Elliptic semiplanes and group divisible designs with orthogonal resolutions

In this paper we prove that there exists an elliptic semiplaneS(v, k, m) withk –m 2 if and only if there exists a group divisible design GDD _k ((k –m)(k – 1);k –m; 0, 1) withm pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplaneW(45, 7, 3) and show thatW is isomorphic to the elliptic semiplaneS(45, 7, 3) given by R. D. Baker.     

Codes Based on Complete Graphs

We consider the problem of embedding the even graphical code based on the complete graph onn vertices into a shortening of a Hamming code of length 2^m-1, wherem = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based onK _n. As a consequence, we are able to determineh(n) exactly for alln of the form 2 ^k + 1 and to narrow down the possibilities in general to two or three conceivable values.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe research for this note was done while the first author was visiting the University of Waterloo and the University of Rome, respectively. He thanks his colleagues there for their hospitality and also acknowledges the financial support of the Consiglio Nazionale delle Ricerche (Italy). The third author acknowledges the support of the National Science and Engineering Research Council of Canada given under grant #0GP0009258.     

On the structure of regular pairwise balanced designs

In this paper we obtain determinantal conditions necessary for the existence of (r,λ)-designs. The work is based on a paper of Connor [2]. In [3] Deza establishes an inequality which must be satisfied by the column vectors of an equidistant code; or, equivalently, the block sizes in an (r,λ)-design. We obtain a generalization of this inequality.     

Improving the parallelized Pollard lambda search on anomalous binary curves

The best algorithm known for finding logarithms on an elliptic curve is the (parallelized) Pollard lambda collision search. We show how to apply a Pollard lambda search on a set of equivalence classes derived from , which requires fewer iterations than the standard approach. In the case of anomalous binary curves over , the new approach speeds up the standard algorithm by a factor of .

     

A basic identity in mixed exterior algebra

To each finite-dimensional vector space E can canonically associate the space ΛE^* ⊗ ΛE. This space has a natural inner product (bilinear, symmetric and non-degenerate) and two (algebraic) product structures. Identities relating these products should be important for understanding the structure of these algebras. Indeed such identities have been used, both to develop Mixed Exterior Algebra and to apply it. In the present paper, we obtain a new identity of this type and show that the identities mentioned above are consequences of it. In this sense, it may be regarded as basic to the subject.     

A construction for equidistant permutation arrays of index one

An equidistant permutation array (EPA) which we denote by A(r, λ; ν) is a ν × r array such that every row is a permutation of the integers 1, 2,…, r and such that every pair of distinct rows has precisely λ columns in common. R(r, λ) is the maximum ν such that there exists an A(r, λ; ν). In this paper we show that R(n² + n + 2, 1) ? 2n² + n where n is a prime power.     

Higher order symmetrizer and application to an unusual transport equation

We study a class of stationary transport equation with nonlocal low-order tems We obtain the existence and uniqueness of a solution in sobolev spaces     

求解复杂湍流的非线性涡黏性系数模型和代数应力模型

非线性涡黏性系数模型和代数应力模型联系了线性涡黏性系数湍流模型和完整的微分 雷诺应力模型.随着它们受到日益关注,其形式也越来越多样化.本篇综述的目的是对这些模 型加以总结并比较它们之间的共同点及不同之处,指出它们与完整微分雷诺应力模型之间的 关系,以及相对于线性涡黏性系数模型而言它们在预报流场上所具有的优势.     

Orthogonal resolutions in odd balanced tournament designs

An odd balanced tournament design,OBTD(n), is ann × 2n + 1 array of pairs defined on a (2n + 1)-setV such that (1) every row of the array contains each element ofV twice, (2) every column of the array contains 2n distinct elements ofV, and (3) the pairs of the array form a (2n + 1, 2, 1)-BIBD. In this paper, we investigate the spectrum of odd balanced tournament designs with orthogonal resolutions. These designs can be used to construct doubly near resolvable (v, 3, 2)-BIBDs.