Uniqueness and regularity results for local vector-valued generalized minimizers and for local stress tensors associated to variational problems with linear growth conditions are established. Assuming that the energy density f has the structure f(Z) = h(|Z|), only very weak ellipticity assumptions are required. For the proof we combine arguments from measure theory and convex analysis with the ...

We check that there exists a model structure on the category of flows whose weak equivalences are the S-homotopy equivalences. As an application, we prove that the generalized T-homotopy equivalences preserve the branching and merging homology theories of a flow. The method of proof is completely different from the one of the third part of this series of papers.

We discuss the structure and asymptotic long-time properties of coupled equations for the moments of a Brownian particle's momentum p(n)((t)) derived microscopically beyond the lowest approximation in the weak coupling parameter λ. Generalized fluctuation-dissipation relations are derived and shown to ensure convergence to thermal equilibrium to any order in λ.

We construct an equivalence between the categories of vertex operator algebras and vertex operator coalgebras. We then investigate to what degree weak modules, generalized modules and ordinary modules carry corresponding comodule structures, as well as when various comodules carry module structure.

Conventional class of weak keys on RC4 stream cipher is defined as a specific case that combinations of the first three bytes of secret key satisfy two relational equations. This paper expands and generalizes the classes of weak keys using generalized relational equations and special classes of the internal state (called predictive state). We derive the probability that generalized classes of w...

The paper considers empirical distribution functions of stationary causal processes. Weak convergence of normalized empirical distribution functions to Gaussian processes is established and sample path properties are discussed. The Chibisov-O’Reilly Theorem is generalized to dependent random variables. The proposed dependence structure is related to the sensitivity measure, a quantity appearing...

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...