý2kνý, ýr0=min{νý,ý1−ν}ý,ý k=min{2rk−1ý,ý1−2rk−1} and Rk=1−rk.
    Keywords: Heinz mean?, ?Hilbert-Schmidt norm?, ?Kantorovich constant?, ?Young inequality?
  • Z. Wang *, J. Zhang Pages 1313-1321
    ýIn this paper we investigate the dilations of completely positive definite representationsý ýof C∗-dynamical systems with abelian groups on Hilbert C∗-modulesý. ýWe show that if (Aý,ýG,α) is a C∗-dynamical system with G an abelian groupý, ýthen every completely positive definite covariant representation (π,φ,E) of (Aý,ýG,α) on a Hilbert C∗-module E admits an unitary dilation ((π^,φ^,E^)).
    Keywords: Dilation, covariant representation, Cast-dynamical system, Hilbert Cast-module
  • M. Adib* Pages 1323-1332
    ýAssume that A is a Banach algebraý. ýWe define theý ýβ−topology and the γ−topology on the space QMel(A∗) of all bounded extended left quasi-multipliers of A∗.ý ýWe establish further properties of (QMel(A∗),γ) when A is a C∗−algebraý. ýIn particularý, ýwe characterize the γ−dualý ýof QMel(A∗) and prove that (QMel(A∗),γ)∗, under the topology of bounded convergenceý, ýis isomorphic to A∗∗∗.
    Keywords: Quasi-multiplierý, ýmultiplierý, ýBanach algebraý, ýArens regularityý, ýstrict topologyý
  • P. Danchev * Pages 1333-1339
    We show that if R is a ring with an arbitrary idempotent e such that eRe and (1−e)R(1−e) are both strongly nil-clean ringsý, ýthen R/J(R) is nil-cleaný. ýIn particularý, ýunder certain additional circumstancesý, ýR is also nil-cleaný. ýThese results somewhat improves on achievements due to Diesl in Jý. ýAlgebra (2013) and to Ko\c{s}an-Wang-Zhou in Jý. ýPure Applý. ýAlgebra (2016)ý. ýIn additioný, ýwe also give a new transparent proof of the main result of Breaz-Calugareanu-Danchev-Micu in Linear Algebra Applý. ý(2013) which says that if R is a commutative nil-clean ringý, ýthen the full n×n matrix ring Mn(R)
    is nil-cleaný.
    Keywords: Nil-clean rings?, ?strongly nil-clean rings?, ?idempotents?, ?nilpotents?, ?Jacobson radical?
  • M. Shahriari * Pages 1341-1355
    In this manuscriptý, ýwe study various by uniqueness results for inverse spectral problems of Sturm--Liouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditionsý. ýWe consider both the cases of classical Robin and eigenparameter dependent boundary conditions.
    Keywords: Inverse Sturm--Liouville problem?, ?eigenparameter dependent boundary conditions?, ?internal discontinuities?, ?three spectra?, ?Weyl--Titchmarsh m-function?
  • L. Shiri, M. Zarebnia * Pages 1357-1375
    In this paperý, ýthe numerical solutions of linear and nonlinear Volterra integralý ýequations with nonvanishing delay are considered by two methodsý. ýThe methods are developed by means ofý ýthe sinc approximation with the single exponential (SE) and double exponential (DE)ý ýtransformationsý. ýThe existence and uniqueness of sinc-collocation solutions for these equations are providedý. ýThese methods improve conventional results and achieve exponential convergenceý. ýNumerical results are included to confirm the efficiency and accuracy of the methods.
    Keywords: Volterra integral equations?, ?nonvanishing delay?, ?sinc-collocation?
  • M. Boualem*, M. Cherfaoui, N. Djellab, D. Aissani Pages 1377-1397
    In this worký, ýwe derive insensitive bounds for various performance measures of a single-serverý ýretrial queue with generally distributed inter-retrial times and Bernoulli scheduleý, ýunder the specialý ýassumption that only the customer at the head of the orbit queue (i.e.ý, ýaý ýFCFS discipline governing the flow from the orbit to the server) is allowedý ýto occupy the serverý. ýThe methodology is strongly based on stochastic comparison techniquesý. ýInstead of studying a performance measure in a quantitative fashioný, ýthis approach attempts to reveal the relationship between the performance measures and the parameters of the systemý. ýWe prove the monotonicity of the transition operator of the embedded Markov chain relative to strong stochastic ordering and increasing convex orderingý. ýWe obtain comparability conditions for the distribution of the number of customers in the systemý. ýBounds are derived for the stationary distribution andý ýsome simple bounds for the mean characteristics of the systemý. ýThe proofs of these results are based on the validation of some inequalities for some cumulative probabilities associated with every state (mý,ýn) of the systemý. ýFinallyý, ýthe effects of various parameters on the performance of the system have been examined numerically.
    Keywords: Retrial queuesý, ýperformance measuresý, ýstochastic ordersý, ýmonotonicityý, ýsimulationý
  • M. Ghaznavi *, Z. Azizi Pages 1399-1415
    ýIn this paperý, ýwe present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)ý, ýwhere the constraints and the objective functions are convexý. ýWe provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated pointsý. ýThe proposed algorithm can be applied for differentiable or nondifferentiable convex MOPsý. ýTo illustrate efficiency of the proposed algorithm for convex MOPsý, ýwe provide numerical examples.
    Keywords: Multiobjective optimization?, ?convexity?, ?nondominated point?, ?efficient solution?, ?approximation algorithm?, ?differentiable problem?
  • A. Rafiei *, M. Bollhoefer Pages 1417-1456
    ýIn this paperý, ýwe use a complete pivoting strategy to compute the IUL preconditioner obtained as the by-product of the Backward Factored APproximate INVerse processý. ýThis pivoting is based on the complete pivoting strategy of the Backward IJK version of Gaussian Elimination processý. ýThere is a parameter α to control the complete pivoting processý. ýWe have studied the effect of different values of α on the quality of the IUL preconditionerý. ýFor the numerical experiments sectioný, ýthe IUL factorization which is coupled with the complete pivoting is compared to the ILUTP and to the left-looking version of RIF which is coupled with the complete pivoting strategyý. ýAs the preprocessingý, ýwe have applied the maximum weighted matching coupled the Reverse Cuthill-Mckee (RCM) and multilevel nested dissection reordering.
    Keywords: Backward factored APproximate INVerse?, ?IUL preconditioner?, ?backward IJK version of Gaussian elimination?, ?complete pivoting?, ?ILUTP?, ?left-looking RIF with pivoting?
  • Y. Kurtulmaz * Pages 1457-1465
    An element a in a ring R is very clean in case there existsý ýan idempotent e∈R such that ae=ea and either aý−ýe or aýýe is invertibleý. ýAn element a in a ring R is very J-cleaný ýprovided that there exists an idempotent e∈R such that ae=ýýea and either a−e∈J(R) or aýýe∈J(R)ý. ýLet R be aý ýlocal ringý, ýand let s∈C(R)ý. ýWe prove that A∈Ks(R) isý ývery clean if and only if A∈U(Ks(R))ý, ýI±A∈U(Ks(R))ý ýor A∈Ks(R) is very J-cleaný.
    Keywords: Local ring?, ?very clean ring?, ?very? ?J-clean ring?
  • J.R. Long * Pages 1467-1478
    For a meromorphic function f in the complex plane, we shall introduce the definition of five-value rich line of f, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of f is its five-value rich line, and the inverse statement holds when f is of infinite order.
    Keywords: Borel direction, five-value rich line, meromorphic function, sharing value, uniqueness
  • T. Petik *, H. Ozdemir Pages 1479-1493
    ýA rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operationsý. ýMoreoverý, ýby using this equality and Theorems 8 and 10 in [Chen Mý. ýand et alý. ýOn the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applicationsý, ýThe Scientific World Journal 2014 (2014)ý, ýArticle ID 702413ý, ý7 pagesý.]ý, ýsome other rank equalities for tripotent matrices are givený. ýFurthermoreý, ýwe obtain several rank equalities related to some special types of matricesý, ýsome of which are available in the literatureý, ýfrom the results establishedý.
    Keywords: Rank, elementary block matrix operations, idempotent matrix, tripotent matrix
  • L. Shi, Z.-G. Wang, A. Rasila *, Y. Sun Pages 1495-1510
    ýIn this paperý, ýwe study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappingsý. ýSufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derivedý. ýSeveral examples of univalent harmonic mappings constructed by using these methods are presented to illustrate potential applications of the main results.
    Keywords: Harmonic mapping?, ?slit mapping?, ?convex combination?, ?shear construction?
  • B.Q. Hung *, H.Q. Toan Pages 1511-1528
    This article shows the existence of weak solutions of a resonance problem for nonuniformly p-Laplacian system in a bounded domain in RN ý. ýOur arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type conditioný.
    Keywords: Semilinear elliptic equation, non-uniform, Landesman-Lazer condition, minimum principle
  • A. Azarang * Pages 1529-1530
    ýOur aim in this very short note is to show that the proof of theý ýfollowing well-known fundamental lemma of Zariski follows from aný ýargument similar to the proof of the fact that the rational fieldý ýQ is not a finitely generated Z-algebra.
    Keywords: Zariski's Lemma, PID, Field
  • N. Ahanjideh, L. Mousavi, B. Taeri * Pages 1531-1542
    ýFor a finite group Gý, ýlet nse(G)={mk∣k∈πe(G)}ý, ýwhere mk is the number of elements of order k in Gý ýand πe(G) is the set of element orders of Gý. ýIn this paperý, ýwe prove that G≅Lm(2) if and only if p∣|G| and nse(G)=nse(Lm(2))ý, ýwhere m∈{n,n} and 2n−1=p is a prime number.
    Keywords: Set of the numbers of elements of the same order?, ?prime graph?, ?Mersenne number?
  • F. Abdmouleh*, I. Walha Pages 1543-1558
    In this paperý, ýwe discuss the essential spectrum of sum of two bounded operatorsý ýusing measure of non strict singularityý. ýBased on this new investigationý, ýa problem of one-speed neutron transport operator is presentedý.
    Keywords: Fredholm operatorsý, ýlower (respectively upper) semi-Fredholm operatorsý, ýessential spectrumý, ýmeasure of non-strict-singularityý, ýone-speed neutron transport operatorý