Complete List of Authors: Chen, Min; Peking University Health Science Center, Department of Physiology and Pathophysiology Li, Wenjing; Peking University Health Science Center, Department of Physiology and Pathophysiology Wang, Nanping; Peking University Health Science Center, Department of Physiology and Pathophysiology Zhu, Yi; Peking University Health Science Center, Department of Physiology...

Let φ : Cn×Cn → C, φ((x1, ..., xn), (y1, ..., yn)) = (x1−y1)+ ...+ (xn − yn). We say that f : Rn → Cn preserves distance d ≥ 0 if for each x, y ∈ Rn φ(x, y) = d implies φ(f(x), f(y)) = d. We prove that if x, y ∈ Rn (n ≥ 3) and |x − y| = ( √ 2 + 2/n)k · (2/n)l (k, l are nonnegative integers) then there exists a finite set {x, y} ⊆ Sxy ⊆ Rn such that each unit-distance preserving mapping from Sxy...

We present a simple proof of the interior approximate controllability for the following broad class of second-order equations in the Hilbert space L2 Ω : ÿ Ay 1ωu t , t ∈ 0, τ , y 0 y0, ẏ 0 y1, where Ω is a domain in N N ≥ 1 , y0, y1 ∈ L2 Ω , ω is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u belongs to L2 0, τ ;L2 Ω , and A : D A ⊂...

A complete solution for an inverse problem needs five main steps: choice of basis functions for discretization, determination of the order of the model, estimation of the hyperparameters, estimation of the solution, and finally, characterization of the proposed solution. Many works have been done for the three last steps. The first two have been neglected for a while, in part due to the complex...

Let Y = (y1, y2, . . . ), y1 ≥ y2 ≥ · · · , be the list of sizes of the cycles in the composition of c n transpositions on the set {1, 2, . . . , n}. We prove that if c > 1/2 is constant and n → ∞, the distribution of f(c)Y/n converges to PD(1), the Poisson-Dirichlet distribution with paramenter 1, where the function f is known explicitly. A new proof is presented of the theorem by Diaconis, Ma...

This paper is a continuation of [8]. Let A and B be two first order structures of the same vocabulary L. We denote the domains of A and B by A and B respectively. All vocabularies are assumed to be relational. The Ehrenfeucht-Fräıssé-game of length γ of A and B denoted by EFGγ(A,B) is defined as follows: There are two players called ∀ and ∃. First ∀ plays x0 and then ∃ plays y0. After this ∀ pl...

Let φ : Cn×Cn → C, φ((x1, ..., xn), (y1, ..., yn)) = (x1−y1)+ ...+ (xn − yn). We say that f : Rn → Cn preserves distance d ≥ 0 if for each x, y ∈ Rn φ(x, y) = d2 implies φ(f(x), f(y)) = d2. We prove that if x, y ∈ Rn (n ≥ 3) and |x − y| = ( √ 2 + 2/n)k · (2/n)l (k, l are nonnegative integers) then there exists a finite set {x, y} ⊆ Sxy ⊆ Rn such that each unit-distance preserving mapping from S...

This paper is a continuation of [8]. Let A and B be two first order structures of the same vocabulary L. We denote the domains of A and B by A and B respectively. All vocabularies are assumed to be relational. The Ehrenfeucht-Fräıssé-game of length γ of A and B denoted by EFGγ(A,B) is defined as follows: There are two players called ∀ and ∃. First ∀ plays x0 and then ∃ plays y0. After this ∀ pl...

A broadcast channel given by p(y 1 , y 2 |x) is said to be (physically degraded) if p(y 1 , y 2 |x) = p(y 1 |x)p(y 2 |y 1), ∀x ∈ X , ∀y 1 ∈ Y 1 , ∀y 2 ∈ Y 2. A broadcast channel given by p(y 1 , y 2 |x) is said to be (stochastic degraded) if its conditional marginal distributions p(y 1 |x) and p(y 2 |x) are the same as that of a physically degraded broadcast channel; that is, if there exists a ...

For a random sample of size n obtained from a p-variate normal population, the likelihood ratio test (LRT) for the covariance matrix equal to a given matrix is considered. By using the Selberg integral, we prove that the LRT statistic converges to a normal distribution under the assumption p/n → y ∈ (0, 1]. The result for y = 1 is much different from the case for y ∈ (0, 1). Another test is stu...