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...

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

In this paper, we give a fixed point theorem for $(psi,varphi)$-weakly contractive mappings in complete $b$-metric spaces. We also give a common fixed point theorem for such mappings in complete $b$-metric spaces via altering functions. The given results generalize two known results in the setting of metric spaces. Two examples are given to verify the given results.

In this paper is introduced a new type of generalization of metric spaces called $S_b$ metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem.

In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.

in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...