The focal point of this paper is the probabilistically constrained linear program (PCLP) and how it can be applied to control system design under risk constraints. The PCLP is the counterpart of the classical linear program, where it is assumed that there is random uncertainty in the constraints and, therefore, the deterministic constraints are replaced by probabilistic ones. It is shown that f...

Theorem 0.1. Let K be an abstract elementary class (AEC) with amalgamation and no maximal models. Let λ > LS(K). If K is categorical in λ, then the model of cardinality λ is Galois-saturated. This answers a question asked independently by Baldwin and Shelah. We deduce several corollaries: K has a unique limit model in each cardinal below λ, (when λ is big-enough) K is weakly tame below λ, and t...

Vesicle formation in aqueous mixtures of the hydrolyzed copolymer of styrene-maleic anhydride (HSMA) and a series of single-tailed cationic surfactants (C(n)H(2n+1)N(C(m)H(2m+1))3Br, n = 8, 10, 12, 16, m = 1, 2, 3, 4) was studied by fluorescence measurement, zeta potential measurement, and transmission electron microscopy. The driving forces of vesicle formation in this kind of system are attri...

in this paper. (1) we determine the complex-valued solutions of the following variant of van vleck's functional equation $$int_{s}f(sigma(y)xt)dmu(t)-int_{s}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin s,$$ where $s$ is a semigroup, $sigma$ is an involutive morphism of $s$, and $mu$ is a complex measure that is linear combinations of dirac measures $(delta_{z_{i}})_{iin i}$, such that for all $iin i$,...

We give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions. The firstone concerns generic types and the non-superstability of such groups in many cases. The second-one concerns the connectedness of most free products of groups without amalgamation. First-order theories of free products of groups have been recently investigated in [...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...