DSpace Community: 2004
http://hdl.handle.net/10525/1720
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A Note on Elementary Derivations
http://hdl.handle.net/10525/1755
Title: A Note on Elementary Derivations<br/><br/>Authors: Khoury, Joseph<br/><br/>Abstract: Let R be a UFD containing a field of characteristic 0, andBm = R[Y1, . . . , Ym] be a polynomial ring over R. It was conjectured in [5]that if D is an R-elementary monomial derivation of B3 such that ker D isa finitely generated R-algebra then the generators of ker D can be chosen tobe linear in the Yi ’s. In this paper, we prove that this does not hold for B4.We also investigate R-elementary derivations D of Bm satisfying one or theother of the following conditions:(i) D is standard.(ii) ker D is generated over R by linear constants.(iii) D is fix-point-free.(iv) ker D is finitely generated as an R-algebra.(v) D is surjective.(vi) The rank of D is strictely less than m.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.Thu, 01 Jan 2004 00:00:00 GMTRegular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces
http://hdl.handle.net/10525/1754
Title: Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces<br/><br/>Authors: Argyros, Spiros; Arvanitakis, Alexander<br/><br/>Abstract: For weakly compact subsets of Hilbert spaces K, we study theexistence of totally disconnected spaces L, such that C(K) is isomorphicto C(L). We prove that the space C(BH ) admits a Pełczyński decomposition andwe provide a starshaped weakly compact K, subset of BH with non-emptyinterior in the norm topology, and such that C(K) ~= C(L) with L totally disconnected.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.Thu, 01 Jan 2004 00:00:00 GMTInformation Matrix for Beta Distributions
http://hdl.handle.net/10525/1753
Title: Information Matrix for Beta Distributions<br/><br/>Authors: Aryal, Gokarna; Nadarajah, Saralees<br/><br/>Abstract: The Fisher information matrix for three generalized beta distributions are derived.<br/><br/>Description: 2000 Mathematics Subject Classification: 33C90, 62E99.Thu, 01 Jan 2004 00:00:00 GMTEssential Cover and Closure
http://hdl.handle.net/10525/1752
Title: Essential Cover and Closure<br/><br/>Authors: Andruszkiewicz, R.<br/><br/>Abstract: We construct some new examples showing that Heyman andRoos construction of the essential closure in the class of associative ringscan terminate at any finite or the first infinite ordinal.<br/><br/>Description: 2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05.Thu, 01 Jan 2004 00:00:00 GMTSymmetric and Asymmetric Gaps in Some Fields of Formal Power Series
http://hdl.handle.net/10525/1751
Title: Symmetric and Asymmetric Gaps in Some Fields of Formal Power Series<br/><br/>Authors: Galanova, N.<br/><br/>Abstract: We consider a construction of fields with symmetric gaps that are not semi-η1. By this construction we give examples of fields with different asymmetric gaps.<br/><br/>Description: 2000 Mathematics Subject Classification: 03E04, 12J15, 12J25.Thu, 01 Jan 2004 00:00:00 GMTA Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process
http://hdl.handle.net/10525/1750
Title: A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process<br/><br/>Authors: González, M.; Martínez, R.; Mota, M.<br/><br/>Abstract: In this work, the problem of the limiting behaviour of an irreducible Multitype Galton-Watson Branching Process with period d greaterthan 1 is considered. More specifically, almost sure convergence of somelinear functionals depending on d consecutive generations is studied underhypothesis of non extinction. As consequence the main parameters of themodel are given a convenient interpretation from a practical point of view.For a better understanding of the theoretical results, an illustrative exampleis provided.<br/><br/>Description: 2000 Mathematics Subject Classification: 60J80.Thu, 01 Jan 2004 00:00:00 GMTDirect and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices
http://hdl.handle.net/10525/1749
Title: Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices<br/><br/>Authors: Zagorodnyuk, S.<br/><br/>Abstract: We give an easy procedure for solving of the direct and the inverse spectral problemsfor the equation. Guseynov used a procedure of the Gelfand-Levitan typefor the case N = 1. We use another procedure and this procedure is moreeasy and transparent.<br/><br/>Description: 2000 Mathematics Subject Classification: 42C05.Thu, 01 Jan 2004 00:00:00 GMTBinomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation
http://hdl.handle.net/10525/1747
Title: Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation<br/><br/>Authors: Gateva-Ivanova, Tatiana<br/><br/>Abstract: Let k be a field and X be a set of n elements. We introduce and study a class of quadratic k-algebras called quantum binomial algebras.Our main result shows that such an algebra A defines a solution of the classical Yang-Baxter equation (YBE), if and only if its Koszul dual A!is Frobenius of dimension n, with a regular socle and for each x, y ∈ X an equality of the type xyy = αzzt, where α ∈ k \{0}, and z, t ∈ X is satisfied in A. We prove the equivalence of the notions a binomial skew polynomial ring and a binomial solution of YBE. This implies that the Yang-Baxter algebra of such a solution is of Poincaré-Birkhoff-Witt type, and possesses a number of other nice properties such as being Koszul, Noetherian, and an Artin-Schelter regular domain.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.Thu, 01 Jan 2004 00:00:00 GMTRemarks on the Nagata Conjecture
http://hdl.handle.net/10525/1746
Title: Remarks on the Nagata Conjecture<br/><br/>Authors: Strycharz-Szemberg, Beata; Szemberg, Tomasz<br/><br/>Abstract: The famous Nagata Conjecture predicts the lowest degree ofa plane curve passing with prescribed multiplicities through given pointsin general position. We explain how this conjecture extends naturally viamultiple point Seshadri constants to ample line bundles on arbitrary surfaces.We show that if there exist curves of unpredictable low degree, then theymust have equal multiplicities in all but possibly one of the given points.We use this restriction in order to obtain lower bounds on multiple pointSeshadri constants on a surface. We discuss also briefly a seemingly newpoint of view on the Nagata Conjecture via the bigness of the involvedlinear series.<br/><br/>Description: 2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.Thu, 01 Jan 2004 00:00:00 GMTInvariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras
http://hdl.handle.net/10525/1745
Title: Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras<br/><br/>Authors: Drensky, Vesselin<br/><br/>Abstract: The classical theorem of Weitzenböck states that the algebra of invariants K[X]^g of a single unipotent transformation g ∈ GLm(K) acting on the polynomial algebra K[X] = K[x1, . . . , xm] over a field K of characteristic 0 is finitely generated.<br/><br/>Description: 2000 Mathematics Subject Classification: 16R10, 16R30.Thu, 01 Jan 2004 00:00:00 GMTHenselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory
http://hdl.handle.net/10525/1744
Title: Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory<br/><br/>Authors: Chipchakov, I.<br/><br/>Abstract: This paper gives a characterization of Henselian discrete valuedfields whose finite abelian extensions are uniquely determined by their normgroups and related essentially in the same way as in the classical local classfield theory. It determines the structure of the Brauer groups and charactergroups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms of the local reciprocity law for such fields. It shows that, in contrast to the special cases of local fieldsor strictly PQL-fields algebraic over a given global field, the norm groupsof finite separable extensions of the considered fields are not necessarilyequal to norm groups of finite Galois extensions with Galois groups of easilyaccessible structure.<br/><br/>Description: 2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.Thu, 01 Jan 2004 00:00:00 GMTLinearly Normal Curves in P^n
http://hdl.handle.net/10525/1743
Title: Linearly Normal Curves in P^n<br/><br/>Authors: Pasarescu, Ovidiu<br/><br/>Abstract: We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In the present paper we apply the same idea to the curves lying on some rational surfaces from P^n, constructed in [12, 3, 2] (see [13, 14] also).<br/><br/>Description: 2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.Thu, 01 Jan 2004 00:00:00 GMTKneser and Hereditarily Kneser Subgroups of a Profinite Group
http://hdl.handle.net/10525/1742
Title: Kneser and Hereditarily Kneser Subgroups of a Profinite Group<br/><br/>Authors: Basarab, Şerban<br/><br/>Abstract: Given a profinite group Γ acting continuously on a discrete quasi-cyclic group A, certain classes of closed subgroups of Γ (radical, hereditarily radical, Kneser, almost Kneser, and hereditarily Kneser) having natural field theoretic interpretations are defined and investigated. One proves that the hereditarily Kneser subgroups of Γ form a closed subspace of the irreducible spectral space of all closed subgroups of Γ, and a hereditarily Kneser criterion for hereditarily radical subgroups is provided.<br/><br/>Description: 2000 Mathematics Subject Classification: 20E18, 12G05, 12F10, 12F99.Thu, 01 Jan 2004 00:00:00 GMTMinimal Codewords in Linear Codes
http://hdl.handle.net/10525/1741
Title: Minimal Codewords in Linear Codes<br/><br/>Authors: Borissov, Yuri; Manev, Nickolai<br/><br/>Abstract: Cyclic binary codes C of block length n = 2^m − 1 and generator polynomial g(x) = m1(x)m2^s+1(x), (s, m) = 1, are considered. The cardinalities of the sets of minimal codewords of weights 10 and 11 in codes C and of weight 12 in their extended codes ^C are determined. The weight distributions of minimal codewords in the binary Reed-Mullercodes RM (3, 6) and RM (3, 7) are determined. The applied method enablescodes with larger parameters to be attacked.<br/><br/>Description: 2000 Mathematics Subject Classification: 94B05, 94B15.Thu, 01 Jan 2004 00:00:00 GMTCohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)
http://hdl.handle.net/10525/1740
Title: Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)<br/><br/>Authors: Kędzierski, Oskar<br/><br/>Abstract: In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic groupnot in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to construct a dual basis to the integral cohomology on the resolution.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.Thu, 01 Jan 2004 00:00:00 GMTA Smooth Four-Dimensional G-Hilbert Scheme
http://hdl.handle.net/10525/1739
Title: A Smooth Four-Dimensional G-Hilbert Scheme<br/><br/>Authors: Sebestean, Magda<br/><br/>Abstract: When the cyclic group G of order 15 acts with some specific weights on affine four-dimensional space, the G-Hilbert scheme is a crepantresolution of the quotient A^4 / G. We give an explicit description of this resolution using G-graphs.<br/><br/>Description: 2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.Thu, 01 Jan 2004 00:00:00 GMT