Let G be a linear algebraic group acting linearly on vector space (or more generally, an affine variety) V, and let k[V]G the corresponding algebra of invariant polynomial functions. A separating set S⊆k[V]G is polynomials with property that for all v,w∈V, if there exists f∈k[V]G $v$ $w$, then f∈S $w$. In this article, we consider action G=GL2⁡(C) C-vector M2n n-tuples 2×2 matrices by simultane...

We show that if E is an arbitrary acyclic graph then the Leavitt path algebra LK(E) is locally K-matricial; that is, LK(E) is the direct union of subalgebras, each isomorphic to a finite direct sum of finite matrix rings over the fieldK. As a consequence we get our main result, in which we show that the following conditions are equivalent for an arbitrary graph E: (1) LK (E) is von Neumann regu...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

In this paper, we are interested in finding an approximate solution $ \hat{\mathcal{X}} of the tensor least-squares minimization problem$ \min_{\mathcal{X}}\left\|\mathcal{X}\times_1A^{(1)}\times_2A^{(2)}\times_3\cdots\times_NA^{(N)}-\mathcal{G}\right\|$, where \mathcal{G}\in \mathbb{R}^{J_1\times J_2\times \cdots \times J_N}$ and A^{(i)}\in \mathbb{R}^{J_i\times I_i} ($ i=1,\ldots,N $) known \...

It is well-known that the sum of two $z$-ideals in $C(X)$ is either $C(X)$ or a $z$-ideal. The main aim of this paper is to study the sum of strongly $z$-ideals in ${mathcal{R}} L$, the ring of real-valued continuous functions on a frame $L$. For every ideal $I$ in ${mathcal{R}} L$, we introduce the biggest strongly $z$-ideal included in $I$ and the smallest strongly $z$-ideal containing ...

background and aims: the ectodomain of matrix protein of influenza virus is a weak immunogen that is highly conserved among all subtypes of influenza a virus. tandem repeats of these genes along with linker were used to enhance immunogenicity of m2e protein and so it can be served as a universal vaccine in both humans and livestock. materials and methods: in this study, the sequences of extra-d...