Perturbations of Generalized Frames in a Hilbert Space

In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.

FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient conditions for the finite extensions of generalizedBessel sequences to generalized frames or tight generalized frames are provided, and everyresult is illustrated by the corresponding example.

Some Applications of Orthogonal Projections in Generalized Frames

Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.

Generalized Frames and Frame Operators

In this paper, we introduce and study the generalized frame in a separableHilbert space H. Using operator-theoretic-methods, we give some conditions for a gen-eralized frame to be a tight frame, a dual frame, or an independent frame in H. We alsoprove some results concerning generalized frame operators.

The Sum of Standard Generalized Frames in Hilbert W^＊-Module

In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.

A Characterization of Generalized Frame MRAs Deriving Orthonormal Wavelets

In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA （GFMRA）. In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets, and show a general approach to the constructions of non-MRA wavelets. Finally we present two examples to illustrate the theory.

A Simplified Approach to Analysis of High-Rise Frame Tube Structures

Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness matrices for beam and column line are derived by using the displacement functions that describe the nodal displacements and displacement transforms. Furthermore, the formulas for the generalized stiffness matrix of generalized strip element and load arrays corresponding to the displacement parameters were developed. It is shown through a series of numerical computation that the nodal angular displacements at the same floor in a generalized strip element are approximately identical. A comparison of the finite element method and the finite strip method shows that the simplified approach not only is accurate, but also reduces the number of basic unknown quantities.

Gravidynamics,spinodynamics and electrodynamics within the framework of gravitational quantum field theory

By noticing the fact that the charged leptons and quarks in the standard model are chirality-based Dirac spinors since their weak interaction violates maximally parity symmetry though they behave as Dirac fermions in electromagnetic interaction,we show that such a chirality-based Dirac spinor possesses not only electric charge gauge symmetry U(1)but also inhomogeneous spin gauge symmetry WS(1,3)=SP(1,3)?W1,3,which reveals the nature of gravity and spacetime.The gravitational force and spin gauge force are governed by the gauge symmetries W1,3and SP(1,3),respectively,and a biframe spacetime with globally fiat Minkowski spacetime as base spacetime and locally fiat gravigauge spacetime as a fiber is described by the gravigauge field through emergent non-commutative geometry.The gauge-geometry duality and renormalizability in gravitational quantum field theory(GQFT)are carefully discussed.A detailed analysis and systematic investigation on gravidynamics and spinodynamics as well as electrodynamics are carried out within the framework of GQFT.A full discussion on the generalized Dirac equation and Maxwell equation as well as Einstein equation and spin gauge equation is made in biframe spacetime.New effects of gravidynamics as extension of general relativity are particularly analyzed.All dynamic equations of basic fields are demonstrated to preserve the spin gauge covariance and general coordinate covariance due to the spin gauge symmetry and emergent general linear group symmetry GL(1,3,R),so they hold naturally in any spinning reference frame and motional reference frame.

K-fusion Frames and the Corresponding Generators for Unitary Systems

Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of closed subspaces and weights to be a K-fusion frame are obtained, and operators preserving K-fusion frames are discussed. In particular, we are interested in the K-fusion frames with the structure of unitary systems. Given a unitary system which has a complete wandering subspace, we give a necessary and sufficient condition for a closed subspace to be a K-fusion frame generator.

Near generalized balanced tournament designs with block sizes 4 and 5

A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.