and Applied Analysis 3 2. Several Reproducing Kernel Spaces In this section, several reproducing kernels needed are constructed in order to solve 1.1 and 1.2 using RKHSmethod. Before the construction, we utilize the reproducing kernel concept. Throughout this paper C is the set of complex numbers, L2 a, b {u | ∫b a u2 x dx < ∞}, l2 {A | ∑∞i 1 Ai 2 < ∞}, and the superscript n in u n t denotes th...

Let Fq be a finite field of characteristic p and let W2(Fq) the ring Witt vectors length two over Fq. We prove that for any integer n such divides n, groups SLn(Fq[t]/t2) SLn(W2(Fq)) have same number irreducible representations dimension d, each d.

(NSHAP) is designed to provide new data to explore how social support and personal relationships are associated with the health and aging in a representative sample of older community-dwelling Americans. NSHAP now has completed two rounds of data collection. There were two important objectives for carrying out the second wave of data collection. First, given the dynamics of health and aging, it...

We develop a rigorous second order analysis on the space of probability measures on a Riemannian manifold M endowed with the quadratic optimal transport distance W2. Our discussion comprehends: definition of covariant derivative, discussion of the problem of existence of parallel transport, calculus of the Riemannian curvature tensor, differentiability of the exponential map and existence of Ja...

i Given any word w, the reduced word w associated to w is any word obtained from w by reduction, such that wi cannot be reduced any further. Given two words w1 and w2 of A, the concatenation of w1 and w2 is the word w = w1w2. The empty word is denoted e. The set of all reduced words is denoted FA. With product defined as the reduced concatenation, this set becomes a group, called the free group...