Let (Ω,F ,P) be a probability space and S = {S1, . . . , SK} a discrete-topological space that consists of K real d-by-d matrices, where K and d both ≥ 2. In this paper, we study the pointwise stabilizability of a discrete-time, time-homogeneous, stationary (p, P)-Markovian jump linear system Ξ = (ξn) n=1 where ξn : Ω → S. Precisely, Ξ is called “pointwise convergent”, if to any initial state x...

We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the ...

Let (Ω,F ,P) be a probability space and S = {S1, . . . , SK} a discrete-topological space that consists of K real d-by-d matrices, where K and d both ≥ 2. In this paper, we study the pointwise stabilizability of a discrete-time, time-homogeneous, stationary (p, P)-Markovian jump linear system Ξ = (ξn) n=1 where ξn : Ω → S. Precisely, Ξ is called “pointwise convergent”, if to any initial state x...

It is shown that the application of Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the Many-Hilbert-Space theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian...

A trie data structure stores an ordered set of keys; the branching structure of a trie depends on the lexical properties of its keys independent of the order of insertion. Compact implementations of PATRICIA binary tries called crit-bit trees [2] have just two words of overhead per item stored. A hash array mapped trie (HAMT) [1] has wide fan-out, indexing each tree node using several hashed ke...

In this paper we generalize work of Amice and Lazard from the early sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the open unit disk over Cp. Lazard showed that this ring has a divisor theory and that the classes of closed, finitely generated, and principal ideals in this ring coincide. W...

Quadratic programming is concerned with minimizing a convex quadratic function subject to linear inequality constraints. The variables are assumed to be nonnegative. The unique solution of quadratic programming (QP) problem (QPP) exists provided that a feasible region is non-empty (the QP has a feasible space). A method for searching for the solution to a QP is provided on the basis of statisti...

We investigate the asymptotic behavior of curvatures of the Weil-Petersson metric in Teichmüller space. We use a pointwise curvature estimate to study directions, in the tangent space, of extremely negative curvature and directions of asymptotically zero curvatures.

It is shown that the p-adic Banach spaces introduced by Emerton, are isomorphic to the cohomology groups of the sheaf of continuous Qp-valued functions on a certain space. Some applications of this result are discussed.

Let p be a fixed prime number. Throughout this paper, the symbols Z, Zp, Qp, and Cp denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers. The normalized valuation in Cp is denoted by | · |p with |p|p 1/p. Let UD Zp be the space of uniformly differe...