Multiple fractional integrals

Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly identified. Received: 23 February 1998 / Revised version: 31 July 1998     

Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

Consider the flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1. We prove that if {D} is a nontrivial 2-(v, k, λ) symmetric design with (k, λ) = 1 and G≤Aut({D}) is flag-transitive with Soc(G) = A_n for n≥5, then {D} is the projective space PG₂(3,2) and G = A₇.     

On semi-Eulerian partially ordered sets with boundary

Eulerian posets are motivated by the posets from triangulations of spheres; semi-Eulerian posets are motivated by the posets from triangulations of manifolds. Motivated by investigation (Proc. Natl. Acad. Sci. USA 95 (1998) 9093; Adv. Appl. Math. 19 (1997) 144; J. Combin. Theory Ser. A 85 (1999) 1; Adv. Appl. Math. 21 (1998) 22) on the number of faces of triangulations of manifolds with boundary, we introduce semi-Eulerian posets with boundary in this paper, and generalize the reciprocity laws, the Dehn–Sommerville equations, and the combinatorial Alexander duality to semi-Eulerian posets with boundary.     

Once more nice equations for nice groups

In a previous paper, nice quintinomial equations were given for unramified coverings of the affine line in nonzero characteristic with the projective symplectic isometry group PSp and the (vectorial) symplectic isometry group Sp as Galois groups where is any integer and is any power of . Here we deform these equations to get nice quintinomial equations for unramified coverings of the once punctured affine line in characteristic with the projective symplectic similitude group PGSp and the (vectorial) symplectic similitude group GSp as Galois groups.

     

Double Walsh series with coefficients of bounded variation of higher order

Let denote the Cesàro sums of order of the Walsh functions. The estimates of given by Fine back in 1949 are extended to the case . As a corollary, the following properties are established for the rectangular partial sums of those double Walsh series whose coefficients satisfy conditions of bounded variation of order , and for some : (a) regular convergence; (b) uniform convergence; (c) -integrability and -metric convergence for ; and (d) Parseval's formula. Extensions to those with coefficients of generalized bounded variation are also derived.

     

The generalized Hodge conjecture for the quadratic complex of lines in projective four–space

We verify the generalized Hodge conjecture GHC(X,5,2) for the quadratic complex of lines in projective four–space. Received: 27 February 1998 / Revised version: 13 May 1998     

A note on norm attaining functionals

We are concerned in this paper with the density of functionals which do not attain their norms in Banach spaces. Some earlier results given for separable spaces are extended to the nonseparable case. We obtain that a Banach space is reflexive if and only if it satisfies any of the following properties: (i) admits a norm with the Mazur Intersection Property and the set of all norm attaining functionals of contains an open set, (ii) the set of all norm one elements of contains a (relative) weak* open set of the unit sphere, (iii) has and contains a (relative) weak open set of the unit sphere, (iv) is , has and contains a (relative) weak open set of the unit sphere. Finally, if is separable, then is reflexive if and only if contains a (relative) weak open set of the unit sphere.

     

Asymptotics for Sobolev orthogonal polynomials with coherent pairs: The Jacobi case, type 1

Define and as the th monic orthogonal polynomials with respect to and respectively. The pair is called a coherent pair if there exist non-zero constants such that

One can divide the coherent pairs into two cases: the Jacobi case and the Laguerre case. There are two types for each case: type 1 and 2. We investigate the asymptotic properties and zero distribution of orthogonal polynomials with respect to Sobolev inner product

for the coherent pair : the Jacobi case, type 1.

     

Bourgain's analytic projection revisited

For a positive function on the unit circle with , the following two statements are equivalent: (a) ; (b) there is an operator projecting onto for all at once and having weak type (1,1) with respect to .

     

The Contraction of S2p−1 to Hp−1

 A contraction of the sphere , considered as the homogeneous space , to the Heisenberg group is defined. The infinite dimensional irreducible unitary representations of Heisenberg group are then shown to be the limits of the irreducible representations of which are class-1 with respect to . Our results generalise the earlier results of Fulvio Ricci. (Received 1 July 1998; in revised form 3 November 1998)     

New 5-designs constructed from the lifted Golay code over ℤ4

It is shown that the lifted Golay code over ℤ₄ contains several 5-designs. In particular, a 5-(24, 12, 1584) design and a 5-(24, 12, 1632) design are constructed for the first time. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 225–229, 1998     

A note on Kamenev type theorems for second order matrix differential systems

Some oscillation criteria are given for the second order matrix differential system , where and are real continuous matrix functions with symmetric, . These results improve oscillation criteria recently discovered by Erbe, Kong and Ruan by using a generalized Riccati transformation , where is the identity matrix, is a given function on and .

     

A volume comparison theorem for Finsler manifolds

Let be a symmetric Finsler manifold, endowed with the Busemann volume form, and let be its unit disk bundle endowed with the canonical symplectic volume form. It is shown that , where is the volume of the unit disk in . Moreover, equality holds if and only if is Riemannian.

     

Cusp forms for congruence subgroups of and theta functions

In this paper we use theta functions with rational characteristic to construct cusp forms for congruence subgroups of .The action of the quotient group on these forms is conjugate to the linear action of on . We show that these forms are higher-dimensional analogues of the Fricke functions.

     

Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators

For a compact subset of symmetric with respect to conjugation and a continuous function, we obtain sharp conditions on and that insure that can be approximated uniformly on by polynomials with nonnegative coefficients. For a real Banach space, a closed but not necessarily normal cone with , and a bounded linear operator with , we use these approximation theorems to investigate when the spectral radius of belongs to its spectrum . A special case of our results is that if is a Hilbert space, is normal and the 1-dimensional Lebesgue measure of is zero, then . However, we also give an example of a normal operator (where is unitary and ) for which and .

     

Picard groups and infinite matrix rings

We describe a connection between the Picard group of a ring with local units and the Picard group of the unital overring . Using this connection, we show that the three groups , , and are isomorphic for any unital ring . Furthermore, each element of arises from an automorphism of , which yields an isomorphsm between and . As one application we extend a classical result of Rosenberg and Zelinsky by showing that the group is abelian for any commutative unital ring .

     

The Method of Fundamental Solutions for Stokes flows with a free surface

We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667–678, 1998     

Rescaled contact processes converge to super-Brownian motion in two or more dimensions

We show that in dimensions two or more a sequence of long range contact processes suitably rescaled in space and time converges to a super-Brownian motion with drift. As a consequence of this result we can improve the results of Bramson, Durrett, and Swindle (1989) by replacing their order of magnitude estimates of how close the critical value is to 1 with sharp asymptotics. Received: 2 February 1998 / Revised version: 28 August 1998     

Eigenvalues of some distal functions

In this paper we construct distal functions of another type discussed by Salehi (1991). Let be an almost periodic function with the mean value 0, which has unbounded integral, and a continuous periodic function with the prime period 1. If satisfies some additional condition, then is a distal function, which is not almost periodic, and the set of eigenvalues of is the module of .