in this paper, a fuzzy version of the analytic form of hahn-banachextension theorem is given. as application, the hahn-banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

LATERAL SAFE is a subproject of the PREVENT Integrated Project cofunded by the European Commission under the 6th Framework Programme. LATERAL SAFE introduces a cluster of safety applications of the future vehicles in order to prevent lateral/rear related accidents and assist the driver in adverse or low visibility conditions and blind spot areas. LATERAL SAFE applications include a lateral and ...

We study the $S$-matrix and inclusive cross-section for general dressed states in quantum electrodynamics. obtain an infrared factorization formula of elements states. It enables us to what lead infrared-safe elements. The condition can be interpreted as memory effect which is nothing but conservation law asymptotic symmetry. derive generalized soft photon theorem also compute using necessary u...

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

The proposed theorem in this paper is indicative of a kind of duality in the propagation of waves in the dual media of and in the spherical structures. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, this theorem holds true in case of any change in any of these conditions. Theorem: Consider a plane wave incident on a multilayered spheric...

We think that the approach to safe system extension proposed in this paper presents many advantages. From a software engineering perspective, the architectural principles presented in Section 3 considerably simplify the task of building and extending theorem provers safely. The concept of OMRS is a rst small step towards complex reasoning systems built by composing existing modules, or extended...