DSpace Collection: Volume 32, Number 2-3
http://hdl.handle.net/10525/2511
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Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring
http://hdl.handle.net/10525/2534
Title: Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring<br/><br/>Authors: Szigeti, Jeno<br/><br/>Abstract: For an n×n matrix A over an arbitrary unitary ring R, we obtain the following Cayley-Hamilton identity with right matrix coefficients:(λ0I+C0)+A(λ1I+C1)+… +An-1(λn-1I+Cn-1)+An (n!I+Cn) = 0,where λ0+λ1x+…+λn-1 xn-1+n!xn is the right characteristic polynomial of A in R[x], I ∈ Mn(R) is the identity matrix and the entries of the n×n matrices Ci, 0 ≤ i ≤ n are in [R,R]. If R is commutative, then C0 = C1 = … = Cn-1 = Cn = 0 and our identity gives the n! times scalar multiple of the classical Cayley-Hamilton identity for A.<br/><br/>Description: 2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.Finite Groups as the Union of Proper Subgroups
http://hdl.handle.net/10525/2533
Title: Finite Groups as the Union of Proper Subgroups<br/><br/>Authors: Zhang, Jiping<br/><br/>Abstract: As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum group. Results by J. H. E. Cohn and M. J. Tomkinson are thus extended and further generalizations are possible.<br/><br/>Description: 2000 Mathematics Subject Classification: 20D60,20E15.Kadec Norms on Spaces of Continuous Functions
http://hdl.handle.net/10525/2530
Title: Kadec Norms on Spaces of Continuous Functions<br/><br/>Authors: Burke, Maxim R.; Wiesaw, Kubis; Stevo, Todorcevic<br/><br/>Abstract: We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the class of compact metrizable spaces under inverse limits of transfinite continuous sequences of retractions, then C(K1×K2) has a pointwise Kadec renorming. We also prove a version of the three-space property for such renormings.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35.Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space
http://hdl.handle.net/10525/2527
Title: Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space<br/><br/>Authors: Petkova, Violeta<br/><br/>Abstract: We prove a representation theorem for bounded operators commuting with translations on L2ω(G,H), where G is a locally compact abelian group, H is a Hilbert space and ω is a weight on G. Moreover, in the particular case when G = R, we characterize completely the spectrum of the shift operator S1,ω on Lω2(R,H).<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 43A22, 43A25.On the Residuum of Concave Univalent Functions
http://hdl.handle.net/10525/2523
Title: On the Residuum of Concave Univalent Functions<br/><br/>Authors: Wirths, K.-J.<br/><br/>Abstract: Let D denote the open unit disc and f:D→[`C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [`C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p).We determine for fixed p ∈ (0,1) the set of variability of the residuum of f, f ∈ Co(p).<br/><br/>Description: 2000 Mathematics Subject Classification: 30C25, 30C45.Some generalization of Desargues and Veronese configurations
http://hdl.handle.net/10525/2520
Title: Some generalization of Desargues and Veronese configurations<br/><br/>Authors: Prazmowska, Malgorzata; Krzysztof, Prazmowski<br/><br/>Abstract: We propose a method of constructing partial Steiner triple system, which generalizes the representation of the Desargues configuration as a suitable completion of three Veblen configurations. Some classification of the resulting configurations is given and the automorphism groups of configurations of several types are determined.<br/><br/>Description: 2000 Mathematics Subject Classification: 51E14, 51E30.Hausdorff Measures of Noncompactness and Interpolation Spaces
http://hdl.handle.net/10525/2519
Title: Hausdorff Measures of Noncompactness and Interpolation Spaces<br/><br/>Authors: da Silva, Eduardo Brandani; Fernanadez, Dicesar L.<br/><br/>Abstract: A new measure of noncompactness on Banach spaces is defined from the Hausdorff measure of noncompactness, giving a quantitative version of a classical result by R. S. Phillips. From the main result, classical results are obtained now as corollaries and we have an application to interpolation theory of Banach spaces.<br/><br/>Description: 2000 Mathematics Subject Classification: 46B50, 46B70, 46G12.Moduli stacks of polarized K3 surfaces in mixed characteristic
http://hdl.handle.net/10525/2517
Title: Moduli stacks of polarized K3 surfaces in mixed characteristic<br/><br/>Authors: Rizov, Jordan<br/><br/>Abstract: In this note we define moduli stacks of (primitively) polarized K3 spaces. We show that they are representable by Deligne-Mumford stacks over Spec(Z). Further, we look at K3 spaces with a level structure. Our main result is that the moduli functors of K3 spaces with a primitive polarization of degree 2d and a level structure are representable by smooth algebraic spaces over open parts of Spec(Z). To do this we use ideas of Grothendieck, Deligne, Mumford, Artin and others.These results are the starting point for the theory of complex multiplication for K3 surfaces and the definition of Kuga-Satake abelian varieties in positive characteristic given in our Ph.D. [J. Rizov. Moduli of K3 Surfaces and Abelian Variaties. Ph. D. thesis, University of Utrecht, 2005]. thesis.<br/><br/>Description: 2000 Mathematics Subject Classification: 14J28, 14D22.Lp extremal polynomials. Results and perspectives
http://hdl.handle.net/10525/2514
Title: Lp extremal polynomials. Results and perspectives<br/><br/>Authors: Laskri, Yamina; Benzine, Rachid<br/><br/>Abstract: Let α = β+γ be a positive finite measure defined on the Borel sets of C, with compact support, where β is a measure concentrated on a closed Jordan curve or on an arc (a circle or a segment) and γ is a discrete measure concentrated on an infinite number of points.In this survey paper, we present a synthesis on the asymptotic behaviour of orthogonal polynomials or Lp extremal polynomials associated to the measure α. We analyze some open problems and discuss new ideas related to their solving.<br/><br/>Description: 2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.