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Bulletin of Iranian Mathematical Society - Volume:43 Issue: 3, 2017

Bulletin of Iranian Mathematical Society
Volume:43 Issue: 3, 2017

  • تاریخ انتشار: 1396/05/10
  • تعداد عناوین: 30
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  • H.-C. O., J.-J. Jo, S.-Y. Kim, S.-G. Jon Pages 575-599
    ýThe aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in Rý. ýAgliardiý, ýA comprehensive structural model for defaultable fixed-income bondsæ Quantý. ýFinance 11 (2011)ý, ýnoý. ý5ý, ý749--762.) into a comprehensive unified model of structural and reduced form modelsý. ýIn our model the bond holders receive the deterministic coupon at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is consideredý. ýThe expected default event occurs when the equity value is not enough to pay coupon or debt at the coupon dates or maturity and an unexpected default event can occur at any time interval with the probability of given default intensityý. ýWe consider the model and pricing formula for equity value and using it calculate expected default barrierý. ýThen we provide pricing model and formula for defaultable corporate bonds with discrete couponsý, ýand consider the duration and the effect of the government taxesý.
    Keywords: Defaultable corporate bond, discrete coupon, tax, default intensity, default barrier
  • MÝ. Ý Briki_S. Djebali_T. Moussaoui Pages 601-615
    In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.
    Keywords: Impulsive BVPs, unbounded interval, critical point, minimization principal, mountain-pass theorem
  • F. Moradlou, S. Alizadeh Pages 617-627
    ýIn this paperý, ýwe prove some theorems related to properties ofý ýgeneralized symmetric hybrid mappings in Banach spacesý. ýUsing Banachý ýlimitsý, ýwe prove a fixed point theorem for symmetric generalizedý ýhybrid mappings in Banach spacesý. ýMoreoverý, ýwe prove some weaký ýconvergence theorems for such mappings by using Ishikawa iterationý ýmethod in a uniformly convex Banach space.
    Keywords: Fixed pointý, ýhybrid methodý, ýOpial's conditioný, ýuniformlyý ýconvex Banach spaceý, ýweak convergenceý
  • N.V. Thin Pages 629-647
    ýThe paper concerns interesting problems related to the field of Complex Analysisý, ýin particular, Nevanlinna theory of meromorphicý ýfunctionsý. ýWe have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing aý ýsmall functioný. ýOutsideý, ýin this paperý, ýwe also consider the uniqueness of q− shift differenceý - ýdifferential polynomialsý ýof meromorphic functions sharing small function or a set in the complex plane.
    Keywords: Uniqueness theorem, q-shift differential polynomials, value distribution, meromorphic function
  • D.W. Yoon Pages 649-658
    In the present paper, we study surfaces invariant under the 1-parameter subgroup in Sol space Sol3. Also, we characterize the surfaces in Sol3 whose coordinate functions of an immersion of the surface are eigenfunctions of the Laplacian Δ of the surface.
    Keywords: Sol space, finite type surface, invariant surface
  • C. Zhang Pages 659-663
    n this paper we prove that a finite group G having at most threeý ýconjugacy classes of non-normal non-abelian proper subgroups isý ýalways solvable except for G≅A5ý, ýwhich extends Theorem 3.3ý ýin [Some sufficient conditions on the number ofý ýnon-abelian subgroups of a finite group to be solvableý, ýActa Mathý. ýSinica (English Series) 27 (2011) 891--896.]ý. ýMoreoverý, ýwe show that aý ýfinite group G with at most three same order classes of non-normalý ýnon-abelian proper subgroups is always solvable except for G≅ýA5.
    Keywords: Non-abelian subgroupý, ýnon-normalý, ýconjugacy classý, ýsame order classý
  • F. Ahmadi Zeidabadi, S.M. Hoseini Pages 665-681
    Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equationý, ýsoliton perturbation theory is developed for the F=1 bright spinor Bose-Einstein condensatesý. ýA small disturbance of the integrability condition can be considered as a small correction to the integrable equationý. ýBy choosing appropriate perturbationý, ýthe soliton solution for small deviation from the integrability condition is foundý. ýNumerical simulations exhibit good agreement with analytical results.
    Keywords: Bose-Einstein condensateý, ýIntegrable 2times2 matrixý, ýnonlinear Schrödinger equationý, ýsoliton perturbation theoryý, ýdiscrete, continuous eigenfunctionsý
  • T. Wetere Tulu, T. Boping Pages 683-693
    Mathematical models are the most important tools in epidemiology to understand previous outbreaks of diseases and to better understand the dynamics of how infections spread through populationsý. ýMany existing models closely approximate historical disease patternsý. ýThis article investigates the mathematical model of the deadly disease with severe and uncontrollable bleedingý, ýEbola which is currently becoming the headache of the whole world though effort to control is undergoingý. ýIn this paper a new mathematical model of the Ebola epidemic is builtý. ýBesidesý, ýthe basic reproduction number is calculated and the stability of both disease free and endemic equilibrium is provedý. ýFinallyý, ýnumerical simulations are executed to further consolidate the analysis of the deadly disease Ebola.
    Keywords: Basic reproduction numberý, ýglobal stabilityý, ýequilibriumý, ýepidemic model
  • M. Nasehi Pages 695-706
    In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension fiveý. ýThen we explicitly give the flag curvature formulae and the S-curvature formulae for the Randers metrics of Douglas type on these spacesý. ýMoreoverý, ýwe prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of Douglas type which are Ricci-quadratic have a three-dimensional centreý. ýWe also prove that all simply connected five-dimensional two-step homogeneous Randers nilmanifolds of Douglas type are never weakly symmetricý. ýThe existence of homogeneous Randers spaces of Douglas type with vanishing S -curvature which are never g.oý. ýFinsler spaces is also proved and some examples of locally projectively flat Finsler spaces are also obtained.
    Keywords: Two-step homogeneous nilmanifoldsý, ýRanders metrics of Douglas typeý, ýg.oý. ýFinsler spacesý, ýweakly symmetric spacesý
  • S. Sun, Y. Zhao, P. Zhao, Z. Han Pages 707-725
    In this paperý, ýwe develop the theory of hybrid differentialý ýequations on time scalesý. ýAn existence theorem for hybridý ýdifferential equations on time scales is given under Lipschitz ýconditionsý. ýSome fundamental fractional differential inequalitiesý ýare also established which are utilized to prove the existence ofý ýextremal solutionsý. ýNecessary tools are considered and theý ýcomparison principle is proved which will be useful for furtherý ýstudy of qualitative behavior of solutionsý. ýOur results in this ýpaper extend and improve some known results.
    Keywords: Differential inequalitiesý, ýexistence theoremý, ýcomparison principleý, ýtime scalesý
  • S. Ersoy, I. Ince, M. Bilgin Pages 727-734
    In this paperý, ýwe introduce the notion of strongly k−spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)ý. ýWe characterize the strongly k−spaces and investigate the relationships between preclosednessý, ýlocally strongly compactnessý, ýpre-first countableness and being strongly k−space.
    Keywords: Strongly compact setsý, ýpreopen setsý, ýk−spacesý
  • X.H. Mo, H.M. Zhu Pages 735-746
    In this paper we study Finsler metrics with orthogonal invarianceý. ýWeý ýfind a partial differential equation equivalent to these metrics being locally projectively flatý. ýSome applications are givený. ýIn particularý, ýwe give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.
    Keywords: Finsler metricý, ýlocally projectively flatý, ýflag curvatureý, ýorthogonally invariantý
  • Y. Aydin, A. Pancar Pages 747-753
    In this studyý, ýFrattini supplement subgroup and Frattini supplemented groupý ýare defined by Frattini subgroupý. ýBy these definitionsý, ýit's shown thatý ýfinite abelian groups are Frattini supplemented and every conjugate of aý ýFrattini supplement of a subgroup is also a Frattini supplementý. ýA group actioný ýof a group is defined over the set of Frattini supplements of a normalý ýsubgroup of the group by conjugation and in this study new characterizationý ýof primitivity of groups has obtained in terms of Frattini supplementedý ýgroups by this actioný. ýMoreover, Frat-series of a group is defined based oný ýFrattini supplements of normal subgroups of the group and it is shown thatý ýsubgroups and factor groups of groups with Frat-series also have Frat-seriesý ýunder some special conditionsý. ýFurthermoreý, ýwe determined a characterization of soluble groups which have Frat-series.
    Keywords: Frattini subgroupý, ýprimitive groupý, ýgroup actionsý
  • S.M. Jafarian Amiri, H. Rostami Pages 755-762
    A finite group G is called a CC-group (G∈CC) if the centralizer of each noncentral element of G is cyclicý. ýIn this article we determine all finite CC-groups.
    Keywords: Finite groupý, ýCA-groupý, ýCC-groupý, ýcentralizer
  • M.S. Mojahedi Moakhar Pages 763-769
    In this noteý, ýwe consider the concentration function problem for a continuous action of a locally compact group G on a locally compact Hausdorff space Xý. ýWe prove a necessary and sufficient condition for the concentration functions of aý ýspread-out irreducible probability measure μ on G to converge to zero.
    Keywords: Concentration functioný, ýirreducibleý, ýspread-outý, ýstationary measureý
  • G. OztÜrk, S. BÜyÜkkÜtÜk, Ikisi Pages 771-780
    In the present studyý, ýwe consider a regular curve in Galileaný ý4-space G4 whose position vector is written as aý ýlinear combination of its Frenet vectorsý. ýWe characterize suchý ýcurves in terms of their curvature functionsý. ýFurtherý, ýwe obtainý ýsome results of rectifyingý, ýconstant ratioý, ýT-constant andý ýN-constant curves in G4.
    Keywords: Frenet frame, constant-ratio curves, rectifying curves
  • R. Zaare-Nahandi, R. Jafarpour-Golzari Pages 781-787
    Unmixed bipartite graphs have been characterized by Ravindra andý ýVillarreal independentlyý. ýOur aim in this paper is toý ýcharacterize unmixed r -partite graphs under a certain conditioný, ýwhich is a generalization of Villarreal's theorem on bipartiteý ýgraphsý. ýAlso, we give some examples and counterexamples in relevance to this subjectý.
    Keywords: r-partite graph, well-covered, unmixed, perfect matching, clique
  • M.R. Hamidi, N. Nyamoradi Pages 789-805
    In this paperý, ýwe study the existence of solutions for aý ý fractional boundary value problemý. ýBy using critical point theoryý ý and variational methodsý, ýwe give some new criteria to guaranteeý ý thatý ý the problems have at least one solution and infinitely many solutions.
    ý
    Keywords: Fractional differential equationsý, ýsolutionsý, variational methodsý, ýMorse theoryý, ýfountain Theorem
  • R. Jahani-Nezhad, F. Khoshayand Pages 807-816
    The aim of this paper is to generalize theý ýnotion of almost valuation domains to arbitrary commutativeý ýringsý. ýAlsoý, ýwe consider relations between almost valuation rings ýand pseudo-almost valuation ringsý. ýWe prove that the class ofý ýalmost valuation rings is properly contained in the class ofý ýpseudo-almost valuation ringsý. ýAmong the properties of almostý ývaluation ringsý, ýwe show that a quasilocal ring R with regularý maximal ideal M is a pseudo-almost valuation ring if and onlyý ýif V=(Mý:ýM) is an almost valuation ring with maximal idealý ýRadV(M) ý. ýFurthermoreý, ýwe show that pseudo-almost valuationýýrings are precisely the pullbacks of almost valuation ringsý.
    Keywords: Strongly prime ideal, Almost valuation domain, Pseudo-almost valuation ring
  • S. Ranjbar Pages 817-834
    In this paperý, ýwe generalize the proximal point algorithm to complete CAT(0) spaces and showý ýthat the sequence generated by the proximal point algorithmý w-converges to a zero of the maximalý ýmonotone operatorý. ýAlsoý, ýwe prove that if fý:ýX→ýý]−∞ý,ý∞] is a properý, ýconvex and lower semicontinuousý ýfunction on the complete CAT(0) space Xý, ýthen the proximal point algorithm w-converges to a zero of the subdifferential of fý, ýi.e., a minimizer of fý. ýSome strong convergence results (convergence in metric) are also presented with additional assumptions on the monotone operator andý ýthe convex function f.
    Keywords: Hadamard space, maximal monotone operator, Proximal point algorithm, w-convergence, subdifferential
  • A. R. Aliabad, V. Bagheri, M. Karavan Jahromi Pages 835-852
    A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closedý. ýHereý, ýwe study a variety of spaces some of which have already been studied in C(X)ý. ýAmong them areý, ýmost importantlyý, ýquasi P-spaces and pointwise quasi P-spacesý. ýWe obtain some new useful topological characterizations of quasi P-spaces and pointwise quasi P -spacesý. ýConsequentlyý, ýwe obtain a close relation between these latter spaces and submaximal and nodec spacesý.
    Keywords: Quasi P-space, Pointwise QP-space, Submaximal space, Nodec space, I-space
  • W.-R. Xu, G.-L. Chen Pages 853-865
    The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an n-tuple σ=(1,λ2,λ3,…,λn)∈Rn with |λi|≤1, i=1,2,…,ný, ýto be the spectrum of an n×n symmetric doubly stochastic matrix Aý. ýIf there exists an n×n symmetric doubly stochastic matrix A with σ as its spectrumý, ýthen the list σ is s.d.sý. ýrealizableý, ýor such that A s.d.sý. realizes σ ý. ýIn this paperý, ýwe propose a new sufficient condition for the existence of the symmetric doubly stochastic matrices with prescribed spectrumý. ýFinallyý, ýsome results about how to construct new s.d.sý. ýrealizable lists from the known lists are presented.
    Keywords: Inverse eigenvalue problemý, ýsymmetric doubly stochastic matrixý, ýsufficient conditioný
  • J. Shi, Z. Wu, R. Hou Pages 867-874
    Let G be a finite groupý. ýBy MT(G)=(m1,⋯,mk) we denote the type ofý ýconjugacy classes of maximal subgroups of Gý, ýwhich implies that G has exactly k conjugacy classes ofý ýmaximal subgroups and m1,…,mk are the numbers of conjugatesý ýof maximal subgroups of Gý, ýwhere m1≤⋯≤mký. ýIn this paperý, ýweý ýgive some new characterizations of finite groups by the type ofý ýconjugacy classes of maximal subgroupsý. By πt(G) we denoteý ýthe set of indices of all maximal subgroups of G ý. ýWe also investigateý ýthe influence of the set of indices of all maximal subgroups on the structure ofý ýfinite groupsý.
    Keywords: Maximal subgroup, non-abelian simple group, the type of conjugacy classes, the set of indices
  • M. R. Azimi, M. R. Jabbarzadeh, M. Ýjafari Bakhshkandi Pages 875-883
    In this paper, we study two types of the reducing subspaces for the weighted composition operator W:f→u⋅f∘φ on L2(Σ). A necessary and sufficient condition is given for W to possess the reducing subspaces of the form L2(ΣB) where B∈Σsigma(u). Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form L2(A) reduce W . All of these are basically discussed by using the conditional expectation properties. To explain the results some examples are then presented.
    Keywords: Reducing subspace, weighted composition operators, conditional expectation
  • D. Ahmadi Dastjerdi, M. Dabbaghian Amiri Pages 885-896
    Let (ΣP,σP) be the space of a spacing shifts where P⊂N0=N∪{0} and ΣP={s∈{0,1}N0:ýsi=sj=1 if |i−j|∈P∪{0}} and σP the shift mapý. ýWe will show that ΣP is mixing if and only if it has almost specification property with at least two periodic pointsý. ýMoreoverý, ýwe show that if h(σP)=0ý, ýthen ΣP is almost specified and if h(σP)>0 and ΣP is almost specifiedý, ýthen it is weak mixingý. ýAlsoý, ýsome sufficient conditions for a coded ΣP being renewal or uniquely decipherable is givený. ýAt last we will show that here are only two conjugacies from a transitive ΣP to a subshift of {0,1}N0.
    Keywords: Spacing shiftsý, ýalmost specificationý, ýrenewalý, ýuniquely decipherable
  • R. Bai, Y. Gao, Y. Zhang, Z. Li Pages 897-910
    After introducing double derivations of n-Lie algebra L weý ýdescribe the relationship between the algebra D(L) of double derivations and the usualý ýderivation Lie algebra Der(L)ý. ýIn particularý, ýwe prove that the inner derivation algebra ad(L)ý ýis an ideal of the double derivation algebra D(L); we also show that if L is a perfect n-Lie algebraý ýwith certain constraints on the base field then the centralizer of ad(L) in D(L) isý ýtrivial and D(L) is centerlessý. ýIn additioný, ýwe obtain that for every perfect n-Lieý ýalgebra L with zero centerý, ýthe triple derivations of the derivation algebra Der(L) are exactlyý ýthe derivations of Der(L)ý, ýand the triple derivations of the inner derivation algebra ad(L) areý ýprecisely the derivations of ad(L).
    Keywords: n-Lie algebra, double derivation, Derivation, inner derivation
  • Y. Talebi, M. Hosseinpour, A.R. Moniri Hamzekolaee Pages 911-922
    A module M is lifting if and only if M is amply supplemented andý ýevery coclosed submodule of M is a direct summandý. ýIn this paperý, ýwe areý ýinterested in a generalization of lifting modules by removing the conditioný"ýamply supplementedý" ýand just focus on modules such that every non-cosingularý ýsubmodule of them is a summandý. ýWe call these modules NSý. We investigate some general properties of NS-modulesý. ýSeveralý ýexamples are provided to separate different conceptsý. ýIt is shown that every non-cosingularý ýNS-module is a direct sum of indecomposable modulesý. ýWeý ýalso discuss on finite direct sums of NS-modules.
    Keywords: Non-cosingular submoduleý, ýamply supplemented moduleý, ýNS-moduleý
  • B. Liu, F. Li Pages 923-942
    This note deals with the systems of parabolic equations with local and localized sources involving n componentsý. ýWe obtained the exponent regionsý, ýwhere k∈{1,2,⋯,n} components may blow up simultaneously while the other (n−k) ones still remain bounded under suitable initial dataý. ýIt is proved that different initial data can lead to different blow-up phenomena even in the same exponent regionsý, ýand moreoverý, ýdifferent blow-up mechanism leads to different blow-up rates and blow-up sets.
    Keywords: Non-simultaneous blow-upý, ýsimultaneous blow-upý, ýblow-up rateý, ýblow-up setý
  • M. Kondo Pages 943-949
    We give a simple and independent axiomatization of reticulations on residuated latticesý, ýwhich were axiomatized by five conditions in [Cý. Mureşaný, ýThe reticulation of a residuated latticeý, ýBullý. ýMathý. ýSocý. ýSciý. ýMathý. ýRoumanieý ý51 (2008)ý, ýnoý. ý1ý, ý47--65]ý. ýMoreoverý, ýwe show that reticulations can be considered as lattice homomorphisms between residuated lattices and bounded distributive latticesý. ýConsequentlyý, ýthe result proved by Muresan in 2008ý, ýfor any two reticulattions (L1ý,ýλ1)ý,ý(L2ý,ýλ2) of a residuated lattice X there exists an isomorphism fý:ýL1→L2 such that f∘λ1=λ2ý, ýcan be considered as a homomorphism theoremý.
    Keywords: Reticulationý, ýresiduated latticeý, ýprincipal filterý
  • Y. Pakravesh, Ali Iranmanesh Pages 951-974
    In this paper, we determine all of connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p2, where p is a prime number.
    Keywords: Cayley graph, normal edge-transitive, vertex-transitive, edge-transitive