For a given bounded positive (semidefinite) linear operator $A$ on complex Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$, we consider the semi-Hilbertian \cdot\rangle_A \big)$ where ${\langle x, y\rangle}_A := Ax, y\rangle$ for every $x, y\in\mathcal{H}$. The $A$-numerical radius of an $A$-bounded $T$ $\mathcal{H}$ is by\[\omega_A(T)=\sup\Big\{\big|{\langle Tx, x\rangle}_A...

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 \...

We investigate the large-time asymptotics of solution for Cauchy problem nonlocal focusing modified Kortweg-de Vries (MKdV) equation with step-like initial data, i.e., $u_0(x)\rightarrow 0$ as $x\rightarrow-\infty$, A$ $x\rightarrow+\infty$,where $A$ is an arbitrary positive real number. firstly develop direct scattering theory to establish basic Riemann-Hilbert (RH) associated data. Thanks sym...

We propose definitions of complex manifolds $\mathcal{P}_M(X,m,n)$ that could potentially be used to construct the symplectic Khovanov homology $n$-stranded links in lens spaces. The are defined as moduli spaces Hecke modifications rank 2 parabolic bundles over an elliptic curve $X$. To characterize these spaces, we describe all possible vector $X$, and use results define a canonical open embed...

Given a topological property $$\mathcal{P}$$ , space $$X$$ is called star- if for any open cover $$\mathcal{U}$$ of the there exists set $$Y\subseteq X$$ with such that $$St(Y,\mathcal{U})=X$$ ; $$Y$$ star kernel . In this paper, we introduce and study spaces Menger, is, determined by Menger spaces, denoted $$S_{\rm fin}(\mathcal{O},\mathcal{O})$$ Some examples are given to show relationship so...

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...

We show that tilting modules for quantum groups over local Noetherian domains of characteristic 0 exist and the indecomposable are parametrized by their highest weight. For this, we introduce a model category X = A ( R ) ${\mathcal {X}}={\mathcal {X}}_{\mathcal A}(R)$ associated with Z [ v , − 1 ] ${\mathbb {Z}}[v,v^{-1}]$ -domain A}$ root system $R$ . if is $\hskip.001pt 0$ contains all U $U_{...

We study the decay behaviors of fully bottom tetraquark states within diquark-antidiquark picture and calculate their relative branching ratios through Fierz rearrangement. Our results suggest that $C=+$ can be searched for in ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\mathrm{\ensuremath{\Upsilon}}(1S)$ ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\mathrm{\ensuremat...

Given a domain $\Omega \subseteq \mathbb{R}^2$, let $\mathcal{D}(\Omega,x,R)$ be the number of lattice points from $\mathbb{Z}^2$ in $R\Omega-x$, for $R \ge 1$ and $x\in \mathbb{T}^2$, minus area $R\Omega$: $$\mathcal{D}(\Omega,x,R) = \# \{ (j,k) \in \mathbb{Z}^2 :(j-x_1,k-x_2) R\Omega \} - R^2|\Omega|.$$ We call $\int_{\mathbb{T}^2}|\mathcal{D}(\Omega,x,R)|^pdx$ $p$-th moment discrepancy funct...