In this paper we prove that the set of properties check-able by a Turing machine in DSPACEn k ] is exactly equal to the set of properties describable by a uniform sequence of rst-order sentences using at most k + 1 distinct variables. We prove that this is also equal to the set of properties describable using an iterative definition for a nite set of relations of arity k. This is a reenement of...

We generalize the 1/k-ensemble algorithm so that it can be used for both discrete and continuous systems, and show that the generalization is correct numerically and mathematically. We also compare the efficiencies of the generalized 1/k-ensemble algorithm and the generalized Wang-Landau algorithm through a neural network example. The numerical results favor to the generalized 1/k-ensemble algo...

We use the theory of lecture hall partitions to de ne a generalization of the Eulerian polynomials, for each positive integer k. We show that these 1=k-Eulerian polynomials have a simple combinatorial interpretation in terms of a single statistic on generalized inversion sequences. The theory provides a geometric realization of the polynomials as the h -polynomials of k-lecture hall polytopes. ...

In recent years, K 0 L CP-violation experiments have improved our knowledge of CP-violation parameters and their consistency with the expectations of CP T invariance and uni-tarity. For definitions of K 0 L CP-violation parameters and a brief discussion of the theory, see the article " CP Violation " by L. Wolfenstein in the Reviews, Tables, and Plots section of this Review. This note describes...

Let M be an m× n matrix. A k-assignment is a set of k matrix entries of which no two are in the same row or the same column. The value of a k-assignment is the sum of its entries. A k-assignment is optimal if its value is no larger than the value of any other k-assignment. If the entries of the matrix M are random variables then so is the value of the optimal k-assignment, here denoted by mink(...

There has been relatively little research emphasis on the effect of vitamin K on bone health during childhood. Recent interesting data from an observational study of healthy young girls (aged 3-16 years) in the United States suggests that better vitamin K status is associated with lower levels of markers of bone resorption and bone formation, suggesting a lower rate of bone turnover. However, i...

This paper presents the results of assays for antihemorrhagic activity carried out on an array of naphthoquinones and related compounds synthesized as described in a series of previous papers. Some of the compounds were prepared as synthetic models of the structural types postulat.ed (1) for vitamins K1 and Kz (l-5); others were synthesized subsequent to the establishment of the structure of vi...

Summarg 1. The dose-response relationship between the oral anticoagulant, warfarin, and its effect on the metabolism of phylloquinone (vitamin K,) has been examined in normal male volunteer subjects. 2. In each study the subject received a single, oral dose of warfarin and, 2 h later, an intravenous injection of [l ',2'-3H2 Jphylloquinone. Changes in the metabolism of phylloquinone were assesse...

The association between dietary vitamin K intake and the risk of fractures is controversial. Therefore we perform a meta-analysis of cohort or nested case-control studies to investigate the relationship between dietary vitamin K intake and the risk of fractures. A comprehensive search of PubMed and EMBASE (to July 11, 2016) was performed to identify cohort or nested case-control studies providi...

OBJECTIVE Vitamin K has a potentially beneficial role in insulin resistance, but evidence is limited in humans. We tested the hypothesis that vitamin K supplementation for 36 months will improve insulin resistance in older men and women. RESEARCH DESIGN AND METHODS This was an ancillary study of a 36-month, randomized, double-blind, controlled trial designed to assess the impact of supplement...