The relative entropy of entanglement $E_R$ is defined as the distance a multi-partite quantum state from set separable states measured by entropy. We show that this optimisation always achieved, i.e. any admits closest state, even in infinite dimensions; also, everywhere lower semi-continuous. use to derive dual variational expression for terms an external supremum instead infimum. These result...

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ with respect to the pseudo-monotonicity its Clarke-Rockafellar Sub-differential. We extend results characterizations non-smooth monotonicity sub-differentials spaces.

In this experiment, raw milk and commercially available full-cream UHT milk, semi-skimmed UHT milk, skimmed UHT milk, full-cream pasteurized milk, semi-skimmed pasteurized milk and infant formulas for babies between 6 and 12 months of age were analyzed by RIA, with a method using an antibody directed against human leptin and human leptin as reference standard. Raw milk and full-cream UHT milk d...

Given positive integers m and k, a k-term semi-progression of scope m is a sequence x1, x2, ..., xk such that xj+1 − xj ∈ {d, 2d, . . . ,md}, 1 ≤ j ≤ k − 1, for some positive integer d. Thus an arithmetic progression is a semi-progression of scope 1. Let Sm(k) denote the least integer for which every 2-coloring of {1, 2, ..., Sm(k)} yields a monochromatic k-term semi-progression of scope m. We ...

We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players’common prior belief, with respect to the total variation metric on beliefs. This is unlike the case of general Bayesian games, where lower semi-continuity of Bayesian equilibrium (BE) payo¤s rests on the "almost uniform" convergence of conditional beliefs. We also show upper semi-continuity (USC...

Abstract—Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and c...

Abstract: The structure of natural tornadoes and simulated analogs are sensitive to the lower boundary condition for friction. Three-dimensional numerical simulations of storms require a choice for turbulence parameterizations and resolution of wind near the lower boundary. This article explores some of the consequences of choices of a surface drag coefficient on the structure of a mature simul...

We prove that every multi-player perfect-information game with bounded and lower-semi-continuous payoffs admits a subgame-perfect ε-equilibrium in pure strategies. This result complements Example 3 in Solan and Vieille (2003), which shows that a subgame-perfect ε-equilibrium in pure strategies need not exist when the payoffs are not lower-semi-continuous. In addition, if the range of payoffs is...