Curran猜想的解答

本文确定了能作为有限群自同构群的Ｐ－群的最佳下最，彻底解决了Ｃｕｒｒａｎ在１９８９年提出的关于此最佳下界的三个猜想。     

A Flaw in the Use of Minimal Defining Sets for Secret Sharing Schemes

It is shown that in some cases it is possible to reconstruct a block design uniquely from incomplete knowledge of a minimal defining set for . This surprising result has implications for the use of minimal defining sets in secret sharing schemes.     

Generalized Latin squares and their defining sets

A generalized Latin square of type (n,k) is an n×n array of symbols 1,2,…,k such that each of these symbols occurs at most once in each row and each column. Let d(n,k) denote the cardinality of the minimal set S of given entries of an n×n array such that there exists a unique extension of S to a generalized Latin square of type (n,k). In this paper we discuss the properties of d(n,k) for k=2n-1 and k=2n-2. We give an alternate proof of the identity d(n,2n-1)=n²-n, which holds for even n, and we establish the new result . We also show that the latter bound is tight for n divisible by 10.     

Completely J —positive linear systems of finite order

Completely J — positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J — positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J — symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J — symmetric realizations are discussed.     

On quasi-complete intersections of codimension

In this paper, we prove that if , , is a locally complete intersection of pure codimension and defined scheme-theoretically by three hypersurfaces of degrees , then for using liaison theory and the Arapura vanishing theorem for singular varieties. As a corollary, a smooth threefold is projectively normal if is defined by three quintic hypersurfaces.

     

Braid groups in genetic code

For every genetic code with finitely many generators and at most one relation, a braid group is introduced. The construction presented includes the braid group of a plane, braid groups of closed oriented surfaces, Artin— Brieskorn braid groups of series B, and allows us to study all of these groups from a unified standpoint. We clarify how braid groups in genetic code are structured, construct words in the normal form, look at torsion, and compute width of verbal subgroups. It is also stated that the system of defining relations for a braid group in two-dimensional manifolds presented in a paper by Scott is inconsistent. Supported by RFBR grant No. 02-01-01118. __________ Translated from Algebra i Logika, Vol. 45, No. 2, pp. 131–158, March–April, 2006.     

In situ IR monitoring of complexation reaction between 2,6-bis(3,5-dimethylpyrazoyl)pyridine and some metal ions

In situ complexation reactions between 2,6-bis(3,5-dimethylpyrazoyl)pyridine (bdmpp) and some transition metals (Cu²⁺, Co²⁺ and Ni²⁺) were studied with a new method in liquid cell using FT-IR. In this method, the FT-IR spectrum of the solution of ligand was defined as a background, and then the changes in the FT-IR spectra by the addition of the metal salts were investigated. This method allows one to obtain the spectra of the ligand-metal complex before yielding the solid-state product. Complexation ratios (M/L) of these metals with bdmpp were found 1/1, 1/2 and 1/2, for Cu, Co and Ni, respectively. Studying with Mg²⁺ and Ca²⁺ ions showed that there were no interaction between bdmpp and these metal ions in methanol.     

Smallest defining sets of directed triple systems

A directed triple system of order v, , is a pair (V,B) where V is a set of v elements and B is a collection of ordered triples of distinct elements of V with the property that every ordered pair of distinct elements of V occurs in exactly one triple as a subsequence. A set of triples in a D is a defining set for D if it occurs in no other on the same set of points. A defining set for D is a smallest defining set for D if D has no defining set of smaller cardinality. In this paper we are interested in the quantity