The Beijing Astronomical Observatory supernova survey (II)

Six supernovae (SNe) discovered in 1996 by the Beijing Astronomical Observatory Supernova (SN) Survey (BAOSS) are reported. SN 1996W, the first supernova discovered by the survey, has been monitored photometrically and spectroscopically for a long time. The spectra and photometry showed that it was a typical type II-P supernova. SN 1996cb, the sixth SN discovered in 1996 and a peculiar one like SN 1993J, has also been observed intensively for a long time. Project supported by the National Natural Science Foundation of China (Grant No. 19733020).     

Multiplicity of homoclinics for a class of time recurrent second order Hamiltonian systems

We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in of the form , where we assume the existence of a sequence such that and as for any . Moreover, under a suitable non degeneracy condition, we prove that this class of systems admits multibump solutions. Received February 2, 1996 / In revised form July 5, 1996 / Accepted October 10, 1996     

On various semiconvex hulls in the calculus of variations

We show that for any compact set , if and only if , , and being the closed lamination convex hull, quasiconvex hull and convex hull of respectively. When , we show that if and only if , where is the polyconvex hull of . We give some estimates of these relations by using quasiconvexifications of distance functions. Received April 9, 1996 / In final revised form November 8, 1996 / Accepted December 17, 1996     

A regularity theory for variational integrals with L\ln L-Growth

In the present paper we study regularity for local minimizers of the convex variational integral defined on certain classes of vector–valued functions . The underlying energy spaces are natural from the point of view of existence theory. We then show that local minimizers are of class apart from a closed singular set with vanishing Lebesgue measure, provided . For twodimensional problems we obtain smoothness in the interior of . Received June 21, 1996 / In revised form December 2, 1996 / Accepted December 17, 1996     

On the syntactic algorithm for the word problem of left distributivity

Here we investigate the ‘natural’ syntactic algorithm for the word problem of left distributivity, and we establish a sufficient condition which explains the convergence for all terms of a reasonable size. An algorithm for left division is also constructed. Received February 8, 1996; accepted in final form October 3, 1996     

Gromov-Witten invariants in algebraic geometry

Gromov-Witten invariants for arbitrary non-singular projective varieties and arbitrary genus are constructed using the techniques from [K. Behrend, B. Fantechi. The Intrinsic Normal Cone.] Oblatum 26-II-1996 & 27-VI-1996     

Inégalités de Poincaré cinétiques

In this Note we prove Poincaré type inequalities for a family of kinetic equations. We apply this inequality to the variational solution of a linear kinetic model by generalizing the STILS method (Azerad, 1996 [1]; Azerad and Pousin, 1996 [2]) to a kinetic setting.     

On consistent solutions for strategic games

Nash equilibria for strategic games were characterized by Peleg and Tijs (1996) as those solutions satisfying the properties of consistency, converse consistency and one-person rationality.  There are other solutions, like the ɛ-Nash equilibria, which enjoy nice properties and appear to be interesting substitutes for Nash equilibria when their existence cannot be guaranteed. They can be characterized using an appropriate substitute of one-person rationality. More generally, we introduce the class of “personalized” Nash equilibria and we prove that it contains all of the solutions characterized by consistency and converse consistency. Received January 1996/Final version December 1996     

Hölder Regularity of Compactly Supported p -Wavelets: p =3,4,5

We provide exact asymptotic estimates for the H?lder regularity index of compactly supported minimal length p -wavelets in cases p=3,4,5 . February 28, 1996. Date revised: October 7, 1996.     

Convergence of eigenvalues and Green functions under surgery type degeneration of Riemannian manifolds

We study the asymptotics for the eigenvalues and eigenfunctions and the Green function for sequences of Riemannian metrics that converge to a smooth compact limit of different topology in a controlled manner, as encountered in surgery constructions. A model case is the Bergman metric on a family of degenerating Riemann surfaces with reducible limit. Received February 26, 1996 / Accepted March 15, 1996     

Extremal Properties of 0/1-Polytopes

We provide lower and upper bounds for the maximal number of facets of a d-dimensional 0/1-polytope, and for the maximal number of vertices that can appear in a two-dimensional projection (``shadow') of such a polytope. Received June 14, 1996, and in revised form September 30, 1996.     

On Helly's Theorem: Algorithms and Extensions

This paper studies algorithmic Helly-type problems in the framework of the algorithmic theory of convex bodies developed by Gr?tschel, Lovász, and Schrijver. Various oracle-polynomial-time algorithms are presented that are complemented by -hardness results for polytopes. In addition, some new Helly-type theorems are derived. Received June 15, 1996, and in revised form August 16, 1996.     

Real connective K-theory and the quaternion group

Let be the real connective K-theory spectrum. We compute and for groups whose Sylow 2-subgroup is quaternion of order 8. Using this we compute the coefficients of the fixed points of the Tate spectrum for and . The results provide a counterexample to the optimistic conjecture of Greenlees and May [9, Conj. 13.4], by showing, in particular, that is not a wedge of Eilenberg-Mac Lane spectra, as occurs for groups of prime order.

     

Ending laminations for hyperbolic group extensions

((Without abstract)) Submitted: March 1996, revised version: October 1996.     

Asymptotic semismoothness probabilities

We call an integer semismooth with respect to and if each of its prime factors is , and all but one are . Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let be the asymptotic probability that a random integer is semismooth with respect to and . We present new recurrence relations for and related functions. We then give numerical methods for computing , tables of , and estimates for the error incurred by this asymptotic approximation.

     

Weighted inequalities for the maximal geometric mean operator

For nonnegative Borel measures on and for the maximal geometric mean operator , we characterize the weight pairs for which is of weak type and of strong type , . No doubling conditions are needed. We also note that a previously published different characterization for the strong type inequality for has an incorrect proof.

     

Abstract functions with continuous differences and Namioka spaces

Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.

     

Completely distributive CSL algebras with no complements in

Anoussis and Katsoulis have obtained a criterion for the space to have a closed complement in , where is a completely distributive commutative subspace lattice. They show that, for a given , the set of for which this complement exists forms an interval whose endpoints are harmonic conjugates. Also, they establish the existence of a lattice for which has no complement for any . However, they give no specific example. In this note an elementary demonstration of a simple example of this phenomenon is given. From this it follows that for a wide range of lattices , fails to have a complement for any .

     

-Fréchet-Urysohn property of Franklin compact spaces

Franklin compact spaces defined by maximal almost disjoint families of subsets of are considered from the view of its -sequentiality and -Fréchet-Urysohn-property for ultrafilters . Our principal results are the following: CH implies that for every -point there are a Franklin compact -Fréchet-Urysohn space and a Franklin compact space which is not -Fréchet-Urysohn; and, assuming CH, for every Franklin compact space there is a -point such that it is not -Fréchet-Urysohn. Some new problems are raised.