In 1988 M. Fellows conjectured that if a finite, connected graph admits a finite planar emulator, then it admits a finite planar cover. We construct a finite planar emulator for K4,5 − 4K2. D. Archdeacon [2] showed that K4,5 − 4K2 does not admit a finite planar cover; thus K4,5 − 4K2 provides a counterexample to Fellows’ Conjecture. It is known that S. Negami’s Planar Cover Conjecture is true i...

In 1988 M. Fellows conjectured that if a finite, connected graph admits a finite planar emulator, then it admits a finite planar cover. We construct a finite planar emulator for K4,5 − 4K2. D. Archdeacon [2] showed that K4,5 − 4K2 does not admit a finite planar cover; thus K4,5 − 4K2 provides a counterexample to Fellows’ Conjecture. It is known that S. Negami’s Planar Cover Conjecture is true i...

Recently, Doroudiani and Karimipour [Phys. Rev. A 102 012427(2020)] proposed the notation of planar maximally entangled states which are a wider class multipartite than absolutely states. There they presented their constructions in systems but number particles is restricted to be even. Here, we first solve remaining cases, i.e., on with odd particles. In addition, generalized PME k-uniform whos...

The crystal structure of the title Schiff base complex is obtained by single-crystal X-ray diffraction data.The solid state structure determination reveals that the coordination geometry around the copper(II) center istetrahedrally distorted square-planar. The crystal packing shows one dimensional infinite chains which arisesfrom the intermolecular interaction and stabilize the crystal packing.

for the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. when the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. in this paper we will consider the polynomial planar vector fields ...

In this paper we propose an accurate and fast numerical method to obtain scattering fields from lossy dispersive inhomogeneous planar layers for both TE and TM polarizations. A new method is introduced to analyze lossy Inhomogeneous Planar Layers. In this method by applying spline based Galerkin’s method of moment to scalar wave equation and imposing boundary conditions we obtain reflection and...