A limit theorem for sequences generated by Weyl transformation: Disappearance of dependence

 We prove a limit theorem for certain pseudo-random sequences generated by Weyl transformations, thereby extending a result of Sugita in [3]. Received: 8 June 2001 / Revised version: 4 March 2002 / Published online: 22 August 2002     

Projectively flat Randers metrics with constant flag curvature

 We classify locally projectively flat Randers metrics with constant Ricci curvature and obtain a new family of Randers metrics of negative constant flag curvature. Received: 19 July 2001 / Revised version: 15 March 2002 / Published online: 16 October 2002     

Normal bases for Hopf-Galois algebras

Let be a Hopf algebra over a commutative ring such that is a finitely generated, projective module over , let be a right -comodule algebra, and let be the subalgebra of -coinvariant elements of . If is a Galois extension of and is a local subalgebra of the center of , then is a cleft right -comodule algebra or, equivalently, there is a normal basis for over .

     

Ginzburg-Landau minimizers near the first critical field have bounded vorticity

We prove that for fields close enough to the first critical field, minimizers of the Ginzburg-Landau functional have a number of vortices bounded independently from the Ginzburg-Landau parameter. This generalizes a result proved in [SS1] and shows that locally minimizing solutions of the Ginzburg-Landau equation found in [S1, S3] are actually global minimizers. It also gives a partial answer to a question raised by F. Bethuel and T. Rivière in [BR]. Received: 10 July 2002 / Accepted: 23 January 2002 / Published online: 5 September 2002     

On a resonant-superlinear elliptic problem

We start by discussing the solvability of the following superlinear problem where , is a smooth bounded domain and f satisfies a one-sided Landesman-Lazer condition. We also consider systems of semilinear elliptic equations with nonlinearities of the above form, so exhibiting superlinearity as and resonance as . A priori bounds for the solutions of the equation and the system are obtained by using Hardy-type inequalities . Existence of solutions is then obtained using topological degree arguments. Received: 18 March 2002 / Accepted: 8 May 2002 / Published online: 5 September 2002     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

Degenerate fibres in the Stone-Cech compactification of the universal bundle of a finite group

Applied to a continuous surjection of completely regular Hausdorff spaces and , the Stone-Cech compactification functor yields a surjection . For an -fold covering map , we show that the fibres of , while never containing more than points, may degenerate to sets of cardinality properly dividing . In the special case of the universal bundle of a -group , we show more precisely that every possible type of -orbit occurs among the fibres of . To prove this, we use a weak form of the so-called generalized Sullivan conjecture.

     

Index of B-Fredholm operators and generalization of a Weyl theorem

The aim of this paper is to show that if and are commuting B-Fredholm operators acting on a Banach space , then is a B-Fredholm operator and , where means the index. Moreover if is a B-Fredholm operator and is a finite rank operator, then is a B-Fredholm operator and We also show that if is isolated in the spectrum of , then is a B-Fredholm operator of index if and only if is Drazin invertible. In the case of a normal bounded linear operator acting on a Hilbert space , we obtain a generalization of a classical Weyl theorem.     

Energy quantization for triholomorphic maps

Let be weakly convergent stationary triholomorphic maps from a hyperkähler manifold M to another hyperkähler manifold N. We establish an energy quantization for the density function of the defect measure on the concentration set.Received: 10 July 2002, Accepted: 30 September 2002, Published online: 17 December 2002     

The stable signature of a regular cyclic action

Let be an odd prime and a smooth map of order . Suppose that the cyclic action defined by is regular and has fixed point set . If the -signature Sign is a rational integer and , then there exists a choice of orientations such that Sign Sign .     

Subelliptic harmonic maps from Carnot groups

For subelliptic harmonic maps from a Carnot group into a Riemannian manifold without boundary, we prove that they are smooth near any -regular point (see Definition 1.3) for sufficiently small . As a consequence, any stationary subelliptic harmonic map is smooth away from a closed set with zero H^Q-2 measure. This extends the regularity theory for harmonic maps (cf. [SU], [Hf], [El], [Bf]) to this subelliptic setting.Received: 24 April 2002, Accepted: 30 September 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 35B65, 58J42     

Local dual spaces of Banach spaces of vector-valued functions

We show that is a local dual of , and is a local dual of , where is a Banach space. A local dual space of a Banach space is a subspace of so that we have a local representation of in satisfying the properties of the representation of in provided by the principle of local reflexivity.

     

Algebraic obstructions and a complete solution of a rational retraction problem

For each compact smooth manifold containing at least two points we prove the existence of a compact nonsingular algebraic set and a smooth map such that, for every rational diffeomorphism and for every diffeomorphism where and are compact nonsingular algebraic sets, we may fix a neighborhood of in which does not contain any regular rational map. Furthermore is not homotopic to any regular rational map. Bearing in mind the case in which is a compact nonsingular algebraic set with totally algebraic homology, the previous result establishes a clear distinction between the property of a smooth map to represent an algebraic unoriented bordism class and the property of to be homotopic to a regular rational map. Furthermore we have: every compact Nash submanifold of containing at least two points has not any tubular neighborhood with rational retraction.

     

On the predictability of discrete dynamical systems

Let be a metric space. A function is said to be non-sensitive at a point if for every 0$"> there is a 0$"> such that for any choice of points , , , we have that for every . Let be the set of all homeomorphisms from onto endowed with the topology of uniform convergence. The main goal of the present paper is to prove that for certain spaces , ``most' functions in are non-sensitive at ``most' points of .

     

Backward SDEs and Cauchy problem for semilinear equations in divergence form

 We extend the definition of solutions of backward stochastic differential equations to the case where the driving process is a diffusion corresponding to symmetric uniformly elliptic divergence form operator. We show existence and uniqueness of solutions of such equations under natural assumptions on the data and show its connections with solutions of semilinear parabolic partial differential equations in Sobolev spaces. Received: 22 January 2002 / Revised version: 10 September 2002 / Published online: 19 December 2002 Research supported by KBN Grant 0253 P03 2000 19. Mathematics Subject Classification (2002): Primary 60H30; Secondary 35K55 Key words or phrases: Backward stochastic differential equation – Semilinear partial differential equation – Divergence form operator – Weak solution     

On the Glauberman and Watanabe correspondences for blocks of finite -solvable groups

If is a finite -solvable group for some prime , a solvable subgroup of the automorphism group of of order prime to such that stabilises a -block of and acts trivially on a defect group of , then there is a Morita equivalence between the block and its Watanabe correspondent of , given by a bimodule with vertex and an endo-permutation module as source, which on the character level induces the Glauberman correspondence (and which is an isotypy by Watanabe's results).

     

On the completeness of factor rings

Let be a complete local domain containing the integers with maximal ideal such that is at least the cardinality of the real numbers. Let be a nonmaximal prime ideal of such that is a regular local ring. We construct an excellent local ring such that the completion of is , the generic formal fiber of is local with maximal ideal and if is a nonzero ideal of , then is complete.

     

LCM-splitting sets in some ring extensions

Let be a saturated multiplicative set of an integral domain . Call an lcm splitting set if and are principal ideals for every and . We show that if is an -stable overring of (that is, if whenever and is principal, it follows that and if is an lcm splitting set of , then the saturation of in is an lcm splitting set in . Consequently, if is Noetherian and is a (nonzero) prime element, then is also a prime element of the integral closure of . Also, if is Noetherian, is generated by prime elements of and if the integral closure of is a UFD, then so is the integral closure of .