In [5] Witzgall proved that any weak metric defined on a real vector space, which is convex in each of the arguments, is determined by a weak gauge. In this paper we extend this result to any continuous weak metric defined on the positive cone in a totally ordered vector space, which is convex in each of the arguments.

We prove that in a certain class E of nonseparable Banach spaces the norm topology of the dual ball is definable in terms of its weak∗ topology. Thus, if X, Y ∈ E and f : BX∗ −→ BY ∗ is a weak ∗-to-weak∗ homeomorphism, then f is automatically norm-to-norm continuous.

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)− hL(y)| ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x)− hW (y)| ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing w...

We derive a result on the boundedness of the multiplicity of the singular values for Hankel operator, whose symbol is of the form F (z) := ∫ dλ(t ) z − t +R(z), where λ is a complex measure with infinitely many points in its support which is contained in the interval (−1,1), and whose argument has bounded variation there, while R is a rational function with all its poles inside of the unit disk...

We provide a simple set of sufficient conditions for the weak convergence of discrete Galton-Watson branching processes with immigration to continuous time and continuous state branching processes with immigration. Mathematics Subject Classification (2000): 60J80

In this paper we study strong and weak bisimulation equivalences for continuous-time Markov decision processes (CTMDPs) and the logical characterizations of these relations with respect to the continuous-time stochastic logic (CSL). For strong bisimulation, it is well known that it is strictly finer than CSL equivalence. In this paper we propose strong and weak bisimulations for CTMDPs and show...

A detailed structured backward error analysis for four kinds of Palindromic Polynomial Eigenvalue Problems (PPEP) ( d ∑ l=0 Alλ l ) x = 0, Ad−l = εA ⋆ l for l = 0, 1, . . . , ⌊d/2⌋, where ⋆ is one of the two actions: transpose and conjugate transpose, and ε ∈ {±1}. Each of them has its application background with the case ⋆ taking transpose and ε = 1 attracting a great deal of attention lately ...

In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths Cð1⁄20; 1 ;R Þ. Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generali...