the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-toNeumann map for a nonuniformly elliptic problem. Thus, we consider an equivalent formulation with a nonuniformly elliptic operator as state equation. The rapid decay of the solution to this problem suggests a...

A fully automated method uses Landsat Thematic Mapper data to map snow cover in the Sierra Nevada and make quantitative estimates of the fractional snow-covered area within each pixel. We model winter and spring reference scenes as linear mixtures of image end member spectra to produce the response variables for tree-based regression and classification models. Decision trees identify cloud cove...

A procedure is presented that synthesizes fractional crystallization separation processes to obtain pure solids from multi-component solutions. The method includes a procedure to generate a network flow model to identify alternative process designs for fractional crystallization. The main advantage of this systematic procedure with respect to other reported procedures is using non-equilibri...

Fractional order maps are a hot research topic; many new mathematical models suitable for developing applications in different areas of science and engineering. In this paper, class 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The has no equilibrium lines points, depending on values system parameters. All chaotic attractors generated by proposed hidden...

We study linear fractional boundary value problems consisting of an α-th order Riemann-Liouville fractional differential equation with 2 < α ≤ 3 and certain fractional boundary conditions. We derive several Lyapunovtype inequalities and apply them to establish nonexistence, uniqueness, and existence-uniqueness of solutions for related homogeneous and nonhomogeneous linear fractional boundary va...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice and it is a major open question is to explain why this is true. We give a natural condition under which we can provably perform MAP inference in polynomial time—we require tha...