In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection be...In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.展开更多
Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） o...Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.展开更多
In this note, we investigate the generalized modulus of convexity δ（λ） and the generalized modulus smoothness p（λ）. We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coeffici...In this note, we investigate the generalized modulus of convexity δ（λ） and the generalized modulus smoothness p（λ）. We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX（λ）. We show that, for a wide class of class the sequence spaces X, if for some ε∈（0, 9/10] holds δx（e） 〉 1/3（1- √3/2）ε, then X has normal structure.展开更多
Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are ...Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.展开更多
In this paper, we introduce a new geometric constant C;（a, X） of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, w...In this paper, we introduce a new geometric constant C;（a, X） of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized Garc′?a-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.展开更多
A subgroup H of a group G is said to be weakly normal in G if Hg ≤ NG（H） implies that g E NG（H）. In this paper, using the condition that the minimal subgroups or subgroups of prime square order of G are weakly no...A subgroup H of a group G is said to be weakly normal in G if Hg ≤ NG（H） implies that g E NG（H）. In this paper, using the condition that the minimal subgroups or subgroups of prime square order of G are weakly normal in G, we get some results about formation.展开更多
Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for per...Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for perceiving harmonic information, but they are often ineffective in perceiving weak harmonic signals because they are based on energy or amplitude analysis. Based on the theory of Normal time-frequency transform (NTFT) and complex correlation coefficient, a new type of spectrum, the Harmonicity Spectrum (HS), is developed to perceive harmonic information in time series. HS is based on the degree of signal harmony rather than energy or amplitude analysis, and can therefore perceive very weak harmonic information in signals sensitively. Simulation examples show that HS can detect harmonic information that cannot be detected by Fourier spectrum or time-frequency spectrum. Acoustic data analysis shows that HS has better resolution than traditional LOFAR spectrum.展开更多
基金the Science Research Foundation of Qingdao Technological University(C2002-214)
文摘In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.
基金Supported by the National Natural Science Foundation of China under Grant No 61371170the Fundamental Research Funds for the Central Universities under Grant Nos NP2015404 and NS2016038+1 种基金the Aeronautical Science Foundation of China under Grant No 20152052028the Funding of Jiangsu Innovation Program for Graduate Education under Grant No KYLX15_0282
文摘Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.
基金supported by National Fund for Scientific Research of the Bulgarian Ministry of Education and Science, Contract MM-1401/04
文摘In this note, we investigate the generalized modulus of convexity δ（λ） and the generalized modulus smoothness p（λ）. We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX（λ）. We show that, for a wide class of class the sequence spaces X, if for some ε∈（0, 9/10] holds δx（e） 〉 1/3（1- √3/2）ε, then X has normal structure.
基金Supported by the National Natural Science Foundation of China（60375003） Supported by the Chinese Aviation Foundation（03153059）
文摘Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.
文摘In this paper, we introduce a new geometric constant C;（a, X） of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized Garc′?a-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11171243, 11326056） and the Scientific Research Foundation for Doctors, Henan University of Science and Technology （No. 09001610）.
文摘A subgroup H of a group G is said to be weakly normal in G if Hg ≤ NG（H） implies that g E NG（H）. In this paper, using the condition that the minimal subgroups or subgroups of prime square order of G are weakly normal in G, we get some results about formation.
文摘Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for perceiving harmonic information, but they are often ineffective in perceiving weak harmonic signals because they are based on energy or amplitude analysis. Based on the theory of Normal time-frequency transform (NTFT) and complex correlation coefficient, a new type of spectrum, the Harmonicity Spectrum (HS), is developed to perceive harmonic information in time series. HS is based on the degree of signal harmony rather than energy or amplitude analysis, and can therefore perceive very weak harmonic information in signals sensitively. Simulation examples show that HS can detect harmonic information that cannot be detected by Fourier spectrum or time-frequency spectrum. Acoustic data analysis shows that HS has better resolution than traditional LOFAR spectrum.
