We generalize Cauchy’s celebrated theorem on the global rigidity of convex polyhedra in Euclidean 3-space E to the context of circle polyhedra in the 2-sphere S. We prove that any two convex and bounded non-unitary c-polyhedra with Möbiuscongruent faces that are consistently oriented are Möbius-congruent. Our result implies the global rigidity of convex inversive distance circle packings as wel...

in this paper, we introduce the notion of derivation on krasner hyperrings as follows: the function d : r  r isa derivation on a krasner hyperring r if for all , , ry x  ) ( ) ( = ) ( y d x d y x d   andd (x  y) d (x)  y  x  d ( y). then, we investigate some fundamental properties of derivation on krasnerhyperings and prime krasner hyperrings. also, we introduce differential krasner hy...

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During World War I there was much lamentation over the "defects of the draft," and the word "shocking" was in frequent use with reference to the condition of a large proportion of men of military age. When, more recently, it became necessary again for society to interpose a shield of human lives between itself and disaster, its cerebral cells once more became agitated over the report that its y...

$!!!!$ In this paper, the notion of fuzzy $!$ Krasner $!(m, n)$-hyperrings($!F^{(m, n)}!$-hyperrings) by using the notion of$F^m$-hyperoperations and $F^n$-operations is introduced and somerelated properties are investigated. In this regards,relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner$(m, n)$-hyperrings are considered. We shall prove that everyKrasner $F^{(m, n)}$-hyperrin...

We consider the inequality $f \geqslant f\star f$ for real integrable functions on $d$ dimensional Euclidean space where $f\star denotes convolution of $f$ with itself. show that all such are non-negative, which is not case same in $L^p$ any $1 < p \leqslant 2$, defined. also solutions satisfy $\int f(x){\rm d}x \tfrac12$. Moreover, if = \tfrac12$, then must decay fairly slowly: |x| \infty$, an...

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