Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...

We consider a damped/driven nonlinear Schrödinger equation in $$\mathbb {R}^n$$ , where n is arbitrary, $${\mathbb {E}}u_t-\nu \Delta u+i|u|^2u=\sqrt{\nu }\eta (t,x), \quad \nu >0,$$ under odd periodic boundary conditions. Here $$\eta (t,x)$$ random force which white time and smooth space. It known that the Sobolev norms of solutions satisfy $$ \Vert u(t)\Vert _m^2 \le C\nu ^{-m}, uniformly $$t...

Abstract Romyar Sharifi has constructed a map $\varpi _M$ from the first homology of modular curve $X_1(M)$ to K -group $K_2(\operatorname {\mathrm {\mathbf {Z}}}[\zeta _M+\zeta _M^{-1}, \frac {1}{M}]) \otimes \operatorname {Z}}}[1/2]$ , where $\zeta is primitive M th root unity. conjectured that annihilated by certain Eisenstein ideal. Fukaya and Kato proved this conjecture after tensoring wit...

The deoxynucleotide fragment d(GpGpCpCpGpGpCpC) was synthesized and crystallized, and its three-dimensional structure was determined by x-ray diffraction techniques to a resolution of 2.25 A. The molecule forms a right-handed double helix in which the two base pairs at either end of the molecule are in the conventional A-DNA conformation, while the central four base pairs have a modified form i...

Abstract We show that a real-valued function f in the shift-invariant space generated by totally positive of Gaussian type is uniquely determined, up to sign, its absolute values $$\{|f(\lambda )|: \lambda \in \Lambda \}$$ { | f ( λ )<...

In this note, we investigate a kind of double centralizer property for general linear supergroups. For the super space $V=\mathbb{K}^{m\mid n}$ over an algebraically closed field $\mathbb{K}$ whose characteristic is not equal to $2$, consider its $\mathbb{Z}_2$-homogeneous one-dimensional extension $\underline V=V\oplus\mathbb{K}v$, and natural action supergroup $\tilde G:=\text{GL}(V)\times \t...