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An estimation method for the reliability of "consecutive-k-out-of-n system"
http://hdl.handle.net/10525/2812
Title: An estimation method for the reliability of "consecutive-k-out-of-n system"<br/><br/>Authors: Ksir, Brahim<br/><br/>Abstract: This paper is concerned with consecutive-k-out-of-n system in which all the components have the same q lifetime probability, so, it's possible to estimate q from a sample by using the maximum likelihood principle. In the reliability formula of the consecutive-k-out-of-n system appears the term q^k. The goal in this work is to propose a direct estimation of q^k to avoid the accumulated errors owed to the power. More precisely, we establish a new method based on the Markov chains to calculate and estimate the reliability of the system.<br/><br/>Description: 2010 Mathematics Subject Classification: 60K10, 60K20, 60J10, 60J20, 62G02, 62G05, 68M15, 62N05, 68M15.On self-avoiding walks on certain grids and the connective constant
http://hdl.handle.net/10525/2811
Title: On self-avoiding walks on certain grids and the connective constant<br/><br/>Authors: Dangovski, Rumen<br/><br/>Abstract: We consider self-avoiding walks on the square grid graph. More precisely we investigate the number of walks of a fixed length on Z×{-1,0,1}. Using combinatorial arguments we derive the related generating function. We present the asymptotic estimates of the number of walks in consideration, as well as important connective constants.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary: 05C81. Secondary: 60G50.Generalized homogeneous Besov spaces and their applications
http://hdl.handle.net/10525/2810
Title: Generalized homogeneous Besov spaces and their applications<br/><br/>Authors: Mejjaoli, Hatem<br/><br/>Abstract: In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^d, and we give a complete analysis on these spaces and same applications.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary 35L05. Secondary 46E35, 35J25, 22E30.Resonances of two-dimensional Schrödinger operators with strong magnetic fields
http://hdl.handle.net/10525/2809
Title: Resonances of two-dimensional Schrödinger operators with strong magnetic fields<br/><br/>Authors: Tuan Duong, Anh<br/><br/>Abstract: The purpose of this paper is to study the Schrödinger operator P(B,w) = (Dx-By^2+Dy^2+w^2x^2+V(x,y),(x,y) О R^2, with the magnetic field B large enough and the constant w № 0 is fixed and proportional to the strength of the electric field. Under certain assumptions on the potential V, we prove the existence of resonances near Landau levels as B®Ґ. Moreover, we show that the width of resonances is of size O(B^-Ґ).<br/><br/>Description: 2010 Mathematics Subject Classification: 81Q20 (35P25, 81V10).Approximation par des morphismes de chaînes et points fixes des applications multivoques
http://hdl.handle.net/10525/2808
Title: Approximation par des morphismes de chaînes et points fixes des applications multivoques<br/><br/>Authors: Robert, Cauty<br/><br/>Abstract: In this paper, we consider u.s.c. multivalued maps with compact point images. We develop a notion of approximation of such maps by chain mappings between the singular chain complexes of the spaces, and use this notion to prove fixed point theorems.<br/><br/>Description: 2010 Mathematics Subject Classification: 54C60, 54H25.A Basis for the Graded Identities of the Pair (M2(K), gl2(K))
http://hdl.handle.net/10525/2807
Title: A Basis for the Graded Identities of the Pair (M2(K), gl2(K))<br/><br/>Authors: Koshlukov, Plamen; Krasilnikov, Alexei<br/><br/>Abstract: Let M2(K) be the algebra of 2×2 matrices over an infinite integral domain K. In this note we describe a basis for the Z2-graded identities of the pair (M2(K),gl2(K)).<br/><br/>Description: 2010 Mathematics Subject Classification: 16R10, 17B01.Characterizing Non-Matrix Properties of Varieties of Algebras in the Language of Forbidden Objects
http://hdl.handle.net/10525/2806
Title: Characterizing Non-Matrix Properties of Varieties of Algebras in the Language of Forbidden Objects<br/><br/>Authors: Finogenova, Olga<br/><br/>Abstract: We discuss characterizations of some non-matrix properties of varieties of associative algebras in the language of forbidden objects. Properties under consideration include the Engel property, Lie nilpotency, permutativity. We formulate a few open problems.<br/><br/>Description: 2010 Mathematics Subject Classification: 16R10, 16R40.Growth Functions of Fr-sets
http://hdl.handle.net/10525/2805
Title: Growth Functions of Fr-sets<br/><br/>Authors: Lomond, Jonny<br/><br/>Abstract: In this paper we consider an open problem from [1], regarding the description of the growth functions of the free group acts. Using the language of graphs, we solve this problem by providing the necessary and sufficient conditions for a function to be a growth function for a free group act.<br/><br/>Description: 2010 Mathematics Subject Classification: 05C30, 20E08, 20F65.Universal Enveloping Algebras of Nonassociative Structures
http://hdl.handle.net/10525/2804
Title: Universal Enveloping Algebras of Nonassociative Structures<br/><br/>Authors: Tvalavadze, Marina<br/><br/>Abstract: This is a survey paper to summarize the latest results on the universal enveloping algebras of Malcev algebras, triple systems and Leibniz n-ary algebras.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary 17D15. Secondary 17D05, 17B35, 17A99.On Ordinary and Z2-graded Polynomial Identities of the Grassmann Algebra
http://hdl.handle.net/10525/2803
Title: On Ordinary and Z2-graded Polynomial Identities of the Grassmann Algebra<br/><br/>Authors: Ribeiro Tomaz da Silva, Viviane<br/><br/>Abstract: The main purpose of this paper is to provide a survey of results concerning the ordinary and Z2-graded polynomial identities of the infinite dimensional Grassmann algebra over a field of characteristic zero, as well as of its sequences of ordinary and Z2-graded codimensions and cocharacters. We also intend to describe briefly the techniques used by the authors in order to illustrate some important methods used in PI-theory.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary: 16R10, Secondary: 16W55.On the Gibson Bounds over Finite Fields
http://hdl.handle.net/10525/2802
Title: On the Gibson Bounds over Finite Fields<br/><br/>Authors: V. Budrevich, Mikhail; E. Guterman, Alexander<br/><br/>Abstract: We investigate the Pólya problem on the sign conversion between the permanent and the determinant over finite fields. The main attention is given to the sufficient conditions which guarantee non-existence of sing-conversion. In addition we show that F3 is the only field with the property that any matrix with the entries from the field is convertible. As a result we obtain that over finite fields there are no analogs of the upper Gibson barrier for the conversion and establish the lower convertibility barrier.<br/><br/>Description: 2010 Mathematics Subject Classification: 15A15, 15A04.Some Numerical Invariants of Multilinear Identities
http://hdl.handle.net/10525/2801
Title: Some Numerical Invariants of Multilinear Identities<br/><br/>Authors: Giambruno, Antonio; Mishchenko, Sergey; Zaicev, Mikhail<br/><br/>Abstract: We consider non-necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe most of the results obtained in recent years on two numerical sequences that can be attached to the multilinear identities satisfied by an algebra: the sequence of codimensions and the sequence of colengths.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary 16R10, 16A30, 16A50, 17B01, 17C05, 17D05, 16P90, 17A, 17D.Full Exposition of Specht's Problem
http://hdl.handle.net/10525/2800
Title: Full Exposition of Specht's Problem<br/><br/>Authors: Belov-Kanel, Alexei; Rowen, Louis; Vishne, Uzi<br/><br/>Abstract: This paper combines [15], [16], [17], and [18] to provide a detailed sketch of Belov’s solution of Specht’s problem for affine algebras over an arbitrary commutative Noetherian ring, together with a discussion of the general setting of Specht’s problem in universal algebra and some applications to the structure of T-ideals. Some illustrative examples are collected along the way.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary: 16R10; Secondary: 16R30, 17A01, 17B01, 17C05.Central A-polynomials for the Grassmann Algebra
http://hdl.handle.net/10525/2799
Title: Central A-polynomials for the Grassmann Algebra<br/><br/>Authors: Pereira Brandão Jr., Antônio; José Gonçalves, Dimas<br/><br/>Abstract: Let F be an algebraically closed field of characteristic 0, and let G be the infinite dimensional Grassmann (or exterior) algebra over F. In 2003 A. Henke and A. Regev started the study of the A-identities. They described the A-codimensions of G and conjectured a finite generating set of the A-identities for G. In 2008 D. Gonçalves and P. Koshlukov answered in the affirmative their conjecture. In this paper we describe the central A-polynomials for G.<br/><br/>Description: 2010 Mathematics Subject Classification: 16R10, 16R40, 16R50.Outer Automorphisms of Lie Algebras related with Generic 2×2 Matrices
http://hdl.handle.net/10525/2798
Title: Outer Automorphisms of Lie Algebras related with Generic 2×2 Matrices<br/><br/>Authors: Fındık, Şehmus<br/><br/>Abstract: Let Fm = Fm(var(sl2(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl2(K) over a field K of characteristic 0. Our results are more precise for m = 2 when F2 is isomorphic to the Lie algebra L generated by two generic traceless 2 × 2 matrices. We give a complete description of the group of outer automorphisms of the completion L^ of L with respect to the formal power series topology and of the related associative algebra W^. As a consequence we obtain similar results for the automorphisms of the relatively free algebra F2/F2^(c+1) = F2(var(sl2(K)) ∩ Nc) in the subvariety of var(sl2(K)) consisting of all nilpotent algebras of class at most c in var(sl2(K)) and for W/W^(c+1). We show that such automorphisms are Z2-graded, i.e., they map the linear combinations of elements of odd, respectively even degree to linear combinations of the same kind.<br/><br/>Description: 2010 Mathematics Subject Classification: 17B01, 17B30, 17B40, 16R30.Asymptotic behaviour of Functional Identities
http://hdl.handle.net/10525/2797
Title: Asymptotic behaviour of Functional Identities<br/><br/>Authors: Gordienko, A. S.<br/><br/>Abstract: We calculate the asymptotics of functional codimensions fcn(A) and generalized functional codimensions gfc n (A) of an arbitrary not necessarily associative algebra A over a field F of any characteristic. Namely, fcn(A) ∼ gfcn(A) ∼ dim(A^2) · (dim A^n) as n → ∞ for any finite-dimensional algebra A. In particular, codimensions of functional and generalized functional identities satisfy the analogs of Amitsur’s and Regev’s conjectures. Also we precisely evaluate fcn(UT2(F)) = gfcn(UT2(F)) = 3^(n+1) − 2^(n+1).<br/><br/>Description: 2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.