where u : (0, T ) × Ω → < is unknown function, Ω ⊂ < is a polygonal convex domain with the boundary Γ, 0 < T <∞, ν is the outward normal to Γ, f(t, x, s) and ac(t, x) are Lipschitz continuous functions and β : < → < is a nondecreasing Lipschitz continuous function. Finally cg is a real number and cg ≥ 0. There are several linear approximation schemes, deal with the Stefan like problems or with ...

Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the general project of establishing a common specification language in order to certify proofs given in a wide range of deductive formalisms. In particular, by usi...

We follow language theoretic approach to synchronizing automata and Černý’s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a strict connection between principal left ideals and synchronizing automata. We characterize regular languages whose minimal deterministic finite automaton is synchroniz...

Improving the previously known best bound, we show that any recursively enumerable language can be generated with a non-returning parallel communicating (PC) grammar system having six contextfree components. We also present a non-returning universal PC grammar system generating unary languages, that is, a system where not only the number of components, but also the number of productions and the...

We consider a simple and well-known category of alternating games (also known as sequential data structures) and several categories derived from it. In each case, we present an extension of Plotkin’s language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types. The quest for such languages results in a novel selection of language primitives for...

Eigenstates of two-dimensional charged electron–hole complexes in magnetic fields are considered. The operator formalism that allows one to partially separate the center-of-mass motion from internal degrees of freedom is presented. The scheme using magnetic translations is developed for calculating in strong magnetic fields the eigenspectra of negatively charged excitons X, a bound state of two...

This paper develops a framework to model the performance of parallel applications executing in a shared network computing environment. For sharing of a single computation node or network link, the actual performance is predicted, while for sharing of multiple nodes and links, performance bounds are developed. The methodology for building such a shared execution performance model is based on mon...

We present a formal method of functional program develop ment based on step by step transformation In their most abstract form speci cations are essentially predicates that relate the result of the speci ed program to the free variables of that pro gram In their most concrete form speci cations are simply programs in a functional programming language Development from abstract speci cations to p...

Here we compute the static potential in scalar QED 3 at leading order in 1/N f. We show that the addition of a non-minimal coupling of Pauli-type (ǫ µνα j µ ∂ ν A α), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic (confining) at large distances. The non-minimal coupling modifies the potentia...

Modular SOS (MSOS) is a variant of conventional Structural Operational Semantics (SOS). Using MSOS, the transition rules for each construct of a programming language can be given definitively, once and for all, and do not need reformulation when further constructs are added to the language. MSOS thus provides an exceptionally high degree of modularity in language descriptions, thereby removing ...