

2018 . 

Bulletin of Iranian Mathematical Society
ISSN 1017060X
دوماهنامه  ( )
5 2017




 Inverse SturmLiouville problems using three spectra with finite number of transmissions and parameter dependent conditions M. Shahriari * Pages 13411355 Abstract Full Text [PDF 162KB]   In this manuscript، we study various by uniqueness results for inverse spectral problems of SturmLiouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditions. We consider both the cases of classical Robin and eigenparameter dependent boundary conditions.
Keywords: Inverse SturmLiouville problem; eigenparameter dependent boundary conditions; internal discontinuities; three spectra; WeylTitchmarsh mfunction
  
 A new characterization of L 2 (q) by the largest element orders Q.H. Jiang , C.G. Shao , W.J. Shi * , Q.L. Zhang Pages 11431151 Abstract Full Text [PDF 136KB]   We characterize the finite simple groups L2(q) by the group orders and the largest element orders، where q is a prime or q=2a، with 2a+1 or 2a−1 a prime.
Keywords: Finite groups; group orders; largest element orders; characterization
  
 Strongly nilclean corner rings P. Danchev * Pages 13331339 Abstract Full Text [PDF 106KB]   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 nilclean rings، then R/J(R) is nilclean. In particular، under certain additional circumstances، R is also nilclean. These results somewhat improves on achievements due to Diesl in J. Algebra (2013) and to Ko\c{s}anWangZhou in J. Pure Appl. Algebra (2016). In addition، we also give a new transparent proof of the main result of BreazCalugareanuDanchevMicu in Linear Algebra Appl. (2013) which says that if R is a commutative nilclean ring، then the full nn matrix ring Mn(R) is nilclean.
Keywords: Nilclean rings; strongly nilclean rings; idempotents; nilpotents; Jacobson radical
  
 A new onestep iterative process for approximating common fixed points of a countable family of quasinonexpansive multivalued mappings in CAT(0) spaces S. Suantai , B. Panyanak , W. Phuengrattana * Pages 11271141 Abstract Full Text [PDF 158KB]   In this paper، we propose a new onestep iterative process for a countable family of quasinonexpansive multivalued mappings in a CAT(0) space. We also prove strong and Deltaconvergence theorems of the proposed iterative process under some control conditions. Our main results extend and generalize many results in the literature.
Keywords: Fixed point; quasinonexpansive multivalued mappings; CAT(0) spaces
  
 Complete pivoting strategy for the IUL preconditioner obtained from Backward Factored APproximate INVerse process A. Rafiei * , M. Bollhoefer Pages 14171456 Abstract Full Text [PDF 446KB]   In this paper، we use a complete pivoting strategy to compute the IUL preconditioner obtained as the byproduct of the Backward Factored APproximate INVerse process. This pivoting is based on the complete pivoting strategy of the Backward IJK version of Gaussian Elimination process. There is a parameter α to control the complete pivoting process. We have studied the effect of different values of α on the quality of the IUL preconditioner. For the numerical experiments section، the IUL factorization which is coupled with the complete pivoting is compared to the ILUTP and to the leftlooking version of RIF which is coupled with the complete pivoting strategy. As the preprocessing، we have applied the maximum weighted matching coupled the Reverse CuthillMckee (RCM) and multilevel nested dissection reordering.
Keywords: Backward factored APproximate INVerse; IUL preconditioner; backward IJK version of Gaussian elimination; complete pivoting; ILUTP; leftlooking RIF with pivoting
  
 A stochastic version analysis of an M/G/1 retrial queue with Bernoulli schedule M. Boualem* , M. Cherfaoui , N. Djellab , D. Aissani Pages 13771397 Abstract Full Text [PDF 544KB]   In this work، we derive insensitive bounds for various performance measures of a singleserver retrial queue with generally distributed interretrial times and Bernoulli schedule، under the special assumption that only the customer at the head of the orbit queue (i.e.، a FCFS discipline governing the flow from the orbit to the server) is allowed to occupy the server. The methodology is strongly based on stochastic comparison techniques. Instead of studying a performance measure in a quantitative fashion، this approach attempts to reveal the relationship between the performance measures and the parameters of the system. We prove the monotonicity of the transition operator of the embedded Markov chain relative to strong stochastic ordering and increasing convex ordering. We obtain comparability conditions for the distribution of the number of customers in the system. Bounds are derived for the stationary distribution and some simple bounds for the mean characteristics of the system. The proofs of these results are based on the validation of some inequalities for some cumulative probabilities associated with every state (m،n) of the system. Finally، the effects of various parameters on the performance of the system have been examined numerically.
Keywords: Retrial queues; performance measures; stochastic orders; monotonicity; simulation
  
 An algorithm for approximating nondominated points of convex multiobjective optimization problems M. Ghaznavi * , Z. Azizi Pages 13991415 Abstract Full Text [PDF 407KB]   In this paper، we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)، where the constraints and the objective functions are convex. We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points. The proposed algorithm can be applied for differentiable or nondifferentiable convex MOPs. To illustrate efficiency of the proposed algorithm for convex MOPs، we provide numerical examples.
Keywords: Multiobjective optimization; convexity; nondominated point; efficient solution; approximation algorithm; differentiable problem
  
 Stochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity E. Salavati * , B.Z. Zangeneh Pages 12871299 Abstract Full Text [PDF 149KB]   Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered. The coefficients are assumed to have linear growth. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed.
Keywords: Stochastic evolution equation; monotone operator; Levy noise; Ito type inequality; stochastic convolution integral
  
 Dilations for Castdynamical systems with abelian groups on Hilbert C astmodules Z. Wang * , J. Zhang Pages 13131321 Abstract Full Text [PDF 123KB]   In this paper we investigate the dilations of completely positive definite representations of C∗dynamical systems with abelian groups on Hilbert C∗modules. We show that if (A،G،α) is a C∗dynamical system with G an abelian group، then every completely positive definite covariant representation (π،φ،E) of (A،G،α) on a Hilbert C∗module E admits an unitary dilation ((π^،φ^،E^)).
Keywords: Dilation; covariant representation; Castdynamical system; Hilbert Castmodule
  
 Some topologies on the space of quasimultipliers M. Adib* Pages 13231332 Abstract Full Text [PDF 120KB]   Assume that A is a Banach algebra. We define the β−topology and the γ−topology on the space QMel(A∗) of all bounded extended left quasimultipliers of A∗. We establish further properties of (QMel(A∗)،γ) when A is a C∗−algebra. In particular، we characterize the γ−dual of QMel(A∗) and prove that (QMel(A∗)،γ)∗، under the topology of bounded convergence، is isomorphic to A∗∗∗.
Keywords: Quasimultiplier; multiplier; Banach algebra; Arens regularity; strict topology
  
 Application of frames in Chebyshev and conjugate gradient methods H. Jamali * , E. Afroomand Pages 12651279 Abstract Full Text [PDF 162KB]   Given a frame of a separable Hilbert space H، we present some iterative methods for solving an operator equation Lu=f، where L is a bounded، invertible and symmetric operator on H . We present some algorithms based on the knowledge of frame bounds، Chebyshev method and conjugate gradient method، in order to give some approximated solutions to the problem. Then we investigate the convergence and optimality of them.
Keywords: Hilbert spaces; dual space; frame; Chebyshev polynomials; iterative method
  
 Efficient quadrature rules for a class of cordial Volterra integral equations: A comparative study H. Majidian* Pages 12451258 Abstract Full Text [PDF 151KB]   A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations. The equations of this class appear in heat conduction problems with mixed boundary conditions. The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes. A comparative study is carried out، which points out that the proposed method is the most efficient one among other existing methods. In fact، the results of this paper introduce a mostefficient decisivechoice for computing the solution of the heat conduction model.
Keywords: Cordial Volterra integral equation; heat conduction problem; mixedtype boundary condition; compound quadrature rule; graded mesh
  
 Very cleanness of generalized matrices Y. Kurtulmaz * Pages 14571465 Abstract Full Text [PDF 112KB]   An element a in a ring R is very clean in case there exists an idempotent e∈R such that ae=ea and either a−e or a+e is invertible. An element a in a ring R is very Jclean provided that there exists an idempotent e∈R such that ae=ea and either a−e∈J(R) or a+e∈J(R). Let R be a local ring، and let s∈C(R). We prove that A∈Ks(R) is very clean if and only if A∈U(Ks(R))، IA∈U(Ks(R)) or A∈Ks(R) is very Jclean.
Keywords: Local ring; very clean ring; very Jclean ring
  
 A study on dimensions of modules E. Momtahan * , M. Motamedi Pages 12271235 Abstract Full Text [PDF 120KB]   In this article we study relations between some algebraic operations such as tensor product and localization from one hand and some wellknown dimensions such as uniform dimension، hollow dimension and type dimension from the other hand. Some minor applications to the ring C(X) are observed.
Keywords: Type dimension; uniform dimension; hollow dimension
  
 On characterizations of hyperbolic harmonic Bloch and Besov spaces X. Fu * Pages 11831194 Abstract Full Text [PDF 139KB]   We define hyperbolic harmonic ωαBloch space Bαω in the unit ball B of Rn and characterize it in terms of ω((1−x2)β(1−y2)α−β)f(x)−f(y)[x،y]γx−y1−γ، where 0≤γ≤1. Similar results are extended to little ωαBloch and Besov spaces. These obtained characterizations generalize the corresponding ones which were obtained by G. Ren and U. K\"{a}hler in 2002 and 2005.
Keywords: Hyperbolic harmonic function; Bloch space; Besov space; majorant
  
 Improvements of Young inequality using the Kantorovich constant M. Khosravi , A. Sheikh Hosseini * Pages 13011311 Abstract Full Text [PDF 148KB]   Some improvements of Young inequality and its reverse for positive numbers with Kantorovich constant K(t،2)=(1+t)24t are given. Using these inequalities some operator inequalities and HilbertSchmidt norm versions for matrices are proved. In particular، it is shown that if a،b are positive numbers and 0⩽ν⩽1، then for all integers k⩾1: K(h12n،2)rna♯νb⩽a∇νb−∑n−1k=0rk((a♯mk2kb)12−(a♯mk+12kb)12)2⩽K(h12n،2 Rna♯νb، where mk=[2kν] is the largest integer not greater than 2kν، r0=min{ν،1−ν}، k=min{2rk−1،1−2rk−1} and Rk=1−rk.
Keywords: Heinz mean; HilbertSchmidt norm; Kantorovich constant; Young inequality
  
 Fivevalue rich lines, Borel directions and uniqueness of meromorphic functions J.R. Long * Pages 14671478 Abstract Full Text [PDF 134KB]   For a meromorphic function f in the complex plane، we shall introduce the definition of fivevalue rich line of f، and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the fivevalue rich line and Borel directions. Finally، the relationship between a fivevalue rich line and a Borel direction is discussed، that is، every Borel direction of f is its fivevalue rich line، and the inverse statement holds when f is of infinite order.
Keywords: Borel direction; fivevalue rich line; meromorphic function; sharing value; uniqueness
  
 Critical fixed point theorems in Banach algebras under weak topology features A. Ben Amar * , A. Tlili Pages 9951015 Abstract Full Text [PDF 186KB]   In this paper، we establish some new critical fixed point theorems for the sum AB+C 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
  
 On certain maximality principles R. Mohammadpour * Pages 12591264 Abstract Full Text [PDF 108KB]   We present streamlined proofs of certain maximality principles studied by Hamkins and Woodin. Moreover، we formulate an intermediate maximality principle، which is shown here to be equiconsistent with the existence of a weakly compact cardinal κ such that Vκ≺V.
Keywords: Hamkins' maximality principle; weakly compact cardinal; consistency result
  
 On pm + and finite character biamalgamation M. Tamekkante , E.M. Bouba* Pages 12371244 Abstract Full Text [PDF 121KB]   Let f:A→B and g:A→C be two ring homomorphisms and let J and J′ be two ideals of B and C، respectively، such that f−1(J)=g−1(J′). The biamalgamation of A with (B،C) along (J،J′) with respect of (f،g) is the subring of BC given by A⋈f،g(J،J′)={(f(a)+j،g(a +j′)/a∈A،(j،j′)∈JJ′}. In this paper، we study the transference of pm+، pm and finite character ringproperties in the biamalgamation.
Keywords: Biamalgamated algebras; pm+rings; pm rings; rings with finite character
  
 On some generalized recurrent manifolds A.A. Shaikh * , I. Roy , H. Kundu Pages 12091225 Abstract Full Text [PDF 159KB]   The object of the present paper is to introduce and study a type of nonflat semiRiemannian manifolds، called، super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [A.A. Shaikh and A. Patra، On a generalized class of recurrent manifolds، Arch. Math. (Brno) 46 (2010) 7178.] and weakly generalized recurrent manifolds [A.A. Shaikh and I. Roy، On weakly generalized recurrent manifolds، Ann. Univ. Sci. Budapest Rolando Eotvos، Sect. Math. 54 (2011) 3545.]. The nature of associated 1forms of a super generalized recurrent manifold is determined and it is proved that on a Roter type manifold [R. Deszcz، On Roter type manifolds، in: 5th Conference on Geometry and Topology of Manifolds، Krynica، Poland، 2003.] such a notion is equivalent to the notion of generalized Riccirecurrent manifold [U.C. De، N. Guha and D. Kamilya، On generalized Riccirecurrent manifolds، Tensor (N.S.) 56 (1995)، no. 3، 312317.]. We 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
  
 Convergence of the sinc method applied to delay Volterra integral equations L. Shiri , M. Zarebnia * Pages 13571375 Abstract Full Text [PDF 179KB]   In this paper، the numerical solutions of linear and nonlinear Volterra integral equations with nonvanishing delay are considered by two methods. The methods are developed by means of the sinc approximation with the single exponential (SE) and double exponential (DE) transformations. The existence and uniqueness of sinccollocation solutions for these equations are provided. These methods improve conventional results and achieve exponential convergence. Numerical results are included to confirm the efficiency and accuracy of the methods.
Keywords: Volterra integral equations; nonvanishing delay; sinccollocation
  
 A numerical method for discrete fractionalorder chemostat model derived from nonstandard numerical scheme M. Zeinadini , M. Namjoo* Pages 11651182 Abstract Full Text [PDF 932KB]   In this paper، the fractionalorder form of three dimensional chemostat model with variable yields is introduced. The stability analysis of this fractional system is discussed in detail. In order to study the dynamic behaviours of the mentioned fractional system، the well known nonstandard (NSFD) scheme is implemented. The proposed NSFD scheme is compared with the forward Euler and fourth order RungeKutta methods. Numerical results show that the NSFD approach is easy and accurate when applied to fractionalorder chemostat model.
Keywords: Chemostat model; fractionalorder differential equation; stability; nonstandard finite difference scheme
  
 Further inequalities for operator space numerical radius on 2*2 operator matrices M. Sattari * Pages 12811285 Abstract Full Text [PDF 101KB]   We present some inequalities for operator space numerical radius of 22 block matrices on the matrix space Mn(X)، when X is a numerical radius operator space. These 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
  
 On the character space of Banach vectorvalued function algebras M. Abtahi * Pages 11951207 Abstract Full Text [PDF 149KB]   Given a compact space X and a commutative Banach algebra A، the character spaces of Avalued function algebras on X are investigated. The class of natural Avalued function algebras، those whose characters can be described by means of characters of A and point evaluation homomorphisms، is introduced and studied. For an admissible Banach Avalued function algebra A on X، conditions under which the character space M(A) is homeomorphic to M(A)M(A) are presented، where A=C(X)∩A is the subalgebra of A consisting of scalarvalued functions. An illustration of the results is given by some examples.
Keywords: Commutative Banach algebras; Banach function algebras; vectorvalued function algebras; vectorvalued characters
  
 Measure of non strict singularity of Schechter essential spectrum of two bounded operators and application F. Abdmouleh* , I. Walha Pages 15431558 Abstract Full Text [PDF 160KB]   In this paper، we discuss the essential spectrum of sum of two bounded operators using measure of non strict singularity. Based on this new investigation، a problem of onespeed neutron transport operator is presented.
Keywords: Fredholm operators; lower (respectively upper) semiFredholm operators; essential spectrum; measure of nonstrictsingularity; onespeed neutron transport operator
  
 Affinization of Segre products of partial linear spaces K. Petelczyc * , M. Ż, , ynel Pages 11011126 Abstract Full Text [PDF 212KB]   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 pointline 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 nondegenerate hyperplanes in the Segre product of partial linear spaces embeddable into projective space is introduced.
Keywords: Segre product; hyperplane; hyperplane complement
  
 A simple proof of Zariski's Lemma A. Azarang * Pages 15291530 Abstract Full Text [PDF 69KB]   Our aim in this very short note is to show that the proof of the following wellknown fundamental lemma of Zariski follows from an argument similar to the proof of the fact that the rational field Q is not a finitely generated Zalgebra.
Keywords: Zariski's Lemma; PID; Field
  
 Existence and blowup of solution of Cauchy problem for the sixth order damped Boussinesq equation Y. Wang * Pages 10571071 Abstract Full Text [PDF 155KB]   In this paper، we consider the existence and uniqueness of the global solution for the sixthorder damped Boussinesq equation. Moreover، the finitetime blowup of the solution for the equation is investigated by the concavity method.
Keywords: Boussinesq equation; Cauchy problem; global solution; blowup
  
 Convex combinations of harmonic shears of slit mappings L. Shi , Z.G. Wang , A. Rasila * , Y. Sun Pages 14951510 Abstract Full Text [PDF 2935KB]   In this paper، we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings. Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived. Several 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
  
 The norm of preSchwarzian derivatives on biunivalent functions of order α H. Rahmatan , Sh. Najafzadeh * , A. Ebadian Pages 10371043 Abstract Full Text [PDF 110KB]   In the present investigation، we give the best estimates for the norm of the preSchwarzian derivative Tf(z)=f′′(z)f′(z) for bistarlike functions and a new subclass of biunivalent functions of order α، where ∥Tf∥=supz<1(1−z2)f′′(z)f′(z).
Keywords: BiUnivalent Functions; bistarlike functions; subordina tion; preSchwarzian derivatives
  
 On a pLaplacian system and a generalization of the LandesmanLazer type condition B.Q. Hung * , H.Q. Toan Pages 15111528 Abstract Full Text [PDF 174KB]   This article shows the existence of weak solutions of a resonance problem for nonuniformly pLaplacian system in a bounded domain in RN . Our arguments are based on the minimum principle and rely on a generalization of the LandesmanLazer type condition.
Keywords: Semilinear elliptic equation; nonuniform; LandesmanLazer condition; minimum principle
  
 Ordertype existence theorem for second order nonlocal problems at resonance F. Wang* , S. Zhang Pages 10451055 Abstract Full Text [PDF 132KB]   This paper gives an abstract ordertype existence theorem for second order nonlocal boundary value problems at resonance and obtain existence criteria for at least two positive solutions، where f is a continuous function. Our results generalize or extend related results in the literature and give a positive answer to the question raised in the literature. An example is given to illustrate the new results.
Keywords: Ordertype existence theorem; nonlocal problems; at resonance
  
 Benson's algorithm for nonconvex multiobjective problems via nonsmooth Wolfe duality N. Shafiei * Pages 975994 Abstract Full Text [PDF 488KB]   In this paper، we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints. We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions. We also formulate an infinitive approximation set of the (weakly) nondominated points of biobjective optimization problems. Moreover، we provide some numerical examples to illustrate the advantage of our algorithm.
Keywords: Multiobjective optimization; approximation algorithm; efficient solution; nondominated point
  
 On two classes of third order boundary value problems with finite spectrum J.J. Ao * Pages 10891099 Abstract Full Text [PDF 140KB]   The spectral analysis of two classes of third order boundary value problems is investigated. For every positive integer m we construct two classes of regular third order boundary value problems with at most 2m+1 eigenvalues، counting multiplicity. These kinds of finite spectrum results are previously known only for even order boundary value problems.
Keywords: Eigenvalues; finite spectrum; third order boundary value problems
  
 Some rank equalities for finitely many tripotent matrices T. Petik * , H. Ozdemir Pages 14791493 Abstract Full Text [PDF 148KB]   A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations. Moreover، by using this equality and Theorems 8 and 10 in [Chen M. and et al. On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications، The Scientific World Journal 2014 (2014)، Article ID 702413، 7 pages.]، some other rank equalities for tripotent matrices are given. Furthermore، we obtain several rank equalities related to some special types of matrices، some of which are available in the literature، from the results established.
Keywords: Rank; elementary block matrix operations; idempotent matrix; tripotent matrix
  
 On annihilator ideals in skew polynomial rings M. Zahiri , A. Moussavi * , R. Mohammadi Pages 10171036 Abstract Full Text [PDF 184KB]   This article examines annihilators in the skew polynomial ring R[x;alpha،delta]. A ring is strongly right AB if every nonzero 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 nilreversible 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; nilreversible ring; rings with Property(A)
  
 A radical extension of the category of S sets M. Haddadi * , M.M. Ebrahimi Pages 11531163 Abstract Full Text [PDF 136KB]   Let SSet be the category of Ssets، sets together with the actions of a semigroup S on them. And، let SPos be the category of Sposets، posets together with the actions compatible with the orders on them. In this paper we show that the category SPos is a radical extension of SSet; that is there is a radical on the category SPos، the order desolator radical، whose torsionfree class is SSet. To do this، first we give a precise definition of a radical on the category SPosand construct some functors between the above mentioned categories and finally we show that SPos is a radical extension of SSet.
Keywords: Radical; Sset; Sposet
  
 NSE characterization of some linear groups N. Ahanjideh , L. Mousavi , B. Taeri * Pages 15311542 Abstract Full Text [PDF 155KB]   For a finite group G، let nse(G)={mk∣k∈πe(G)}، where mk is the number of elements of order k in G and πe(G) is the set of element orders of G. In this paper، we prove that G≅Lm(2) if and only if p∣G and nse(G)=nse(Lm(2))، where m∈{n،n+1} and 2n−1=p is a prime number.
Keywords: Set of the numbers of elements of the same order; prime graph; Mersenne number
  
 Diagonal arguments and fixed points A. Karimi , S. Salehi * Pages 10731088 Abstract Full Text [PDF 245KB]   A universal schema for diagonalization was popularized by N.S. Yanofsky (2003)، based on a pioneering work of F.W. Lawvere (1969)، in which the existence of a (diagonolizedout and contradictory) object implies the existence of a fixedpoint for a certain function. It was shown that many selfreferential paradoxes and diagonally proved theorems can fit in that schema. Here، we fit more theorems in the universal schema of diagonalization، such as Euclid's proof for the infinitude of the primes and new proofs of G.~Boolos (1997) for Cantor's theorem on the nonequinumerosity of a set with its powerset. Then، in Linear Temporal Logic، we show the nonexistence of a fixedpoint in this logic whose proof resembles the argument of Yablo's paradox (1985، 1993). Thus، Yablo's paradox turns for the first time into a genuine mathematicological theorem in the framework of Linear Temporal Logic. Again 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/fixedpoint schema. We also show the existence of dominating (Ackermannlike) functions (which dominate a given countable set of functions، such as primitive recursive functions) in the schema.
Keywords: Diagonal argument; selfreference; fixedpoints; Yablo's paradox; (linear) temporal logic
  
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