In Gateaux or bornologically diierentiable spaces there are two natural generalizations of the concept of a Fr echet subderivative: In this paper we study the viscosity subderivative (which is the more robust of the two) and establish reened fuzzy sum rules for it in a smooth Banach space. These rules are applied to obtain comparison results for viscosity solutions of Hamilton-Jacobi equations ...

This paper considers some path properties of real separable Gaussian processes ~ with parameter set an arbitrary interval. The following results are established, among others. At every fixed point the paths of ~ are continuous, or differentiable, with probability zero or one. If ~ is measurable, then with probability one its paths have essentially the same points .~ of continuity and differenti...

In the paper compressible, stationary Navier-Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions, i.e., the solutions take form (1.12). The approximate soluti...

In this paper, we study linear fuzzy time-variant optimal control systems using the generalized differentiability concept and we present the general form of optimal controls and states. Some examples are provided to illustrate our results.

the non-differentiability and implicit definition of boundary of production possibility set (pps) in data envelopment analysis (dea) are two important difficulties for obtaining directional characteristics, including different elasticity measures and marginal rates of substitution. also, imposing weight restrictions in dea models have some shortcomings and misunderstandings. in this paper we ut...

We present a second order differentiability theory for convex functions on Banach spaces.