The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which availab...The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected. Then, a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices. The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and auto-correlation with the natural frequency of the plaintext being hidden and homogenized.展开更多
The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical...The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical problems and complex control problems. In this work, the authors try to generate matrices such that： （1） the condition number of these types of matrices is controlled and （2） The algorithm used to generate these matrices preserves their structure.展开更多
We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix...We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.展开更多
The 3D fluorescence discrimination of phytoplankton classes was investigated by SA4 multiwavelet,GHM multiwavelet,and coifman-2(coif2) wavelet analysis.Belonging to 35 genera of 7 major phytoplankton divisions in the ...The 3D fluorescence discrimination of phytoplankton classes was investigated by SA4 multiwavelet,GHM multiwavelet,and coifman-2(coif2) wavelet analysis.Belonging to 35 genera of 7 major phytoplankton divisions in the inshore area of China Sea,Single species cultures of 51 phytoplankton species were employed.The second scale vector (Ca2) of SA4,Ca2 of GHM and the third scale vector (Ca3) of coif2 were selected as feature spectra by Bayesian discriminate analysis (BDA).The reference spectra were obtained via hierarchical cluster analysis (HCA).With average high correct discrimination ratios (CDRs),reference spectra were representative to phytoplankton species.For one-algae samples,the average CDRs were 95.6% at genus level and 86.7% at division level.For the laboratory mixed samples,the average CDRs (one division accounted for 25%,75% or 100% of the total biomass) were 86.6%,91.4% and 100% at division level.Moreover,the average CDRs of the dominant species (accounted for 75%) was 79.8% at genus level.Results for the in situ samples were coincided with the microscopic ones at division level with the relative contents of 54.3%-96.5%.The fluorometric discriminating technique was further tested during the cruise in Bohai Sea recently.展开更多
Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we character...Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we characterize Lie derivations of N when char（F） ≠ 2.展开更多
and uses it imply that application In this paper the author gives a method of constructing characteristic matrices, to determine the Buchstaber invariants of all simple convex 3-polytopes, which each simple convex 3-p...and uses it imply that application In this paper the author gives a method of constructing characteristic matrices, to determine the Buchstaber invariants of all simple convex 3-polytopes, which each simple convex 3-polytope admits a characteristic function. As a further of the method, the author also gives a simple new proof of five-color theorem.展开更多
Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identific...Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.展开更多
This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applic...This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.展开更多
We discuss the properties of an ordinal consistency matrix on the base of its directed graph, which benefit deriving the ranking of the compared alternatives.
Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way,we i...Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way,we investigate the quantum discord of the two-qubit system constructed from the Yang–Baxter Equation. The density matrix of this system is generated through the unitary Yang–Baxter matrix R. The analytical expression and numerical result of quantum discord and geometric measure of quantum discord are obtained for the Yang–Baxter system. These results show that quantum discord and geometric measure of quantum discord are only connect with the parameter θ,which is the important spectral parameter in Yang–Baxter equation.展开更多
基金Supported by the National Natural Science Foundation of China (No. 61173036)
文摘The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected. Then, a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices. The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and auto-correlation with the natural frequency of the plaintext being hidden and homogenized.
文摘The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical problems and complex control problems. In this work, the authors try to generate matrices such that： （1） the condition number of these types of matrices is controlled and （2） The algorithm used to generate these matrices preserves their structure.
基金supported by National Natural Science Foundation of China (GrantNo. 60672160)the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093108110001)+3 种基金the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (Grant No. 09YZ13)the Netherlands Organization for Scientific Research (NWO)Singapore MoE Tier 1 Research Grant RG60/07Shanghai Leading Academic Discipline Project (Grant No. J50101)
文摘We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.
基金supported by National High-Tech Research and Development Program of China (863 Program) (2009AA063005)Natural Science Foundation of Shandong Province (ZR2009EM001)Natural Science Foundation of China (40976060)
文摘The 3D fluorescence discrimination of phytoplankton classes was investigated by SA4 multiwavelet,GHM multiwavelet,and coifman-2(coif2) wavelet analysis.Belonging to 35 genera of 7 major phytoplankton divisions in the inshore area of China Sea,Single species cultures of 51 phytoplankton species were employed.The second scale vector (Ca2) of SA4,Ca2 of GHM and the third scale vector (Ca3) of coif2 were selected as feature spectra by Bayesian discriminate analysis (BDA).The reference spectra were obtained via hierarchical cluster analysis (HCA).With average high correct discrimination ratios (CDRs),reference spectra were representative to phytoplankton species.For one-algae samples,the average CDRs were 95.6% at genus level and 86.7% at division level.For the laboratory mixed samples,the average CDRs (one division accounted for 25%,75% or 100% of the total biomass) were 86.6%,91.4% and 100% at division level.Moreover,the average CDRs of the dominant species (accounted for 75%) was 79.8% at genus level.Results for the in situ samples were coincided with the microscopic ones at division level with the relative contents of 54.3%-96.5%.The fluorometric discriminating technique was further tested during the cruise in Bohai Sea recently.
文摘Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we characterize Lie derivations of N when char（F） ≠ 2.
基金the National Natural Science Foundation of China(No.10931005)the Shang-hai National Natural Science Foundation(No.10ZR1403600)the Research Fund for the DoctoralProgram of Higher Education of China(No.20100071110001)
文摘and uses it imply that application In this paper the author gives a method of constructing characteristic matrices, to determine the Buchstaber invariants of all simple convex 3-polytopes, which each simple convex 3-polytope admits a characteristic function. As a further of the method, the author also gives a simple new proof of five-color theorem.
基金supported by National Natural Science Foundation of China(Grant Nos.11401124 and 71271021)the Scientific Research Projects for the Introduced Talents of Guizhou University(Grant No.201343)the Key Program of National Natural Science Foundation of China(Grant No.11431002)
文摘Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.
基金supported by a 2017 University of New South Wales Science Goldstar Grant(Jie Du)the Simons Foundation(Grant Nos. #359360(Brian Parshall) and #359363 (Leonard Scott))
文摘This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.
基金This research is supported by National Natural Science Foundation of China（10201007） and NSF of Shandong.
文摘We discuss the properties of an ordinal consistency matrix on the base of its directed graph, which benefit deriving the ranking of the compared alternatives.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 11247260 and 11305020 and the CUST Foundation for Young Scholars under Grant No. XQNJJ-2011-03
文摘Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way,we investigate the quantum discord of the two-qubit system constructed from the Yang–Baxter Equation. The density matrix of this system is generated through the unitary Yang–Baxter matrix R. The analytical expression and numerical result of quantum discord and geometric measure of quantum discord are obtained for the Yang–Baxter system. These results show that quantum discord and geometric measure of quantum discord are only connect with the parameter θ,which is the important spectral parameter in Yang–Baxter equation.
