In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

the issues that arise in this articles are the causes and the bases of social - and sexual - devience according to a sociological point of view. then a search through a number of 350 files of sexual - crimes in babol, declares the causes on a sociological point of view, cultural transmission & contrast theory. in assessment during this research regarding age, sex & occupation as the main criter...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Let $\mathbb {N}=\{0,1,2,\ldots \}$ and $A\subset \mathbb {N}$. $h\geq 2$ let $r_h(A,n)=\sharp \{ (a_1,\ldots ,a_h) \in A^{h}: a_1+\cdots +a_h=n\}.$ The set $A$ is called an asymptotic basis of order $h$ if $r_h(A,n)\geq 1$ for all sufficiently la

Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...

Given a positive integer M and real number x∈(0,1], we call q∈(1,M+1] univoque simply normal base of x if there exists unique sequence (di)∈{0,1,…,M}N such that x=∑i=1∞diq−i. Similarly, is called irregular x=∑i=1∞diq−i the (di) has no digit frequency. Let USN(x) UIr(x) be sets bases x, respectively. In this paper show for any x∈(0,1] both have full Hausdorff dimension. Furthermore, given finite...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...