We show that the product of n 3 3 matrices of n-bit integers can be computed in P -uniform FNC1. Since this problem is complete [BOC92] for formul in f+; g on n-bit integers, we conclude that \algebraic NC1" on integers is equal to the usual Boolean notion of NC1 functions.

7. Let G be a group of finite order and identity e. Suppose that φ is an automorphism of G onto itself with the following properties: (1) φ(x) = x if and only if x = e; (2) φ(φ(x)) = x for each element x of G. (The mapping φ has the property that it is one-one onto and that φ(xy) = φ(x)φ(y) for each pair x, y of elements of G.) (a) Give an example of a group and automorphism for which these con...

We study the set S nc(p, q) of annular non-crossing permutations of type B, and we introduce a corresponding set NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We prove that the natural bijection between S nc(p, q) and NC (p, q) is a poset isomorphism, where the partial order on S nc(p, q) is induced from the hyperoctahedral group Bp+q, while NC ...

We show that excited baryons in large Nc QCD form multiplets, within which masses are first split at O(1/Nc). The dominant couplings of resonances to various mesons are highly constrained: The N(1535) decays at leading 1/Nc order exclusively to η-N rather than π-N , and vice versa for the N(1650). This multiplet structure is reproduced by a simple large Nc quark model, well studied in the liter...

An NC 1 circuit for division of binary numbers is presented. By results of Beame, Cook and Hoover this also shows that iterated product and powering are in NC 1 , and by a result of Borodin all three operations are in log-space. This settles an open issue in parallel and space bounded arithmetic complexity.

The effect of dietary feeding of rice bran and phytic acid on the glucose metabolism in high fat-fed C57BL/6N mice fed was investigated. The mice were given with either a high fat diet only (HF group) or a high fat diet supplemented with rice bran (HF-RB group) or phytic acid (HF-PA group) for 7 weeks. The control mice (NC group) received a normal diet. At the end of the experimental period, th...

Strategies to manipulate the gut microbiota in infancy have been considered to prevent the development of allergic diseases later in life. We aimed to elucidate the effects of maternal dietary supplementation with a prebiotic oligosaccharide on gut microbiota and spontaneously developing atopic dermatitis-like skin lesions in the offspring of NC/Nga mice. Female NC/Nga mice were fed diets eithe...

Abstract Very low-protein (VLP) diets are beneficial for reducing the nitrogen excretion from swine production, but these depress performance of pigs while supplemented with first four limiting amino acids (FFL; i.e. Lys, Met, Thr and Trp). The objective this study was to investigate effect supplementation Val Ile above NRC (2012) levels on performance, thermal radiation blood metabolites fed V...

Soil enzyme activities are considered to be sensitive to pollution and have been proposed as indicators for measuring the degree of soil degradation. In this work we found that in three galician soils exposed to various degrees of pollution by tanning effluent, hydrocarbons or landfill effluent, the changes in the activities of individual enzyme did not allow precise quantification of soil degr...