In this paper, the universal approximation property of one of the most frequently used type of fuzzy systems is proved. The type of fuzzy system in the present work employs triangle-shaped fuzzy membership functions (TSMF) for its input variables. The proof of the universal approximation property does not use the Stone-Weierstrass theorem because the TSMFs are not closed for the product; instea...

For a Banach space X, the Lidskii trace property is equivalent to the nest approximation property; that is, for every nuclear operator on X that has summable eigenvalues, the trace of the operator is equal to the sum of the eigenvalues if and only if for every nest N of closed subspaces of X, there is a net of finite rank operators on X, each of which leaves invariant all subspaces in N , that ...

By introducing a ubiquity property for rectangles, we prove the mass transference principle from rectangles to i.e., if sequence of forms system (a full measure property), then limsup set defined by shrinking these smaller has Hausdorff or say transfer brevity. The sets generated balls appear at most fundamental level in Diophantine approximation: one follows Dirichlet's theorem, other Minkowsk...

In this paper we consider a uni ed approximation method for node{deletion problems with nontrivial and hereditary graph properties. It was proved 16 years ago that every node{deletion problems for a nontrivial hereditary property is NP{complete via a few generic approximation preserving reductions from the Vertex Cover problem. An open problem posed at that time is concerned with the other dire...

Informally, a class of graphs G is said to have the level-treewidth property (LT-property) if for every G E G there is a layout (breadth first ordering) LG such that the subgraph induced by the vertices in k-consecutive levels in the layout have treewidth O ( f ( k ) ) , for some function f . We show that several important and well known classes of graphs including planar and bounded genus grap...

In this note, we prove that the well known saturation assumption implies that piecewise polynomial interpolation and best approximation in finite element spaces behave in similar fashion. That is, the error in one can be used to estimate the error in the other. We further show that interpolation error can be used as an a posteriori error estimate that is both reliable and efficient.

The usefulness of fuzzy input fuzzy output functions and their interpolation/approximation by different operators in fuzzy control motivate their deeper theoretical study. We obtain some properties of fuzzy B-spline series such as variation and uncertainty diminishing property. We also propose spline approximation of fuzzy input fuzzy output functions. Key–Words: Fuzzy numbers, Fuzzy splines, A...

The Moving Finite Element method for the solution of time-dependent partial diierential equations is a numerical solution scheme which allows the automatic adaption of the nite element approximation space with time. An analysis of how this method models the steady solutions of a general class of parabolic linear source equations is presented. It is shown that under certain conditions the steady...

In this paper, we study the local property of bounded hyperconvex domains Ω which we can approximative each plurisubharmonic function u ∈ F(Ω) by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.