in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.

Motivated by [B. Han and Q. Mo, Adv. Comp. Math. 18 (2003) 211-245] and [B. Han and Z. Shen, Constr. Approx. 29 (2009) 369-406], we propose dual two-direction frames in dual Sobolev spaces (H(R), H−s(R)), with s > 0. Based on the dual two-direction frames from a pair of two-direction refinable functions, dual multiwavelet frames with symmetry {Ψ(x) := (ψ 1(x), ψ 2(x)) T }`=1 and {Ψ̃(x) : = (ψ̃ 1(...

We survey recent developments in the method of moving frames for infinite-dimensional Lie pseudo-groups. These include a new, direct approach to the construction of invariant Maurer–Cartan forms and the Cartan structure equations for pseudo-groups, and new algorithms, based on constructive commutative algebra, for establishing the structure of their differential invariant algebras.

We propose a new, constructive theory of moving frames for Lie pseudo-group actions on submanifolds. The moving frame provides an effective means for determining complete systems of differential invariants and invariant differential forms, classifying their syzygies and recurrence relations, and solving equivalence and symmetry problems arising in a broad range of applications. Mathematics subj...

Progressive collapse is a condition where local failure of a primary structural component leads to the collapse of neighboring members and the whole structure, consequently. In this paper, the progressive collapse potential of seismically designed steel dual systems with buckling restrained braces is investigated using the alternate path method, and their performances are compared with those of...

Pseudo-BL algebras and pseudo-effect algebras arose in two rather different fields: fuzzy logics and quantum logics. In this paper, by introducing the notion of pseudo-weak MV-effect algebra which is non-commutative generalization of weak MV-effect algebra, we investigate the mutual relationship between pseudo-BL algebras and pseudo-effect algebras. We prove that dual pseudo-BL algebra under ce...

A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton’s result on wavelet tight frames in L(IR) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L(IR) are suggested. Finally examples of smooth wavelet tight frames in L(IR) and H(IR) are provided. In...