A space <Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>(<Emphasis Type="Italic">X</Emphasis>) is dominated by irrationals if and only if it is<Emphasis Type="Italic"> K</Emphasis>-analytic

Summary We prove that, for any Tychonoff X, the space C_p(X) is K-analytic if and only if it has a compact cover {K_p: p } such that K_p subset K_q whenever p,q and p q. Applying this result we show that if C_p(X) is K-analytic then C_p(X) is K-analytic as well. We also establish that a space C_p(X) is K-analytic and Baire if and only if X is countable and discrete.     

Two variable <Emphasis Type="Italic">p</Emphasis>-adic <Emphasis Type="Italic">L</Emphasis> functions attached to eigenfamilies of positive slope

Consider a classical cusp eigenform f= _n=1 a _n (f)q ⁿ of weight k2 for ₀(N) with a Dirichlet character mod N, and let L _f (s,)= _n=1 (n)a _n (f)n ^-s denote the L-function of f twisted with an arbitrary Dirichlet character . For a prime number p5, consider a family of cusp eigenforms f _(k) of weight k , k {f _(k)= _n=1 a _n (f _(k))q ⁿ } containing f=f _(k), such that the Fourier coefficients a _n (f _(k)) are given by certain p-adic analytic functions k a _n (f _(k)). The purpose of this paper is to construct a two variable p-adic L function attached to Colemans family {f _(k)} of cusp eigenforms of a fixed positive slope =v _p ( _p )>0 where _p = _p (k ) is an eigenvalue (which depends on k ) of the Atkin operator U=U _p . Our p-adic L-function interpolates the special values L _f(k)(s,) at points (s,k ) with s=1,2,...,k -1. We give a construction using the Rankin-Selberg method and the theory of p-adic integration on a profinite group Y with values in an affinoid K-algebra A, where K is a fixed finite extension of Q _p . Our p-adic L-functions are p-adic Mellin transforms of certain A-valued measures. In their turn, such measures come from Eisenstein distributions with values in certain Banach A-modules M =M (N;A) of families of overconvergent forms over A. To Robert Alexander Rankin in memoriam     

Bipartite <Emphasis Type="Italic">Q</Emphasis>-Polynomial Distance-Regular Graphs

Let denote a bipartite distance-regular graph with diameter D12. We show is Q-polynomial if and only if one of the following (i)–(iv) holds: (i) is the ordinary 2D-cycle. (ii) is the Hamming cube H(D,2). (iii) is the antipodal quotient of H(2D,2). (iv) The intersection numbers of satisfy where q is an integer at least 2. We obtain the above result using the Terwilliger algebra of .AMS 1991 Subject Classification: Primary 05E30Final version received: April 10, 2003     

Any nilpotence degree occurs in mod-<Emphasis Type="Italic">p</Emphasis> cohomology rings of <Emphasis Type="Italic">p</Emphasis>-groups

Let p be an odd prime number and let n be an arbitrary positive integer. We prove that there exists a p-group whose mod-p cohomology ring has a nilpotent element H²() satisfying ⁿ0,^n+p–1=0. As a corollary, we exhibit a p-group whose mod-p cohomology ring contains an element of nilpotency degree n+1.Mathematical Subject Classification (2000): 20J06, 20D15, 55R40To Phuong and Nin     

The Number of Linearly Independent Binary Vectors with Applications to the Construction of Hypercubes and Orthogonal Arrays,Pseudo (<Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">m</Emphasis>, <Emphasis Type="Italic">s</Emphasis>)-Nets and Linear Codes

We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1kn. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.This revised version was published online in October 2004 with a corrected Received date.     

Small Ball Estimates in <Emphasis Type="Italic">p</Emphasis>-Variation for Stable Processes

Let Z _t , t 0 be a strictly stable process on with index (0, 2]. We prove that for every p > , there exists = _{, p} and such that

<Emphasis Type="Italic">K</Emphasis>-homology of <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">*</Emphasis></Superscript>-categories and symmetric spectra representing <Emphasis Type="Italic">K</Emphasis>-homology

We define K-homology groups K _* () for small C ^* -categories in terms of Hilbert modules over the C ^* -category . We also define a functor A ^f from the category of small C ^* -categories into the category of C ^* -algebras and show that there is a natural isomorphism . In addition, we give an easy construction of a functor from the category of C ^* -algebras into the category of symmetric spectra which represents K-homology, i.e. we show that the functor comes with a natural isomorphism for C ^* -algebras A. It then follows that the composition A ^f provides a functor that can be used in the Davis-Lück approach for constructing the Baum-Connes map.     

Convexity and <Emphasis Type="Italic">w</Emphasis><Superscript><Emphasis Type="Italic">*</Emphasis></Superscript>-compactness in Banach spaces

Suppose X. We construct examples of bounded sets MX, such that These examples show that the previous results of the authors on quantitative versions of Kreins theorem are optimal.Mathematics Subject Classification (2000):46B20, 46B26A. S. Granero supported by DGICYT grant BFM2001-1284. P. Hájek supported by GAR 201/01/1198, A 101 92 05 and UPV grant PPI-02-02.     

A new characterization of <Emphasis Type="Italic">PSU</Emphasis>(<Emphasis Type="Italic">p,q</Emphasis>)

Summary Let G be a finite group. Order components of G were introduced in Chen [5]. Let OC(G) be the set of order components of G. Some finite groups are characterizable by their order components. This assertion was proved for the simple groups PSU(p,q), where p=3, 5, 7 and 11. In this paper, we prove that the simple groups PSU(p,q) can be uniquely determined by their order components, where p&ge;13 is a prime number. Main consequences of our results are the validity of a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.     

Biharmonic maps from <Emphasis Type="Italic">R</Emphasis><Superscript><Emphasis Type="Italic">4</Emphasis></Superscript> into a Riemannian manifold

For a domain R⁴ and a compact Riemannian manifold NR^k without boundary, if uW^2,2(,N) is an extrinsic (or intrinsic, respectively) biharmonic map, then uC(,N).in final form: 1 August 2003     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the biest I. The Walsh case

We prove L^p estimates (Theorem 1.8) for the Walsh model of the biest, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in the sequel [11] biest of this paper.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the biest II. The Fourier case

We prove L^p estimates (Theorem 1.2) for the biest, a trilinear multiplier operator with singular symbol. The methods used are based on the treatment of the Walsh analogue of the biest in the prequel [13] of this paper, but with additional technicalities due to the fact that in the Fourier model one cannot obtain perfect localization in both space and frequency.     

Surfaces of general type with <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">g</Emphasis></Subscript>=0, <Emphasis Type="Italic">K</Emphasis><Superscript>2</Superscript>=6 and non birational bicanonical map

Let S be a minimal surface of general type with p_g=0 and K²=6, such that its bicanonical map is not birational. The map is a morphism of degree 4 onto a surface. The case of deg = 4 is completely classified in [Topology, 40 (5) (2001), 977–991] and the present paper completes the characterization of these surfaces. It is proven that the degree of cannot be equal to 3, and the geometry of surfaces with deg = 2 is analysed in detail. The last section contains three examples of such surfaces, two of which appear to be new.Mathematics Subject Classification (2000): 14J29     

Complete Minors In <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">s,s</Emphasis></Subscript>-Free Graphs

We prove that for a fixed integer s2 every K _s,s -free graph of average degree at least r contains a K _p minor where . A well-known conjecture on the existence of dense K _s,s -free graphs would imply that the value of the exponent is best possible. Our result implies Hadwigers conjecture for K _s,s -free graphs whose chromatic number is sufficiently large compared with s.     

Asymptotic estimates of Dirac and Laplace eigenvalues on warped products over <Emphasis Type="Italic">S</Emphasis><Superscript><Emphasis Type="Italic">1</Emphasis></Superscript>

In this paper we show that the space of spinors over a warped product over S ¹ has a certain splitting =W(k,n) in spaces of spinors of weight k and winding number n which is respected by the Dirac operator. The same holds for the space of functions and the Laplace operator. We give eigenvalue estimates for the eigenvalues _k,n of the Dirac operator with eigenspinors of weight k and winding number n and eigenvalues _m,n of the Laplace operator with eigenfunctions of weight m and winding number n. In particular, we show that ² _k,n ² _k,n holds for large n on S ¹ × _fT ^l where T ^l is a flat torus with the trivial spin structure. Mathematics Subject Classification (2000):34L20, 53C21, 58J50, 58J60     

Partition of <Emphasis Type="Italic">C</Emphasis><Subscript>4</Subscript>-Designs into Minimum and Maximum Number of <Emphasis Type="Italic">P</Emphasis><Subscript>3</Subscript>-Designs

Let be a C₄-design of order n and index , on the vertex set V, |V|=n. If V₁V_m=V is a partition of the vertex set, such that the intersections of the with V_i form a P₃-design of order |V_i| and the same index , for each 1im, then 2m log₃(2n+1). The minimum bound is best possible for every . The maximum bound is best possible for =2, and hence also for every even .Supported by MIUR, Italy and CNR-GNSAGAAlso affiliated with the Department of Computer Science, University of Veszprém, Hungary; supported in part by the Hungarian Scientific Research Fund, grant OTKA T-32969AMS classification: 05B05     

<Emphasis Type="Italic">M</Emphasis>-spherical <Emphasis Type="Italic">K</Emphasis>-modules of a rank one semisimple Lie group

Let G =K A N be an Iwasawa decomposition of a connected, noncompact real semisimple Lie group with finite center and let M be the centralizer of A in K . B. Kostant proved that for every irreducible M-spherical K-module V there exists a unique d (the Kostant degree of V) such that V can be realized as a submodule of the space of all -harmonic homogeneous polynomials of degree d on . Here is a Cartan decomposition of the complexification of the Lie algebra of G .In this paper we give an algorithm to obtain a highest weight vector from any M-invariant vector in an irreducible M-spherical K-module. This algorithm allows us to compute a sharp bound for the Kostant degree d(v) of any M-invariant vector v in a locally finite M-spherical K-module V. The method computes d(v) effectively for any V if G is locally isomorphic to SO(n,1) and for if G is locally isomorphic to SU(n,1).Partially supported by Agencia Córdoba Ciencia and CONICET Mathematics Subject Classification (2000):Primary 22E46, Secondary 43A85     

On the discrete mean square of Dirichlet <Emphasis Type="Italic">L</Emphasis>-functions at 1

There have been many results obtained so far for the mean square of the (absolute) value of the Dirichlet L-function L(s,) in the critical strip 0<<1, especially on the critical line , but relatively few results were known for discrete mean value of |L(1,)|² till W. Zhang had published papers improving the error term step by step, which have recently been superseded by M. Katsurada and K.Matsumoto in which they succeeded in deriving an asymptotic formula for ₀|L(1,)|². The object of our paper is to point out a structural property contained in the formation of the mean square, to find out the niryana–the true body of the above sum.Dedicated to Professor Jean Louis Nicolás on his sixtieth birthdayin final form: 7 October 2003     

Approximation of sine-shaped functions by constants in the spaces <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>, <Emphasis Type="Italic">p</Emphasis> < 1

We investigate the best approximations of sine-shaped functions by constants in the spaces L_p for p < 1. In particular, we find the best approximation of perfect Euler splines by constants in the spaces L_p for certain p(0,1).Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 6, pp. 745–762, June, 2004.     

Shape-preserving Kolmogorov widths of classes of <Emphasis Type="Italic">s</Emphasis>-monotone integrable functions

Let s ₀ and let ₊ ^s be the set of functions x defined on a finite interval I and such that, for all collections of s + 1 pairwise different points t ₀,..., t _s I, the corresponding divided differences [x; t ₀,...,t _s ] of order s are nonnegative. Let ₊ ^s B _{p +} ^s B _p, 1 p where B _p is a unit ball in the space L _p, and let ₊ ^s L _{q +} ^s L _q, 1 q . For every s 3 and 1 q p , we determine the exact orders of the shape-preserving Kolmogorov widths {x - y} \right\ L_q , $$]]>, where M ⁿ is the collection of all affine linear manifolds M ⁿ in L _q such that dim M ⁿ n and M ⁿ ₊ ^s L _q .Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 901–926, July, 2004.