DSpace Community: 2001 http://hdl.handle.net/10525/456 Volume 27, 2001 The Community's search engine Search the Channel search http://sci-gems.math.bas.bg/jspui/simple-search Polynomial Automorphisms Over Finite Fields http://hdl.handle.net/10525/486 Title: Polynomial Automorphisms Over Finite Fields<br/><br/>Authors: Maubach, Stefan<br/><br/>Abstract: It is shown that the invertible polynomial maps over a finitefield Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections inthe case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1it is shown that the tame subgroup of the invertible polynomial maps givesonly the even bijections, i.e. only half the bijections. As a consequence itis shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if#S = q^(n−1). Polynomials of Pellian Type and Continued Fractions http://hdl.handle.net/10525/485 Title: Polynomials of Pellian Type and Continued Fractions<br/><br/>Authors: Mollin, R.<br/><br/>Abstract: We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N,the period length of the simple continued fraction expansion of √fk (X) isconstant. Furthermore, we show that the period lengths of √fk (X) go toinfinity with k. For each member of the families involved, we show howto determine, in an easy fashion, the fundamental unit of the underlyingquadratic field. We also demonstrate how the simple continued fraction ex- pansion of √fk (X) is related to that of √C, where √fk (X) = ak*X^2 +bk*X + C.This continues work in –. Further Generalization of Kobayashi's Gamma Function http://hdl.handle.net/10525/484 Title: Further Generalization of Kobayashi's Gamma Function<br/><br/>Authors: Galue, L.; Alobaidi, G.; Kalla, S.<br/><br/>Abstract: In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z) New Binary \$[70,35,12]\$ Self-Dual and Binary \$[72,36,12]\$ Self-Dual Doubly-Even Codes http://hdl.handle.net/10525/483 Title: New Binary \$[70,35,12]\$ Self-Dual and Binary \$[72,36,12]\$ Self-Dual Doubly-Even Codes<br/><br/>Authors: Dontcheva, Radinka<br/><br/>Abstract: In this paper we prove that up to equivalence there exist 158binary [70, 35, 12] self-dual and 119 binary [72, 36, 12] self-dual doubly-evencodes all of which have an automorphism of order 23 and we present theirconstruction. All these codes are new.<br/><br/>Description: ∗ This work was supported in part by the Bulgarian NSF under Grant MM-901/99 On Projective Plane of Order 13 with a Frobenius Group of Order 39 as a Collineation Group http://hdl.handle.net/10525/482 Title: On Projective Plane of Order 13 with a Frobenius Group of Order 39 as a Collineation Group<br/><br/>Authors: Hoxha, Razim<br/><br/>Abstract: One of the most outstanding problems in combinatorial mathematicsand geometry is the problem of existence of finite projective planeswhose order is not a prime power. Divisible Codes - A Survey http://hdl.handle.net/10525/481 Title: Divisible Codes - A Survey<br/><br/>Authors: Ward, Harold<br/><br/>Abstract: This paper surveys parts of the study of divisibility properties of codes.The survey begins with the motivating background involvingpolynomials over finite fields. Then it presents recent results on bounds andapplications to optimal codes. A Survey of Counterexamples to Hilbert's Fourteenth Problem http://hdl.handle.net/10525/480 Title: A Survey of Counterexamples to Hilbert's Fourteenth Problem<br/><br/>Authors: Freudenburg, Gene<br/><br/>Abstract: We survey counterexamples to Hilbert’s Fourteenth Problem,beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations.Historical framework and pertinent references are provided. We also include8 important open questions. Continuity of Pseudo-differential Operators on Bessel And Besov Spaces http://hdl.handle.net/10525/479 Title: Continuity of Pseudo-differential Operators on Bessel And Besov Spaces<br/><br/>Authors: Moussai, Madani<br/><br/>Abstract: We study the continuity of pseudo-differential operators onBessel potential spaces Hs|p (Rn ), and on the corresponding Besov spacesB^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function. Weak Polynomial Identities for M1,1(E) http://hdl.handle.net/10525/478 Title: Weak Polynomial Identities for M1,1(E)<br/><br/>Authors: Di Vincenzo, Onofrio; La Scala, Roberto<br/><br/>Abstract: We compute the cocharacter sequence and generators of theideal of the weak polynomial identities of the superalgebra M1,1 (E).<br/><br/>Description: * Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”. On a Class of Generalized Elliptic-type Integrals http://hdl.handle.net/10525/477 Title: On a Class of Generalized Elliptic-type Integrals<br/><br/>Authors: Garg, Mridula; Katta, Vimal; Kalla, S.<br/><br/>Abstract: The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication  wehave obtained recurrence relations and asymptotic formula for this generalizedelliptic-type integral. Here we shall obtain some more results whichare single and multiple integral formulae, differentiation formula, fractionalintegral and approximations for this class of generalized elliptic-type integrals. First Order Characterizations of Pseudoconvex Functions http://hdl.handle.net/10525/476 Title: First Order Characterizations of Pseudoconvex Functions<br/><br/>Authors: Ivanov, Vsevolod<br/><br/>Abstract: First order characterizations of pseudoconvex functions areinvestigated in terms of generalized directional derivatives. A connectionwith the invexity is analysed. Well-known first order characterizations ofthe solution sets of pseudolinear programs are generalized to the case ofpseudoconvex programs. The concepts of pseudoconvexity and invexity donot depend on a single definition of the generalized directional derivative. Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order http://hdl.handle.net/10525/475 Title: Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order<br/><br/>Authors: Zagorodniuk, S.<br/><br/>Abstract: Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfythe recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) =λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 =0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) +αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R,n = 0, 1, 2, . . ., α−1 = α−2 = β−1 = 0, p−1 = p−2 = 0, p0 (λ) = 1,p1 (λ) = cλ + b, c > 0, b ∈ C, λ ∈ C.It is shown that they are orthonormal on the real and the imaginary axesin the complex plane ... On some Results Related to Köthe's Conjecture http://hdl.handle.net/10525/474 Title: On some Results Related to Köthe's Conjecture<br/><br/>Authors: Agata, Smoktunowicz<br/><br/>Abstract: The Köthe conjecture states that if a ring R has no nonzero nilideals then R has no nonzero nil one-sided ideals. Although for more than70 years significant progress has been made, it is still open in general. Inthis paper we survey some results related to the Köthe conjecture as well assome equivalent problems. Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem http://hdl.handle.net/10525/473 Title: Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem<br/><br/>Authors: Kostov, Vladimir<br/><br/>Abstract: We consider the variety of (p + 1)-tuples of matrices Aj (resp.Mj ) from given conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C))such that A1 + . . . + A[p+1] = 0 (resp. M1 . . . M[p+1] = I). This variety isconnected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes cj ⊂ gl(n, C) (resp.Cj ⊂ GL(n, C)) so that there exist (p + 1)-tuples with trivial centralizers ofmatrices Aj ∈ cj (resp. Mj ∈ Cj ) whose sum equals 0 (resp. whose productequals I). The matrices Aj (resp. Mj ) are interpreted as matrices-residuaof Fuchsian linear systems (resp. as monodromy operators of regular linearsystems) on Riemann’s sphere. We consider examples of such varieties ofdimension higher than the expected one due to the presence of (p + 1)-tupleswith non-trivial centralizers; in one of the examples the difference betweenthe two dimensions is O(n).<br/><br/>Description: Research partially supported by INTAS grant 97-1644 Groups with Decomposable Set of Quasinormal Subgroups http://hdl.handle.net/10525/472 Title: Groups with Decomposable Set of Quasinormal Subgroups<br/><br/>Authors: de Falco, M.; de Giovanni, F.<br/><br/>Abstract: A subgroup H of a group G is said to be quasinormal if HX =XH for all subgroups X of G. In this article groups are characterized forwhich the partially ordered set of quasinormal subgroups is decomposable. On the 3-Colouring Vertex Folkman Number F(2,2,4) http://hdl.handle.net/10525/471 Title: On the 3-Colouring Vertex Folkman Number F(2,2,4)<br/><br/>Authors: Nenov, Nedyalko<br/><br/>Abstract: In this note we prove that F (2, 2, 4) = 13.