A product-estimate for Ginzburg-Landau and corollaries

We prove a new inequality for the Jacobian (or vorticity) associated to the Ginzburg-Landau energy in any dimension. It allows to retrieve existing lower bounds on the energy, to extend them to the case of unbounded vorticity, and to get a few other corollaries. It also provides a new estimate on the time-variation for time-dependent families, which has applications for the study of Ginzburg-Landau dynamics.     

Construction of nested orthogonal arrays

A (symmetric) nested orthogonal array is a symmetric orthogonal array OA(N,k,s,g) which contains an OA(M,k,r,g) as a subarray, where M<N and r<s. In this communication, some methods of construction of nested symmetric orthogonal arrays are given. Asymmetric nested orthogonal arrays are defined and a few methods of their construction are described.     

Construction of orthogonal multiwavelet bases

We propose a method for constructing orthogonal multiwavelet bases of the space L ²(?) for any known multiscaling functions that generate a multiresolution analysis of dimension greater than 1.     

Strong Skolem starters

This paper concerns a class of combinatorial objects called Skolem starters, and more specifically, strong Skolem starters, which are generated by Skolem sequences. In 1991, Shalaby conjectured that any additive group , where or , admits a strong Skolem starter and constructed these starters of all admissible orders . Only finitely many strong Skolem starters have been known to date. In this paper, we offer a geometrical interpretation of strong Skolem starters and explicitly construct infinite families of them.     

Construction of orthogonal group modules using tableaux

The program of constructing irreducible modules of the classical groups via Young tableaux is extended to include the orthogonal groups O(n) and SO(n). As in Weyl's pioneering work on this topic, each irreducible O(n)-module labelled by a partition λ of l is constructed as a submodule of V _?l. The construction is based on new sets of O(n) and SO(n) standard Young tableaux, closely related to those introduced by Proctor. The reduction of an arbitrary O(n) Young tableau to standard form is accomplished through the use of column antisymmetrisation and Garnir relations, as for GL(n), together with a trace removal process, analogous to that introduced by Bercle for Sp(n). For SO(n) it is necessary to define the associate of a Young tableau to effect the final step of the reduction process. The standardisation procedure is algorithmic and allows matrix representations of the Lie algebras so(n) to be constructed explicitly over the field of rational numbers. It is proved that the matrix elements are rational numbers having only integral powers of 2 in their denominators. All the various steps of the standardisation algorithm are exemplified, as well as the explicit construction of matrices representing elements of so(n). A link between the trace condition on a tableau and a Garnir relation on its associate is established.     

Construction of the mutually orthogonal extraordinary supersquares

Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in $\mathbb{F}_d \times \mathbb{F}_d$ . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in $\mathbb{F}_d \times \mathbb{F}_d$ are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of d ? 1 mutually orthogonal Latin squares is only a special case, namely Type I.     

Construction of doubly diagonalized orthogonal latin squares

A transversal T of a latin square is a collection of n cells no two in the same row or column and such that each of the integers 1, 2, …, n appears in exactly one of the cells of T. A latin square is doubly diagonalized provided that both its main diagonal and off-diagonal are transversals. Although it is known that a doubly diagonalized latin square of every order n ≥ 4 exists and that a pair of orthogonal latin squares of order n exists for every n ≠ 2 or 6, it is still an open question as to what the spectrum is for pairs of doubly diagonalized orthogonal latin squares. The best general result seems to be that pairs of orthogonal doubly diagonalized latin squares of order n exist whenever n is odd or a multiple of 4, except possibly when n is a multiple of 3 but not of 9. In this paper we give a new construction for doubly diagonalized latin squares which is used to enlarge the known class for doubly diagonalized orthogonal squares. The construction is based on Sade's singular direct product of quasigroups.     

Frame starters and adders in dicyclic groups

We construct frame starters in dicyclic groups Q_2n, in particular we construct frame starters with adders in Q_2q, where q = pⁿ and p ≡ 3 mod 4 is a prime. We also deduce the existence of strong frame starters in Z_2n for odd integers n whose prime factors are congruent with 1 modulo 4. The obtained results imply the constructions of classes of Room frames of types 4^p and 2ⁿ. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 347–353, 1998     

多尺度紧支撑向量值正交小波的构造

引入了多尺度向量值多分辨分析．利用矩阵理论,给出多尺度紧支撑向量值正交小波存在的必要条件及其构造方法．     

On strong starters in cyclic groups

Strong starters have been very useful in the construction of Room squares and cubes, Howell designs, Kirkman triple systems and Kirkman squares and cubes. In this paper we investigate various properties of strong starters in cyclic groups. In particular, we enumerate all non-isomorphic strong starters in cyclic groups of order n ⩽ 23 and all non-equivalent ones of order n⩽ 27. We also obtain results on the automorphism groups of the corresponding 1-factorizations and their embeddibility in Kirkman triple systems.     

A multiplication theorem for strong starters

Aequationes mathematicae -     

On Wigner's theorem: Remarks,complements, comments,and corollaries

Summary In this paper we present a unified treatment of Wigner's unitarity-antiunitarity theorem simultaneously in the real and the complex case. Its elementary nature, emphasized by V. Bargmann in 1964, is underlined here by removing unnecessary hypotheses, the most important being the completeness of the inner product spaces involved. At the end, we shall obtain connections to some recent results in geometry.     

Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions

Suppose is a sequence of polynomials orthogonal with respect to the moment functional τ=σ+ν, where σ is a classical moment functional (Jacobi, Laguerre, Hermite) and ν is a point mass distribution with finite support. In this paper, we develop a new method for constructing a differential equation having as eigenfunctions.     

Construction of sliced (nearly) orthogonal Latin hypercube designs

Sliced Latin hypercube designs are very useful for running a computer model in batches, ensembles of multiple computer models, computer experiments with qualitative and quantitative factors, cross-validation and data pooling. However, the presence of highly correlated columns makes the data analysis intractable. In this paper, a construction method for sliced (nearly) orthogonal Latin hypercube designs is developed. The resulting designs have flexible sizes and most are new. With the orthogonality or near orthogonality being guaranteed, the space-filling property of the resulting designs is also improved. Examples are provided for illustrating the proposed method.     

Addition theorems for Legendre functions as corollaries of an addition theorem for Gegenbauer polynomials

Proofs are given for addition theorems for Legendre functions with arbitrary upper and lower indices, based solely on an addition theorem for Gegenbauer polynomials. New versions of these and other similar theorems are given, both in the form of sums and of integrals.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 321–330, September, 1976.