We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

This study digs out some new algebraic properties of an Osborn loop that will help in the future to unveil the mystery behind the middle inner mappings T(x) of an Osborn loop. These new algebraic properties, will open our eyes more to the study of Osborn loops like CC-loops which has received a tremendious attention in this 21st and VD-loops whose study is yet to be explored. In this study, som...

With any connected affine algebraic group G over an algebraically closed field K of characteristic zero, we associate another connected affine algebraic group D over K and a finite central subgroup F of D such that, up to isomorphism of algebraic groups, affine algebraic groups over K abstractly isomorphic to G are precisely of the form D/α(F )×Ks +, where α is an abstract automorphism of D and...

The acoustic properties of a three-dimensional sonic crystal made of square-rod rigid scatterers incorporating a periodic arrangement of quarter wavelength resonators are theoretically and experimentally reported in this work. The periodicity of the system produces Bragg band gaps that can be tuned in frequency by modifying the orientation of the square-rod scatterers with respect to the incide...

Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theore...