Carmeli’s Accelerating Universe is Spatially Flat Without Dark Matter

Carmeli’s 5D brane cosmology has been applied to the expanding accelerating universe and it has been found that the distance redshift relation will fit the data of the high-z supernova teams without the need for dark matter. Also the vacuum energy contribution to gravity, Ω_Λ indicates that the universe is asymptotically expanding towards a spatially flat state, where the total mass/energy density Ω+Ω_Λ→1.     

On Two Conjectures of Steinhaus

We disprove two conjectures of H. Steinhaus by showing that: (1) there is a convex surface S such that for any point x on S and any point y in the set F _x of farthest points from x, there are at most two segments from x to y; (2) the properties and do not characterize the sphere.     

Local differentiability of distance functions

Recently Clarke, Stern and Wolenski characterized, in a Hilbert space, the closed subsets for which the distance function is continuously differentiable everywhere on an open ``tube' of uniform thickness around . Here a corresponding local theory is developed for the property of being continuously differentiable outside of on some neighborhood of a point . This is shown to be equivalent to the prox-regularity of at , which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation. Additional characterizations are provided in terms of being locally of class or such that is convex around for some 0$">. Prox-regularity of at corresponds further to the normal cone mapping having a hypomonotone truncation around , and leads to a formula for by way of . The local theory also yields new insights on the global level of the Clarke-Stern-Wolenski results, and on a property of sets introduced by Shapiro, as well as on the concept of sets with positive reach considered by Federer in the finite dimensional setting.

     

涉及单形内点的几何不等式

建立了涉及n维单形内点的两个几何不等式，作为其特例得到n维Euler不等式的推广。     

Denumerable state semi-Markov decision processes with unbounded costs,average cost criterion

This paper establishes a rather complete optimality theory for the average cost semi-Markov decision model with a denumerable state space, compact metric action sets and unbounded one-step costs for the case where the underlying Markov chains have a single ergotic set. Under a condition which, roughly speaking, requires the existence of a finite set such that the supremum over all stationary policies of the expected time and the total expected absolute cost incurred until the first return to this set are finite for any starting state, we shall verify the existence of a finite solution to the average costs optimality equation and the existence of an average cost optimal stationary policy.     

电流变液中悬浮粒子形状与其固态结构之间的关系

采用近邻相互作用近似方法 ,计算了电流变液中悬浮粒子的形状对电流变液呈固态时基本结构的影响 .结果表明 :基本结构将随着悬浮粒子形状的变化而变化 ,特别是在扁椭球情况下 ,固态结构的相互作用能出现几个数量级的变化     

The excess-mass ellipsoid

The excess-mass ellipsoid is the ellipsoid that maximizes the difference between its probability content and a constant multiple of its volume, over all ellipsoids. When an empirical distribution determines the probability content, the sample excess-mass ellipsoid is a random set that can be used in contour estimation and tests for multimodality. Algorithms for computing the ellipsoid are provided, as well as comparative simulations. The asymptotic distribution of the parameters for the sample excess-mass ellipsoid are derived. It is found that a n^1/3 normalization of the center of the ellipsoid and lengths of its axes converge in distribution to the maximizer of a Gaussian process with quadratic drift. The generalization of ellipsoids to convex sets is discussed.     

Asymptotic independence of distributions of normalized order statistics of the underlying probability measure

Let n denote the sample size, and let r_i ∈ {1,…,n} fulfill the conditions r_i ? r_i?1 ≥ 5 for i = 1,…,k. It is proved that the joint normalized distribution of the order statistics Z_ri:n, i = 1,…,k, is independent of the underlying probability measure up to a remainder term of order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. A counterexample shows that, as far as central order statistics are concerned, this remainder term is not of the order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ if r_i ? r_i?1 = 1 for i = 2,…,k.     

Some first passage problems related to cusum procedures

Let $\text{X}{}_1\text{,}\text{X}{}_2\text{,…}$ be independent random variables, and set W_n = max(0,W_n-1 + X_n), W₀ = 0, n ? 1. The so-called cusum (cumulative sum) procedure uses the first passage time T(h) = inf{n ? 1: W_n?h}for detecting changes in the mean μ of the process. It is shown that lim_h→∞ μET(h)/h = 1 if μ > 0. Also, a cusum procedure for detecting changes in the normal mean is derived when the variance is unknown. An asymptotic approximation to the average run length is given.     

John's Theorem for an Arbitrary Pair of Convex Bodies

We provide a generalization of John's representation of the identity for the maximal volume position of L inside K, where K and L are arbitrary smooth convex bodies in ⁿ . From this representation we obtain Banach–Mazur distance and volume ratio estimates.