COMPACTLY SUPPORTED NON-TENSOR PRODUCT FORM TWO-DIMENSION WAVELET FINITE ELEMENT

Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.

COMPACTLY SUPPORTED BOX-SPLINE WAVELETS

A general procedure for constructing multivariate non-tensor-product wavelets that gen- erate an orthogonal decomposition of L^2(R~),s≥ 1,is described and applied to yield explicit formulas for compactly supported spline-wavelets based on the multiresolution analysis of L^2(R^s),1≤s≤3,generated by any box spline whose direction set constitutes a unimodular matrix.In particular,when univariate cardinal B-splines are considered,the minimally sup- ported cardinal spline-wavelets of Chui and Wang are recovered.A refined computational scheme for the orthogonalization of spaces with compactly supported wavelets is given.A recursive approximation scheme for“truncated”decomposition sequences is developed and a sharp error bound is included.A condition on the symmetry or anti-symmetry of the wavelets is applied to yield symmetric box-spline wavelets.

Construction of Compactly Supported Bivariate Orthogonal Wavelets

For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associated wavelets can be constructed explicitly.

High Density 3D Carbon Tube Nanoarray Electrode Boosting the Capacitance of Filter Capacitor

Electric double-layer capacitors(EDLCs)with fast frequency response are regarded as small-scale alternatives to the commercial bulky aluminum electrolytic capacitors.Creating carbon-based nanoarray electrodes with precise alignment and smooth ion channels is crucial for enhancing EDLCs’performance.However,controlling the density of macropore-dominated nanoarray electrodes poses challenges in boosting the capacitance of line-filtering EDLCs.Herein,a simple technique to finely adjust the vertical-pore diameter and inter-spacing in three-dimensional nanoporous anodic aluminum oxide(3D-AAO)template is achieved,and 3D compactly arranged carbon tube(3D-CACT)nanoarrays are created as electrodes for symmetrical EDLCs using nanoporous 3D-AAO template-assisted chemical vapor deposition of carbon.The 3D-CACT electrodes demonstrate a high surface area of 253.0 m^(2) g^(−1),a D/G band intensity ratio of 0.94,and a C/O atomic ratio of 8.As a result,the high-density 3D-CT nanoarray-based sandwich-type EDLCs demonstrate a record high specific areal capacitance of 3.23 mF cm^(-2) at 120 Hz and exceptional fast frequency response due to the vertically aligned and highly ordered nanoarray of closely packed CT units.The 3D-CT nanoarray electrode-based EDLCs could serve as line filters in integrated circuits,aiding power system miniaturization.

Homological Epimorphisms, Compactly Generated t-Structures and Gorenstein-Projective Modules

The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i*preserves compact objects.As a consequence,given a ladder(T′,T,T′′,T,T′) of height 2,then the certain BBD-induction of compactly generated t-structures is compactly generated.The authors apply them to the recollements induced by homological ring epimorphisms.This is the first part of their work.Given a recollement(D(B-Mod),D(A-Mod),D(C-Mod),i*,i_*,i~!,j!,j*,j_*) induced by a homological ring epimorphism,the last aim of this work is to show that if A is Gorenstein,AB has finite projective dimension and j! restricts to D^b(C-mod),then this recollement induces an unbounded ladder(B-Gproj,A-Gproj,C-Gproj) of stable categories of finitely generated Gorenstein-projective modules.Some examples are described.

Orthogonal M-band compactly supported interpolating wavelet theory

Recently, 2-band interpolating wavelet transform has attracted much attention. It has the following several features: (i) The wavelet series transform coefficients of a signal in the multiresolution subspace are exactly consistent with its discrete wavelet transform coefficients; (ii) good approximation performance; (iii) efficiency in computation. However orthogonal 2-band compactly supported interpolating wavelet transform is only the first order. In order to overcome this shortcoming, the orthogonal M-band compactly supported interpolating wavelet basis is established. First, the unitary interpolating scaling filters of the lengthL =MK are characterized. Second, a scheme is given to design high-order unitary interpolating scaling filters. Third, a parameterization of the unitary interpolating scaling filters of the lengthL = 4M is made. Fourth, the orthogonal 2-order and 3-order three-band compactly supported interpolating scaling functions are constructed. Finally, the properties of the orthogonal M-band compactly supported interpolating wavelets and the approximation performance of the Mallat projection are discussed. For the smooth signal inL 2(?), the asymptotic formula of the approximation enor of the Mallat projection is obtained, and for the band-limited signal, the quantitative estimate of its upper bounds is given. The results show that the Mallat projection has the same approximation order as the orthogonal projection, and particularly for the orthogonal even number-order M-band compactly supported interpolating scaling function, they have the same approximation performance. The quantitative result also shows that the selection of the initial scale depends on the distribution of the signal frequency and the regularity order of the scaling function. For the given scaling function and signal, using these results one can determine the initial scale and at the same time estimate the initial scaling coefficients without prefiltering according to the error requirement

The Parametrization of Orthonormal Compactly Supported Wavelets and Wave Digital Filter

In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishing moment is obtained by building any QMF pair out of elementary factors of the scatteringmatrix. In addition, the optimization of parameter is also presented. As comparison, some examples about orthonormal compactly supported wavelet that has arbitrary number of vanishing moment and the most number of vanishing moment are given respectively. Then we give the efficient lattice structure to implement the transform.

GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS

The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.

QUASI_EQUILIBRIUM PROBLEMS IN NONCOMPACT GENERALIZED CONVEX SPACES

By applying a new fixed point theorem due to the author, some new equilibrium existence theorems of quasi-equilibrium problems are proved in noncompact generalized convex spaces. These theorems improve and generalize a number of important known results in recent literature.

ALMOST PERIODICITY AND EQUICONTINUITY OF THE TOPOLOGICAL TRANSFORMATION GROUP

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.

EQUILIBIA OF NONCOMPACT GENERALIZED GAMES WITH CORRESPONDENCES WITHOUT OPEN LOWER SECTIONS

The new classes of Fc-correspondences and Fc -majorised correspondenceswithout open lower sections is introduced. Some existence theorems of madximal elements ofthe Fc -correspondences and the Fc-majorized correspondences defined on noncompactset in topological vector spaces are obtained. As applications, some existence theoremsof equilibrium points for one-person games, qualitative games and generalized games withthe Fc -majorized correspondences devined on noncompact strategy sets in topologicalvector spaces are also given. These theorems improve and generalize several known resultsin recent literature.

On the Frame Set for the 3-Spline

This paper investigates the fine structure of the Gabor frame generated by the B-spline B3. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B3 is the subset of all parameters (a,b) ∈R2+ for which the time-frequency shifts of B3 along aZ × bZ form a Gabor frame for L2(R).

Reconfiguration of face expressions based on the discrete capture data of radial basis function interpolation

Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.

Nonempty intersection theorems in topological spaces with applications

In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature.

PARETO EQUILIBRIA OF MULTICRITERIA GAMES WITHOUT COMPACTNESS，CONTINUITY AND CONCAVITY

In this paper.by using a minimax inequality obtained by the author,someexistence theorems of Pareto equilibria for multicriteria games without compactness,continuity and concavity are proved in lope toplogical vector spaces and reflexive Banach spaces.

BOUND STATES OF SCHRODINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

We study the bound states to nonlinear Schrodinger equations with electro magnetic fields ihδψ/δt=（h/i -A（x））^2ψ＋V（x）ψ-K（x）｜ψ｜^p-1ψ=0,on R＋ ×R^N. Let G（x）=[V（x）p＋1/p-1-N/2][K（x）]-2/p-1 and suppose that G（x） has k local minimum points. For h 〉 0 small, we find multi-bump bound states ~bh （x, t） ---- e-iE~/huh （X） with Uh concentrating at the local minimum points of G（x） simultaneously as h ~ O. The potentials V（x） and K（x） are allowed to be either compactly supported or unbounded at infinity.

Coincidence Theorems with Applications to Minimax Inequalities,Section Theorem,Best Approximation and Multiobjective Games in Topological Spaces

Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.

A GLKKM Type Theorem for Noncompact Complete L-Convex Metric Spaces with Applications to Variational Inequalities and Fixed Points

In this paper,a new GLKKM type theorem is established for noncompact complete L-convex metric spaces.As applications,the properties of the solution set of variational in-equalities,intersection point sets,Ky Fan sections and maximal element sets are shown,and a Fan-Browder fixed point theorem is obtained.

A New Ky Fan Matching Theorem in Noncompact L-Convex Spaces with the Application to Systems of General Quasiequilibrium Problems

In this paper, a new Ky Fan matching theorem is established in noncompact L-convex spaces. As applications, a fixed point theorem and equilibrium existence theorems for systems of general quasiequilibrium problems and systems of quasiequilibrium problems in noncompact L-convex spaces are obtained.

On the homotopy category of AC-injective complexes

Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call A C-injective complexes, showing that K（AC-Inj）, the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DG- injective complexes are AC-injective and in fact there is a recollement linking K（AC-Inj） to the usual derived category D（R）. This is based on the author＇s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.