In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎. 

This paper discusses techniques for embedding and de-embedding the characteristics of two-port devices described by scattering parameters at microwave frequencies. Such techniques have wide applications in areas such as the measurement of the parameters of a semiconductor device mounted in a fixture, removal of the effects of cables, adapters, etc. and network analyzer calibration using variant...

Graph embedding techniques for bounding eigenvalues of associated matrices have a wide range of applications. The bounds produced by these techniques are not in general tight, however, and may be off by a log n factor for some graphs. Guattery and Miller showed that, by adding edge directions to the graph representation, they could construct an embedding called the current flow embedding, which...