Extending AG(4, 2) to S(4, {5, 6}, 17)

A construction of S(4, {5, 6}, 17) is given using the geometry of AG(4, 2) and PG(3, 2). © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 113–117, 1999     

Updated tables of parameters of (T,M, S)-nets

We present an updated survey of the known constructions and bounds for (t, m, s)- nets as well as tables of upper and lower bounds on their parameters for various bases. © 1999 John Wiley & Sons, Inc. J. Cobin Designs 7: 381–393, 1999     

Multi-separation, centrifugality and centripetality imply chaos

Let be an interval. need not be compact or bounded. Let be a continuous map, and be a trajectory of with or . Then there is a point such that . A point is called a centripetal point of relative to if or , and is centrifugal if or . In this paper we prove that if there exist centripetal points of in , then has periodic points of some odd () period . In addition, we also prove that if ) is multi-separated by Fix(), or there exists a centrifugal point of in , then is turbulent and hence has periodic points of all periods.

     

Overgroups of irreducible linear groups, II

Determining the subgroup structure of algebraic groups (over an algebraically closed field of arbitrary characteristic) often requires an understanding of those instances when a group and a closed subgroup both act irreducibly on some module , which is rational for and . In this paper and in Overgroups of irreducible linear groups, I (J. Algebra 181 (1996), 26-69), we give a classification of all such triples when is a non-connected algebraic group with simple identity component , is an irreducible -module with restricted -high weight(s), and is a simple algebraic group of classical type over sitting strictly between and .

     

Integrability of superharmonic functions, uniform domains, and Hölder domains

Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.

     

Density doubling, double-circulants, and new sphere packings

New nonlattice sphere packings in dimensions 20, 22, and 44-47 that are denser than the best previously known sphere packings were recently discovered. We extend these results, showing that the density of many sphere packings in dimensions just below a power of 2 can be doubled using orthogonal binary codes. This produces new dense sphere packings in for and . For the resulting packings are denser than any packing previously known.

     

Analysis of PSLQ, an integer relation finding algorithm

Let be either the real, complex, or quaternion number system and let be the corresponding integers. Let be a vector in . The vector has an integer relation if there exists a vector , , such that . In this paper we define the parameterized integer relation construction algorithm PSLQ, where the parameter can be freely chosen in a certain interval. Beginning with an arbitrary vector , iterations of PSLQ will produce lower bounds on the norm of any possible relation for . Thus PSLQ can be used to prove that there are no relations for of norm less than a given size. Let be the smallest norm of any relation for . For the real and complex case and each fixed parameter in a certain interval, we prove that PSLQ constructs a relation in less than iterations.

     

On finite {s-2, s}-semiaffine linear spaces

In this paper finite {s-2, s}-semiaffine linear spaces of order n are studied. It is proved that if s= 6 or then there is only a finite number of such linear spaces. Received 28 May 1999; revised 28 December 1999.     

Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups

For a free group of finite rank, it is shown that the fixed subgroup of any set of endomorphisms of has rank , generalizing a recent result of Dicks and Ventura. The proof involves the combinatorics of derivations of groups. Some related questions are examined.

     

Statics, dynamics, and stability of composite panels with gently curved orthotropic layers. 2. Stability

Two approaches to the study of the stability of gently curved laminate structures are developed. The first approach is based on the analytical separation of variables. In the second approach, a polynomial approximation over the transverse coordinate is assumed. The loss of stability of such structures with various contact conditions for layers is examined. For Report 1, see Mech. Compos. Mater.,35, No. 4, 285–292 (1999). Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 643–652, September–October, 1999.     

The similarity degree of an operator algebra, II

For every integer , there is a unital closed subalgebra with similarity degree equal precisely to d, in the sense of our previous paper. This means that for any unital homomorphism we have with independent of u, and the exponent d in this estimate cannot be improved. The proof that the degree is larger than crucially uses an upper bound for the norms of certain Gaussian random matrices due to Haagerup and Thorbj?rnsen. We also include several complements to our previous publications on the same subject. Received: 25 April, 1999; Accepted: 23 June, 1999     

Computation of the Folkman number Fe(3, 3; 5)

With the help of computer algorithms, we improve the lower bound on the edge Folkman number F_e(3, 3; 5) and vertex Folkman number F_v(3, 3; 4), and, thus, show that the exact values of these numbers are 15 and 14, respectively. We also present computer enumeration of all critical graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 41–49, 1999     

Nonexpansive, -continuous antirepresentations have common fixed points

Let be a closed convex subset of a Banach (dual Banach) space . By we denote an antirepresentation of a semitopological semigroup as nonexpansive mappings on . Suppose that the mapping is jointly continuous when has the weak (weak*) topology and the Banach space of bounded right uniformly continuous functions on has a right invariant mean. If is weakly compact (for some the set is weakly* compact) and norm separable, then has a common fixed point in .

     

New 5-designs with automorphism group PSL(2, 23)

Blocks of the unique Steiner system S(5, 8, 24) are called octads. The group PSL(2, 23) acts as an automorphism group of this Steiner system, permuting octads transitively. Inspired by the discovery of a 5-(24, 10, 36) design by Gulliver and Harada, we enumerate all 4- and 5-designs whose set of blocks are union of PSL(2, 23)-orbits on 10-subsets containing an octad. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 147–155, 1999     

A theory of biochemical organization,metabolic pathways,and evolution

Biogenesis and evolution are viewed from the perspective of the universality of the metabolic chart with respect to primary metabolism and the phylogenetic specificity of secondary metabolism. This analysis is developed within the context of the evolution of the universal ancestor through hierarchical networks of chemical reactions. © 1999 John Wiley & Sons, Inc.     

Aspects of strong compactness, measurability, and indestructibility

 We prove three theorems concerning Laver indestructibility, strong compactness, and measurability. We then state some related open questions. Received: 11 December 1999 / Revised version: 17 September 2000 / Published online: 2 September 2002 Mathematics Subject classification (2000): 03E35, 03E55 Keywords or phrases: Measurable cardinal – Strongly compact cardinal – Supercompact cardinal – Indestructibility     

A converse to a theorem of Adamyan, Arov and Krein

A well known theorem of Akhiezer, Adamyan, Arov and Krein gives a criterion (in terms of the signature of a certain Hermitian matrix) for interpolation by a meromorphic function in the unit disc with at most poles subject to an -norm bound on the unit circle. One can view this theorem as an assertion about the Hardy space of analytic functions on the disc and its reproducing kernel. A similar assertion makes sense (though it is not usually true) for an arbitrary Hilbert space of functions. One can therefore ask for which spaces the assertion is true. We answer this question by showing that it holds precisely for a class of spaces closely related to .

     

Braided tensor C*-categories, Hecke symmetries and actions on extended Cuntz algebras

In this paper we deal with braided tensor C*-categories. For every object of the category we associate a C*-algebra denoted by . An analysis of the braiding is carried out by using the conjugate equations. If the braiding is a Hecke symmetry and the -dimension is appropriately chosen, we characterize the C*-algebra as the one generated by the representation given by the Markov trace. This analysis leads to the existence of an action of on . Such actions (Theorem 1) correspond to *-monomorphisms of on which generalize the ones obtained earlier by the author (1997).

     

On the partial regularity of energy-minimizing, area-preserving maps

We prove a partial regularity assertion for a Lipschitz continuous mapping u in the plane that minimizes an appropriate convex (or quasiconvex) energy functional, under the “hard” constraint that det D u = 1 a.e. The primary technical assumption is that u be nondegenerate, meaning that, locally, at least one of its partial derivatives is bounded away from zero a.e. The method of proof is to convert to a related minimization problem for a generating function w, the advantage being that we now have the “soft” constraint . Received March 16, 1999 / Accepted April 23, 1999