Abstract Let $k_0$ be a field of characteristic $0$ with algebraic closure $k$. $G$ connected reductive $k$-group, and let $Y$ spherical variety over $k$ (a homogeneous space or embedding). $G_0$ $k_0$-model ($k_0$-form) $G$. We give necessary sufficient conditions for the existence $G_0$-equivariant $Y$.

In this paper, we describe the Grothendieck group $$K_0(V)$$ of an absolute matrix order unit space V. For purpose, discuss direct limit spaces. We show that $$K_0$$ is a functor from category spaces with morphisms as unital completely $$\vert \cdot \vert$$ -preserving maps to abelian groups. study structure in and prove under certain condition, ordered group. also additive on orthogonal maps.

Let $$k_0$$ be a field of characteristic $$p>0$$ and $$k=k_0(t)$$ , where t is transcendental over . We give an example smooth connected unipotent k-group G such that G(F)/R non-commutative for some finite separable extension F containing k.

Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(l...

‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...

inthis paper, the main aim is to introduce the class $mathcal{u}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p$ and $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p^0$, andinvestigate the properties of the mappings in these classes. first,we give a sufficient condition for mappings to be in $mathcal{u}_p(l...

We study the {\it CP}-averaged branching fractions and CP}-violating asymmetries in pure annihilation decays of $B_s^0 \to a_0^+ a_0^-$ $B_d^0 K_0^{*+} K_0^{*-}$, where $a_0\;[K_0^*]$ denotes scalar $a_0(980)$ $a_0(1450)$ [$K_0^*(800) ( {\rm or}\; \kappa)$ $K_0^*(1430)$], with perturbative QCD factorization approach under assumption two-quark structure for $a_0$ $K_0^*$ states. The numerical re...

Let $k \,=\, \mathbb{Q}(\sqrt[5]{n},\zeta_5)$, where $n$ is a positive integer, $5^{th}$ power-free, whose $5-$class group isomorphic to $\mathbb{Z}/5\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$. $k_0\,=\,\mathbb{Q}(\zeta_5)$ be the cyclotomic field containing primitive root of unity $\zeta_5$. $C_{k,5}^{(\sigma)}$ ambiguous classes under action $Gal(k/k_0)$ = $<\sigma>$. The aim this paper determin...

We investigate the relations between Grothendieck group of coherent modules an algebraic variety and its Chow cycles modulo rational equivalence. Those are in essence torsion phenomena, which we attempt to control by considering action Adams operations on Brown-Gersten-Quillen spectral sequence related objects, such as connective K_0-theory. provide elementary arguments whenever possible. As ap...

We have evaluated the strong decays of $K_0^*(1950)$ and $K_0^*(2130)$ within $^3P_0$ model, by employing meson wave functions from relativized quark model. By comparing with experimental measurements, could be assigned as $K_0^*(3^3P_0)$, while seems like an exotic state, because its width can not reasonably reproduced also predict that $K_0^*(2^3P_0)$ state has a mass about $1811$ MeV $656$ M...