On quasiregular collineation groups of projective planes

We investigate quasiregular collineation groups of type (d) in the Dembowski-Piper classification. We prove that the Sylow 2-subgroup of as well as the Sylow 2-subgroup of its multiplier group have to be cyclic. We use these results to obtain new necessary conditions on the existence of affine difference sets.Research partially supported by NSA grant #MDA 904-90-H-4008.     

Two results on maximum nonlinear functions

Maximum nonlinear functions are widely used in cryptography because the coordinate functions F _β (x) := tr(β F(x)), , have large distance to linear functions. Moreover, maximum nonlinear functions have good differential properties, i.e. the equations F(x + a) − F(x) = b, , have 0 or 2 solutions. Two classes of maximum nonlinear functions are the Gold power functions , gcd(k, m) = 1, and the Kasami power functions , gcd(k, m) = 1. The main results in this paper are: (1) We characterize the Gold power functions in terms of the distance of their coordinate functions to characteristic functions of subspaces of codimension 2 in . (2) We determine the differential properties of the Kasami power functions if gcd(k,m) ≠ 1.      

Minerals in Pregnancy and Their Impact on Child Growth and Development

During pregnancy, women undergo metabolic and physiological changes, and their needs are higher, to maintain growth and development of the fetus. If the nutritional status of the expectant mother is not satisfactory, some maternal and neonatal complications can occur. In the second and third trimester of pregnancy, there is a reserve of nutrients in the fetus that can be utilized after birth; thereby, children present an accelerated growth in the first years of life, which is a proven response to the available nutrition pattern. However, if such a pattern is insufficient, there will be deficits during development, including brain function. Therefore, despite many recent published works about gestational nutrition, uncertainties still remain on the mechanisms of absorption, distribution, and excretion of micronutrients. Further elucidation is needed to better understand the impacts caused either by deficiency or excess of some micronutrients. Thus, to illustrate the contributions of minerals during prenatal development and in children, iodine, selenium, iron, zinc, calcium, and magnesium were selected. Our study sought to review the consequences related to gestational deficiency of the referred minerals and their impact on growth and development in children born from mothers with such deficiencies     

Solving isomorphism problems about 2‐designs from disjoint difference families

Recently, two new constructions of disjoint difference families in Galois rings were presented by Davis, Huczynska, and Mullen and Momihara. Both were motivated by a well‐known construction of difference families from cyclotomy in finite fields by Wilson. It is obvious that the difference families in the Galois ring and the difference families in the finite field are not equivalent. A related question, which is in general harder to answer, is whether the associated designs are isomorphic or not. In our case, this problem was raised by Davis, Huczynska, and Mullen. In this paper, we show that, in most cases, the 2‐ designs arising from the difference families in Galois rings and those arising from the difference families in finite fields are nonisomorphic by comparing their block intersection numbers.     

Cayley Graphs of Diameter Two from Difference Sets

Let and be the largest order of a Cayley graph and a Cayley graph based on an abelian group, respectively, of degree d and diameter k. When , it is well known that with equality if and only if the graph is a Moore graph. In the abelian case, we have . The best currently lower bound on is for all sufficiently large d. In this article, we consider the construction of large graphs of diameter 2 using generalized difference sets. We show that for sufficiently large d and if , and m is odd.     

Erratum: “Studies on Gas Purification by a Pulsed Microwave Discharge at 2.46 GHz in Mixtures of N2/NO/O2 at Atmospheric Pressure” [Plasma Chemistry and Plasma Processing,Vol. 21, No. 2, 2001]

Plasma Chemistry and Plasma Processing -     

Test Function Criteria for Hankel Operators

It is well known that there are classes of test functions such that a Hankel operator is bounded if and only if it is bounded on those functions. Criteria are derived which determine whether a Hankel operator is compact or belongs to a particular Schatten class, in terms of its action on those test functions.