

2018 . 

Bulletin of Iranian Mathematical Society
ISSN 1017060X
دوماهنامه  ( )
3 2017




 A comprehensive unified model of structural and reduced form type for defaultable fixed income bonds H.C. O , J.J. Jo , S.Y. Kim , S.G. Jon Pages 575599 Abstract Full Text [PDF 217KB]   The aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in R. Agliardi، A comprehensive structural model for defaultable fixedincome bonds Quant. Finance 11 (2011)، no. 5، 749762.) into a comprehensive unified model of structural and reduced form models. In 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 considered. The 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 intensity. We consider the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons، and consider the duration and the effect of the government taxes.
Keywords: Defaultable corporate bond; discrete coupon; tax; default intensity; default barrier
  
 Solvability of an impulsive boundary value problem on the halfline via critical point theory M. Briki , S. Djebali , T. Moussaoui Pages 601615 Abstract Full Text [PDF 135KB]   In this paper، an impulsive boundary value problem on the halfline is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.
Keywords: Impulsive BVPs; unbounded interval; critical point; minimization principal; mountainpass theorem
  
 Weak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces F. Moradlou , S. Alizadeh Pages 617627 Abstract Full Text [PDF 106KB]   In this paper، we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits، we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover، we prove some weak convergence theorems for such mappings by using Ishikawa iteration method in a uniformly convex Banach space.
Keywords: Fixed point; hybrid method; Opial's condition; uniformly convex Banach space; weak convergence
  
 Uniqueness of meromorphic functions ans Qdifferential polynomials sharing small functions N.V. Thin Pages 629647 Abstract Full Text [PDF 140KB]   The paper concerns interesting problems related to the field of Complex Analysis، in particular، Nevanlinna theory of meromorphic functions. We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function. Outside، in this paper، we also consider the uniqueness of q− shift difference  differential polynomials of meromorphic functions sharing small function or a set in the complex plane.
Keywords: Uniqueness theorem; qshift differential polynomials; value distribution; meromorphic function
  
 Coordinate finite type invariant surfaces in Sol spaces D.W. Yoon Pages 649658 Abstract Full Text [PDF 112KB]   In the present paper، we study surfaces invariant under the 1parameter 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
  
 On nonnormal nonabelian subgroups of finite groups C. Zhang Pages 659663 Abstract Full Text [PDF 74KB]   n this paper we prove that a finite group G having at most three conjugacy classes of nonnormal nonabelian proper subgroups is always solvable except for G≅A5، which extends Theorem 3.3 in [Some sufficient conditions on the number of nonabelian subgroups of a finite group to be solvable، Acta Math. Sinica (English Series) 27 (2011) 891896.]. Moreover، we show that a finite group G with at most three same order classes of nonnormal nonabelian proper subgroups is always solvable except for G≅A5.
Keywords: Nonabelian subgroup; nonnormal; conjugacy class; same order class
  
 Solitons for nearly integrable bright spinor BoseEinstein condensate F. Ahmadi Zeidabadi , S.M. Hoseini Pages 665681 Abstract Full Text [PDF 159KB]   Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation، soliton perturbation theory is developed for the F=1 bright spinor BoseEinstein condensates. A small disturbance of the integrability condition can be considered as a small correction to the integrable equation. By choosing appropriate perturbation، the soliton solution for small deviation from the integrability condition is found. Numerical simulations exhibit good agreement with analytical results.
Keywords: BoseEinstein condensate; Integrable 2times2 matrix; nonlinear Schrödinger equation; soliton perturbation theory; discrete and continuous eigenfunctions
  
 Mathematical modeling, analysis and simulation of Ebola epidemics T. Wetere Tulu , T. Boping Pages 683693 Abstract Full Text [PDF 151KB]   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 populations. Many existing models closely approximate historical disease patterns. This article investigates the mathematical model of the deadly disease with severe and uncontrollable bleeding، Ebola which is currently becoming the headache of the whole world though effort to control is undergoing. In this paper a new mathematical model of the Ebola epidemic is built. Besides، the basic reproduction number is calculated and the stability of both disease free and endemic equilibrium is proved. Finally، numerical simulations are executed to further consolidate the analysis of the deadly disease Ebola.
Keywords: Basic reproduction number; global stability; equilibrium; epidemic model
  
 On 5dimensional 2step homogeneous randers nilmanifolds of Douglas type M. Nasehi Pages 695706 Abstract Full Text [PDF 121KB]   In this paper we first obtain the nonRiemannian Randers metrics of Douglas type on twostep homogeneous nilmanifolds of dimension five. Then we explicitly give the flag curvature formulae and the Scurvature formulae for the Randers metrics of Douglas type on these spaces. Moreover، we prove that the only simply connected fivedimensional twostep homogeneous Randers nilmanifolds of Douglas type which are Ricciquadratic have a threedimensional centre. We also prove that all simply connected fivedimensional twostep homogeneous Randers nilmanifolds of Douglas type are never weakly symmetric. The existence of homogeneous Randers spaces of Douglas type with vanishing S curvature which are never g.o. Finsler spaces is also proved and some examples of locally projectively flat Finsler spaces are also obtained.
Keywords: Twostep homogeneous nilmanifolds; Randers metrics of Douglas type; g.o. Finsler spaces; weakly symmetric spaces
  
 Theory of hybrid differential equations on time scales S. Sun , Y. Zhao , P. Zhao , Z. Han Pages 707725 Abstract Full Text [PDF 142KB]   In this paper، we develop the theory of hybrid differential equations on time scales. An existence theorem for hybrid differential equations on time scales is given under Lipschitz conditions. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions. Our results in this paper extend and improve some known results.
Keywords: Differential inequalities; existence theorem; comparison principle; time scales
  
 Strongly kspaces S. Ersoy , I. Ince , M. Bilgin Pages 727734 Abstract Full Text [PDF 103KB]   In this paper، we introduce the notion of strongly k−spaces (with the weak (=finest) pretopology generated by their strongly compact subsets). We characterize the strongly k−spaces and investigate the relationships between preclosedness، locally strongly compactness، prefirst countableness and being strongly k−space.
Keywords: Strongly compact sets; preopen sets; k−spaces
  
 On a class of locally projectively flat Finsler metrics X.H. Mo , H.M. Zhu Pages 735746 Abstract Full Text [PDF 127KB]   In this paper we study Finsler metrics with orthogonal invariance. We find a partial differential equation equivalent to these metrics being locally projectively flat. Some applications are given. In particular، we 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 metric; locally projectively flat; flag curvature; orthogonally invariant
  
 Frattini supplements and Frat series Y. Aydin , A. Pancar Pages 747753 Abstract Full Text [PDF 98KB]   In this study، Frattini supplement subgroup and Frattini supplemented group are defined by Frattini subgroup. By these definitions، it's shown that finite abelian groups are Frattini supplemented and every conjugate of a Frattini supplement of a subgroup is also a Frattini supplement. A group action of a group is defined over the set of Frattini supplements of a normal subgroup of the group by conjugation and in this study new characterization of primitivity of groups has obtained in terms of Frattini supplemented groups by this action. Moreover، Fratseries of a group is defined based on Frattini supplements of normal subgroups of the group and it is shown that subgroups and factor groups of groups with Fratseries also have Fratseries under some special conditions. Furthermore، we determined a characterization of soluble groups which have Fratseries.
Keywords: Frattini subgroup; primitive group; group actions
  
 Finite groups all of whose proper centralizers are cyclic S.M. Jafarian Amiri , H. Rostami Pages 755762 Abstract Full Text [PDF 112KB]   A finite group G is called a CCgroup (G∈CC) if the centralizer of each noncentral element of G is cyclic. In this article we determine all finite CCgroups.
Keywords: Finite group; CAgroup; CCgroup; centralizer
  
 The concentration function problem for Gspaces M.S. Mojahedi Moakhar Pages 763769 Abstract Full Text [PDF 90KB]   In this note، we consider the concentration function problem for a continuous action of a locally compact group G on a locally compact Hausdorff space X. We prove a necessary and sufficient condition for the concentration functions of a spreadout irreducible probability measure μ on G to converge to zero.
Keywords: Concentration function; irreducible; spreadout; stationary measure
  
 A characterization of curves in Galilean 4space G4 G. Oztrk , S. Bykktk , IKiSi Pages 771780 Abstract Full Text [PDF 114KB]   In the present study، we consider a regular curve in Galilean 4space G4 whose position vector is written as a linear combination of its Frenet vectors. We characterize such curves in terms of their curvature functions. Further، we obtain some results of rectifying، constant ratio، Tconstant and Nconstant curves in G4.
Keywords: Frenet frame; constantratio curves; rectifying curves
  
 Unmixed rpartite graphs R. ZaareNahandi , R. JafarpourGolzari Pages 781787 Abstract Full Text [PDF 97KB]   Unmixed bipartite graphs have been characterized by Ravindra and Villarreal independently. Our aim in this paper is to characterize unmixed r partite graphs under a certain condition، which is a generalization of Villarreal's theorem on bipartite graphs. Also، we give some examples and counterexamples in relevance to this subject.
Keywords: rpartite graph; wellcovered; unmixed; perfect matching; clique
  
 On boundary value problem for fractional differential equations M.R. Hamidi , N. Nyamoradi Pages 789805 Abstract Full Text [PDF 142KB]   In this paper، we study the existence of solutions for a fractional boundary value problem. By using critical point theory and variational methods، we give some new criteria to guarantee that the problems have at least one solution and infinitely many solutions.
Keywords: Fractional differential equations; solutions; variational methods; Morse theory; fountain Theorem
  
 Almost valuation rings R. JahaniNezhad , F. Khoshayand Pages 807816 Abstract Full Text [PDF 108KB]   The aim of this paper is to generalize the notion of almost valuation domains to arbitrary commutative rings. Also، we consider relations between almost valuation rings and pseudoalmost valuation rings. We prove that the class of almost valuation rings is properly contained in the class of pseudoalmost valuation rings. Among the properties of almost valuation rings، we show that a quasilocal ring R with regular maximal ideal M is a pseudoalmost valuation ring if and only if V=(M:M) is an almost valuation ring with maximal ideal RadV(M) . Furthermore، we show that pseudoalmost valuationrings are precisely the pullbacks of almost valuation rings.
Keywords: Strongly prime ideal; Almost valuation domain; Pseudoalmost valuation ring
  
 Wconvergence of the proximal point algorithm in complete CAT(0) metric spaces S. Ranjbar Pages 817834 Abstract Full Text [PDF 152KB]   In this paper، we generalize the proximal point algorithm to complete CAT(0) spaces and show that the sequence generated by the proximal point algorithm wconverges to a zero of the maximal monotone operator. Also، we prove that if f:X→]−∞،+∞] is a proper، convex and lower semicontinuous function on the complete CAT(0) space X، then the proximal point algorithm wconverges to a zero of the subdifferential of f، i.e.، a minimizer of f. Some strong convergence results (convergence in metric) are also presented with additional assumptions on the monotone operator and the convex function f.
Keywords: Hadamard space; maximal monotone operator; Proximal point algorithm; wconvergence; subdifferential
  
 On quasi Pspaces and their applications in submaximal and nodec spaces A. R. Aliabad , V. Bagheri , M. Karavan Jahromi Pages 835852 Abstract Full Text [PDF 151KB]   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 closed. Here، we study a variety of spaces some of which have already been studied in C(X). Among them are، most importantly، quasi Pspaces and pointwise quasi Pspaces. We obtain some new useful topological characterizations of quasi Pspaces and pointwise quasi P spaces. Consequently، we obtain a close relation between these latter spaces and submaximal and nodec spaces.
Keywords: Quasi Pspace; Pointwise QPspace; Submaximal space; Nodec space; Ispace
  
 Some results on the symmetric doubly stochastic inverse eigenvalue problem W.R. Xu , G.L. Chen Pages 853865 Abstract Full Text [PDF 136KB]   The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an ntuple σ=(1،λ2،λ3،،λn)∈Rn with λi≤1، i=1،2،،n، to be the spectrum of an nn symmetric doubly stochastic matrix A. If there exists an nn symmetric doubly stochastic matrix A with σ as its spectrum، then the list σ is s.d.s. realizable، or such that A s.d.s. realizes σ . In this paper، we propose a new sufficient condition for the existence of the symmetric doubly stochastic matrices with prescribed spectrum. Finally، some results about how to construct new s.d.s. realizable lists from the known lists are presented.
Keywords: Inverse eigenvalue problem; symmetric doubly stochastic matrix; sufficient condition
  
 On the type of conjugacy classes and the set of indices of maximal subgroups J. Shi , Z. Wu , R. Hou Pages 867874 Abstract Full Text [PDF 108KB]   Let G be a finite group. By MT(G)=(m1،⋯،mk) we denote the type of conjugacy classes of maximal subgroups of G، which implies that G has exactly k conjugacy classes of maximal subgroups and m1،،mk are the numbers of conjugates of maximal subgroups of G، where m1≤⋯≤mk. In this paper، we give some new characterizations of finite groups by the type of conjugacy classes of maximal subgroups. By πt(G) we denote the set of indices of all maximal subgroups of G . We also investigate the influence of the set of indices of all maximal subgroups on the structure of finite groups.
Keywords: Maximal subgroup; nonabelian simple group; the type of conjugacy classes; the set of indices
  
 On reducibility of weighted composition operators M. R. Azimi , M. R. Jabbarzadeh , M. Jafari Bakhshkandi Pages 875883 Abstract Full Text [PDF 124KB]   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
  
 Almost specification and renewality in spacing shifts D. Ahmadi Dastjerdi , M. Dabbaghian Amiri Pages 885896 Abstract Full Text [PDF 136KB]   Let (ΣP،σP) be the space of a spacing shifts where P⊂N0=N∪{0} and ΣP={s∈{0،1}N0:si=sj=1 if i−j∈P∪{0}} and σP the shift map. We will show that ΣP is mixing if and only if it has almost specification property with at least two periodic points. Moreover، we show that if h(σP)=0، then ΣP is almost specified and if h(σP)>0 and ΣP is almost specified، then it is weak mixing. Also، some sufficient conditions for a coded ΣP being renewal or uniquely decipherable is given. At last we will show that here are only two conjugacies from a transitive ΣP to a subshift of {0،1}N0.
Keywords: Spacing shifts; almost specification; renewal; uniquely decipherable
  
 Double derivations of nLie algebras R. Bai , Y. Gao , Y. Zhang , Z. Li Pages 897910 Abstract Full Text [PDF 115KB]   After introducing double derivations of nLie algebra L we describe the relationship between the algebra D(L) of double derivations and the usual derivation Lie algebra Der(L). In particular، we prove that the inner derivation algebra ad(L) is an ideal of the double derivation algebra D(L); we also show that if L is a perfect nLie algebra with certain constraints on the base field then the centralizer of ad(L) in D(L) is trivial and D(L) is centerless. In addition، we obtain that for every perfect nLie algebra L with zero center، the triple derivations of the derivation algebra Der(L) are exactly the derivations of Der(L)، and the triple derivations of the inner derivation algebra ad(L) are precisely the derivations of ad(L).
Keywords: nLie algebra; double derivation; Derivation; inner derivation
  
 Modules for which every noncosingular submodule is a summand Y. Talebi , M. Hosseinpour , A.R. Moniri Hamzekolaee Pages 911922 Abstract Full Text [PDF 129KB]   A module M is lifting if and only if M is amply supplemented and every coclosed submodule of M is a direct summand. In this paper، we are interested in a generalization of lifting modules by removing the condition"amply supplemented" and just focus on modules such that every noncosingular submodule of them is a summand. We call these modules NS. We investigate some general properties of NSmodules. Several examples are provided to separate different concepts. It is shown that every noncosingular NSmodule is a direct sum of indecomposable modules. We also discuss on finite direct sums of NSmodules.
Keywords: Noncosingular submodule; amply supplemented module; NSmodule
  
 A note on blowup in parabolic equations with local and localized sources B. Liu , F. Li Pages 923942 Abstract Full Text [PDF 164KB]   This note deals with the systems of parabolic equations with local and localized sources involving n components. We obtained the exponent regions، where k∈{1،2،⋯،n} components may blow up simultaneously while the other (n−k) ones still remain bounded under suitable initial data. It is proved that different initial data can lead to different blowup phenomena even in the same exponent regions، and moreover، different blowup mechanism leads to different blowup rates and blowup sets.
Keywords: Nonsimultaneous blowup; simultaneous blowup; blowup rate; blowup set
  
 Simple axiomatization of reticulations on residuated lattices M. Kondo Pages 943949 Abstract Full Text [PDF 95KB]   We give a simple and independent axiomatization of reticulations on residuated lattices، which were axiomatized by five conditions in [C. Mureşan، The reticulation of a residuated lattice، Bull. Math. Soc. Sci. Math. Roumanie 51 (2008)، no. 1، 4765]. Moreover، we show that reticulations can be considered as lattice homomorphisms between residuated lattices and bounded distributive lattices. Consequently، the result proved by Muresan in 2008، for any two reticulattions (L1،λ1)،(L2،λ2) of a residuated lattice X there exists an isomorphism f:L1→L2 such that f∘λ1=λ2، can be considered as a homomorphism theorem.
Keywords: Reticulation; residuated lattice; principal filter
  
 Normal edgetransitive Cayley graphs on the nonabelian groups of order 4p2, where p is a prime number Y. Pakravesh , Ali Iranmanesh Pages 951974 Abstract Full Text [PDF 199KB]   In this paper، we determine all of connected normal edgetransitive Cayley graphs on nonabelian groups with order 4p2، where p is a prime number.
Keywords: Cayley graph; normal edgetransitive; vertextransitive; edgetransitive
  
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