In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identificat...In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogonal Daubechies families of wavelets are considered and their filters are derived. In particular, the Biorthogonal wavelets Bior3.5, Bior3.9 and Bior6.8 are examined and the zeros distribution of their polynomials associated filters are located. We also examine the locations of these zeros of the filters associated with the two orthogonal wavelets db6 and db8.展开更多
The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavel...The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.展开更多
Applying the theorems of Mobius inverse and Dirichlet inverse, a general algorithm to obtain biorthogonal functions based on generalized Fourier series analysis is introduced. In the algorithm, the orthogonal function...Applying the theorems of Mobius inverse and Dirichlet inverse, a general algorithm to obtain biorthogonal functions based on generalized Fourier series analysis is introduced. In the algorithm, the orthogonal function can be not only Fourier or Legendre series, but also can be any one of all orthogonal function systems. These kinds of biorthogonal function sets are used as scramble signals to construct biorthogonal scramble modulation (BOSM) wireless transmission systems. In a BOSM system, the transmitted signal has significant security performance. Several different BOSM and orthogonal systems are compared on aspects of BER performance and spectrum efficiency, simulation results show that the BOSM systems based on Chebyshev polynomial and Legendre polynomial are better than BOSM system based on Fourier series, also better than orthogonal MCM and OFDM systems.展开更多
In [1], the author introduced a wavelet multigrid method that used the wavelet transform to define the coarse grid, interpolation, and restriction operators for the multigrid method. In this paper, we modify the metho...In [1], the author introduced a wavelet multigrid method that used the wavelet transform to define the coarse grid, interpolation, and restriction operators for the multigrid method. In this paper, we modify the method by using symmetric biorthogonal wavelet transforms to define the requisite operators. Numerical examples are presented to demonstrate the effectiveness of the modified wavelet multigrid method for diffusion problems with highly oscillatory coefficients, as well as for advection-diffusion equations in which the advection is moderately dominant.展开更多
This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The pr...This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.展开更多
The duality solution for elasticity and the biorthogonality relationship have been well researched. Now the couple stress theory becomes a new research spot but there is few research for the biorthogonality relationsh...The duality solution for elasticity and the biorthogonality relationship have been well researched. Now the couple stress theory becomes a new research spot but there is few research for the biorthogonality relationship for couple stress theory comparing to classical elasticity. A new state vector is presented for three dimensional couple stress problems of prismatic structures. A new biorthogonality relation- ship of couple stress is discovered. The dual partial differential equations of couple stress problem are derived by the new state vector. By two important identical equations the new biorthogonality rela- tionship is proved based on the method of separation of variables. The symplectic orthogonality rela- tionship to three dimensional couple stress theory may be decomposed into two independently and symmetrically orthogonality relationships. The new biorthogonality relationship includes the symplec- tic orthogonality relationship. The biorthogonality relationship of couple stress may also be degener- ated into the theory of elasticity. The new state vector and biorthogonality relationship provide theo- retic foundation for the research on the schemes of separation of variables and eigenfunction expan- sion of couple stress theory.展开更多
Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal mul...Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form (?)(x)=(?)a(α)(?)(Mx-α),x∈R<sup>s</sup>, where the vector of functions(?)=((?)<sub>1</sub>,...,(?)<sub>r</sub>)<sup>T</sup> is in(L<sub>2</sub>(R<sup>s</sup>))<sup>r</sup>,a=:(a(α))<sub>α∈Z<sup>s</sup></sub>is a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that lim<sub>n→∞</sub>M<sup>-n</sup>=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.展开更多
We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian tra...We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.展开更多
Due to the particularity of the seismic data, they must be treated by lossless compression algorithm in some cases. In the paper, based on the integer wavelet transform, the lossless compression algorithm is studied. ...Due to the particularity of the seismic data, they must be treated by lossless compression algorithm in some cases. In the paper, based on the integer wavelet transform, the lossless compression algorithm is studied. Comparing with the traditional algorithm, it can better improve the compression rate. CDF (2, n) biorthogonal wavelet family can lead to better compression ratio than other CDF family, SWE and CRF, which is owe to its capability in can- celing data redundancies and focusing data characteristics. CDF (2, n) family is suitable as the wavelet function of the lossless compression seismic data.展开更多
In this paper, algorithms of constructing wavelet filters based on genetic algorithm are studied with emphasis on how to construct the optimal wavelet filters used to compress a given image, due to efficient coding of...In this paper, algorithms of constructing wavelet filters based on genetic algorithm are studied with emphasis on how to construct the optimal wavelet filters used to compress a given image, due to efficient coding of the chromosome and the fitness function, and due to the global optimization algorithm, this method turns out to be perfect for the compression of the images.展开更多
In this paper we have proposed an object tracking method using Dual Tree Complex Wavelet Transform (DTCxWT). The proposed method is capable of tracking the moving object in video sequences. The object is assumed to be...In this paper we have proposed an object tracking method using Dual Tree Complex Wavelet Transform (DTCxWT). The proposed method is capable of tracking the moving object in video sequences. The object is assumed to be deform-able under limit i.e. it may change its shape from one frame to another. The basic idea in the proposed method is to decompose the image into two components: a two dimensional motion and a two dimensional shape change. The motion component is factored out while the shape is explicitly represented by storing a sequence of two dimensional models. Each model corresponds to each image frame. The proposed method performs well when the change in the shape in the consecutive frames is small however the 2-D motion in consecutive frames may be large. The proposed algorithm is capable of handling the partial as well as full occlusion of the object.展开更多
Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length bior...Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.展开更多
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(Rs). Suppose ψ = (ψ1, . . . , ψr)T and ψ = ( ψ1, . . . , ψr)T are two compactly supported vector...In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(Rs). Suppose ψ = (ψ1, . . . , ψr)T and ψ = ( ψ1, . . . , ψr)T are two compactly supported vectors of functions in the Sobolev space (Hμ(Rs))r for some μ > 0. We provide a characterization for the sequences {ψjk : = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jk : = 1, . . . , r, j ∈ Z, k ∈ Zs} to form two Riesz sequences for L2(Rs), where ψjk = mj/2ψ (M j ·k) and ψjk = mj/2 ψ (M j ·k), M is an s × s integer matrix such that limn→∞ Mn = 0 and m = |detM|. Furthermore, let = (1, . . . , r)T and = ( 1, . . . , r)T be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, a and M, where a and a are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1, . . . , ψνr)T and ψν = ( ψν1, . . . , ψ?νr)T , ν = 1, . . . , m 1 such that two sequences {ψjνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} form two Riesz multiwavelet bases for L2(Rs). The bracket product [f, g] of two vectors of functions f, g in (L2(Rs))r is an indispensable tool for our characterization.展开更多
Protein chemical modifications are important tools for elucidating chemical and biological functions of proteins.Several strategies have been developed to implement these modifications,including enzymatic tailoring re...Protein chemical modifications are important tools for elucidating chemical and biological functions of proteins.Several strategies have been developed to implement these modifications,including enzymatic tailoring reactions,unnatural amino acid incorporation using the expanded genetic codes,and recognition-driven transformations.These technologies have been applied in metalloenzyme studies,specifically in dissecting their mechanisms,improving their enzymatic activities,and creating artificial enzymes with non-natural activities.Herein,we summarize some of the recent efforts in these areas with an emphasis on a few metalloenzyme case studies.展开更多
Cysteine chemistry provides a low cost and convenient way for site-specific protein modification.However,recombinant expression of disulfide bonding containing protein with unpaired cysteine is technically challenging...Cysteine chemistry provides a low cost and convenient way for site-specific protein modification.However,recombinant expression of disulfide bonding containing protein with unpaired cysteine is technically challenging and the resulting protein often suffers from significantly reduced yield and activity.Here we used genetic code expansion technique to introduce a surface exposed self-paired dithiol functional group into proteins,which can be selectively reduced to afford active thiols.Two compounds containing self-paired disulfides were synthesized,and their genetic incorporations were validated using green fluorescent proteins(GFP).The compatibility of these self-paired di-thiols with natural disulfide bond was demonstrated using antibody fragment to afford site-specifically labeled antibody.This work provides another valuable building block into the chemical tool-box for site-specific labeling of proteins containing internal disulfides.展开更多
文摘In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogonal Daubechies families of wavelets are considered and their filters are derived. In particular, the Biorthogonal wavelets Bior3.5, Bior3.9 and Bior6.8 are examined and the zeros distribution of their polynomials associated filters are located. We also examine the locations of these zeros of the filters associated with the two orthogonal wavelets db6 and db8.
基金Supported by Natural Science Foundation of Henan Province(0511013500)
文摘The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.
文摘Applying the theorems of Mobius inverse and Dirichlet inverse, a general algorithm to obtain biorthogonal functions based on generalized Fourier series analysis is introduced. In the algorithm, the orthogonal function can be not only Fourier or Legendre series, but also can be any one of all orthogonal function systems. These kinds of biorthogonal function sets are used as scramble signals to construct biorthogonal scramble modulation (BOSM) wireless transmission systems. In a BOSM system, the transmitted signal has significant security performance. Several different BOSM and orthogonal systems are compared on aspects of BER performance and spectrum efficiency, simulation results show that the BOSM systems based on Chebyshev polynomial and Legendre polynomial are better than BOSM system based on Fourier series, also better than orthogonal MCM and OFDM systems.
文摘In [1], the author introduced a wavelet multigrid method that used the wavelet transform to define the coarse grid, interpolation, and restriction operators for the multigrid method. In this paper, we modify the method by using symmetric biorthogonal wavelet transforms to define the requisite operators. Numerical examples are presented to demonstrate the effectiveness of the modified wavelet multigrid method for diffusion problems with highly oscillatory coefficients, as well as for advection-diffusion equations in which the advection is moderately dominant.
文摘This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.
基金Supported by the National Natural Science Foundation of China (Grant No. 50778071)the Hunan Provincial Natural Science Foundation of China (Grant No. 08JJ3011)the Research Committee of City University of Hong Kong (Grant No. 7002315)
文摘The duality solution for elasticity and the biorthogonality relationship have been well researched. Now the couple stress theory becomes a new research spot but there is few research for the biorthogonality relationship for couple stress theory comparing to classical elasticity. A new state vector is presented for three dimensional couple stress problems of prismatic structures. A new biorthogonality relation- ship of couple stress is discovered. The dual partial differential equations of couple stress problem are derived by the new state vector. By two important identical equations the new biorthogonality rela- tionship is proved based on the method of separation of variables. The symplectic orthogonality rela- tionship to three dimensional couple stress theory may be decomposed into two independently and symmetrically orthogonality relationships. The new biorthogonality relationship includes the symplec- tic orthogonality relationship. The biorthogonality relationship of couple stress may also be degener- ated into the theory of elasticity. The new state vector and biorthogonality relationship provide theo- retic foundation for the research on the schemes of separation of variables and eigenfunction expan- sion of couple stress theory.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10071071 and 10471123)the Mathematical Tianyuan Foundation of the National Natural Science Foundation of China NSF(Grant No.10526036)China Postdoctoral Science Foundation(Grant No.20060391063)
文摘Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form (?)(x)=(?)a(α)(?)(Mx-α),x∈R<sup>s</sup>, where the vector of functions(?)=((?)<sub>1</sub>,...,(?)<sub>r</sub>)<sup>T</sup> is in(L<sub>2</sub>(R<sup>s</sup>))<sup>r</sup>,a=:(a(α))<sub>α∈Z<sup>s</sup></sub>is a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that lim<sub>n→∞</sub>M<sup>-n</sup>=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.
基金G.S.is appreciative of support from the NSFC under the Grant Nos.11704186 and 11874220S.P.K is appreciative of support by the National Natural Science Foundation of China under Grant Nos.11674026,11974053,and 12174030.
文摘We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.
文摘Due to the particularity of the seismic data, they must be treated by lossless compression algorithm in some cases. In the paper, based on the integer wavelet transform, the lossless compression algorithm is studied. Comparing with the traditional algorithm, it can better improve the compression rate. CDF (2, n) biorthogonal wavelet family can lead to better compression ratio than other CDF family, SWE and CRF, which is owe to its capability in can- celing data redundancies and focusing data characteristics. CDF (2, n) family is suitable as the wavelet function of the lossless compression seismic data.
基金Supported by the Natural Science Foundation of Education of Hunan Province(21010506)
文摘In this paper, algorithms of constructing wavelet filters based on genetic algorithm are studied with emphasis on how to construct the optimal wavelet filters used to compress a given image, due to efficient coding of the chromosome and the fitness function, and due to the global optimization algorithm, this method turns out to be perfect for the compression of the images.
文摘In this paper we have proposed an object tracking method using Dual Tree Complex Wavelet Transform (DTCxWT). The proposed method is capable of tracking the moving object in video sequences. The object is assumed to be deform-able under limit i.e. it may change its shape from one frame to another. The basic idea in the proposed method is to decompose the image into two components: a two dimensional motion and a two dimensional shape change. The motion component is factored out while the shape is explicitly represented by storing a sequence of two dimensional models. Each model corresponds to each image frame. The proposed method performs well when the change in the shape in the consecutive frames is small however the 2-D motion in consecutive frames may be large. The proposed algorithm is capable of handling the partial as well as full occlusion of the object.
文摘Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123)
文摘In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(Rs). Suppose ψ = (ψ1, . . . , ψr)T and ψ = ( ψ1, . . . , ψr)T are two compactly supported vectors of functions in the Sobolev space (Hμ(Rs))r for some μ > 0. We provide a characterization for the sequences {ψjk : = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jk : = 1, . . . , r, j ∈ Z, k ∈ Zs} to form two Riesz sequences for L2(Rs), where ψjk = mj/2ψ (M j ·k) and ψjk = mj/2 ψ (M j ·k), M is an s × s integer matrix such that limn→∞ Mn = 0 and m = |detM|. Furthermore, let = (1, . . . , r)T and = ( 1, . . . , r)T be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, a and M, where a and a are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1, . . . , ψνr)T and ψν = ( ψν1, . . . , ψ?νr)T , ν = 1, . . . , m 1 such that two sequences {ψjνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} form two Riesz multiwavelet bases for L2(Rs). The bracket product [f, g] of two vectors of functions f, g in (L2(Rs))r is an indispensable tool for our characterization.
基金This research was partially supported by National Science Foundation(CHE-2004109 to P.L.)。
文摘Protein chemical modifications are important tools for elucidating chemical and biological functions of proteins.Several strategies have been developed to implement these modifications,including enzymatic tailoring reactions,unnatural amino acid incorporation using the expanded genetic codes,and recognition-driven transformations.These technologies have been applied in metalloenzyme studies,specifically in dissecting their mechanisms,improving their enzymatic activities,and creating artificial enzymes with non-natural activities.Herein,we summarize some of the recent efforts in these areas with an emphasis on a few metalloenzyme case studies.
基金financially supported by National Key Research and Development Program of China (No.2016YFA0201400)the National Natural Science Foundation of China (No.21778005)+1 种基金Peking University Health Science Center (Nos.BMU20160537 andBMU2017QQ006)the Youth Thousand-Talents Program of China for support
文摘Cysteine chemistry provides a low cost and convenient way for site-specific protein modification.However,recombinant expression of disulfide bonding containing protein with unpaired cysteine is technically challenging and the resulting protein often suffers from significantly reduced yield and activity.Here we used genetic code expansion technique to introduce a surface exposed self-paired dithiol functional group into proteins,which can be selectively reduced to afford active thiols.Two compounds containing self-paired disulfides were synthesized,and their genetic incorporations were validated using green fluorescent proteins(GFP).The compatibility of these self-paired di-thiols with natural disulfide bond was demonstrated using antibody fragment to afford site-specifically labeled antibody.This work provides another valuable building block into the chemical tool-box for site-specific labeling of proteins containing internal disulfides.