This paper provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous. We introduce a very weak notion of continuity, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semicontinuity. It is shown that the condition, tog...

We present the notion of weak local conditional independence (WCLI) between stochastic processes in a large class of semi-martingales that we call D′. The definition is based on measurability condition on the characteristics of the decomposition of the involved semi-martingales. We also give a definition related to the same concept based on certain likelihood processes, using the Girsanov theor...

We study the average density of resonances (DOR) for a semi-infinite disordered chain, coupled to the outside world by a (semi-infinite) perfect lead. A set of equations is derived, which provides the general framework for calculating the average DOR, for an arbitrary disorder and coupling strength. These general equations are applied to the case of weak coupling and an asymptotically exact exp...

In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [5, 8, 9]. The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) is the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a)− f(b)| ≤ k. We formulate the fractional weak...

In this paper we prove the existence for optimal control problems with terminal constraints on time scales. A definition of the solution of semi-linear control systems involving Sobolev space W 1,2 T is proposed and new existence and uniqueness results of this kind of dynamic systems on time scales are presented under a weaker assumption. According to LT strong-weak lower semi-continuity of int...

In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a ...

The nonlinear incompressible Navier-Stokes equations with boundary conditions at far fields and solid walls is considered. Two different formulations of boundary conditions are derived using the energy method. Both formulations are implemented in both strong and weak form and lead to an estimate of the velocity field. Equipped with energy bounding boundary conditions, the problem is approximate...

This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows to perform the semi-classical limit to the associated compressible Navier-Stokes equation. One of the difficulty of the problem is to deal with the degenerat...

The current status of lattice calculation of weak matrix elements for heavy quark systems is reviewed. After an assessment of systematic errors in present simulations, results for the B meson decay constant, the B parameter BB and semi-leptonic heavy-to-light and heavy-to-heavy transitions are discussed. The final topic are lattice results for heavy baryon spectroscopy.

We propose to use Grothendieck institutions based on 2categorical diagrams as a basis for heterogeneous specification. We prove a number of results about colimits and (some weak variants of) exactness. This framework can also be used for obtaining proof systems for heterogeneous theories involving institution semi-morphisms.