This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Ca...This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.展开更多
在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分...在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分量的参数表达.展开更多
It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present ...It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present study is limited to those of solutes, and among them the three ones are involved in the Van der Waals forces, whereas the two ones involved in the hydrogen bonding are left aside at this stage. These three studied parameters, which we call δ, ω and ε, respectively reflect the three types of Van der Waals forces: dispersion, orientation or polarity strictly speaking, and induction-polarizability. These parameters have been experimentally obtained in previous studies for 121 Volatile Organic Compounds (VOC) via an original Multiplicative Matrix Analysis (MMA) applied to a superabundant and accurate GLC data set. Then, also in previous studies, attempts have been made to predict these parameters via a Simplified Molecular Topology procedure (SMT). Because these last published results have been somewhat disappointing, a promising new strategy of prediction is developed and detailed in the present article.展开更多
Innovative viewpoint on the older topic of the van der Waals forces, is of interesting and significant issue to be concerned in both the fields related to the fundamental investigation and thus valuable in guiding the...Innovative viewpoint on the older topic of the van der Waals forces, is of interesting and significant issue to be concerned in both the fields related to the fundamental investigation and thus valuable in guiding the new physiochemical phenomena and processes for both academic research and practical applications. The intermolecular Van der Waals forces involved in solutions have been recently deeply reconsidered as far as the solute side is concerned. More precisely, the solute descriptors (or parameters) experimentally established, have been accurately related to molecular features of a Simplified Molecular Topology. In the present study, an equivalent result is reached on the solvent side. Both experimental parameters have been obtained simultaneously in previous Gas Liquid Chromatographic studies for 121 Volatile Organic Compounds and 11 liquid stationary phases, via an original Multiplicative Matrix Analysis. In that experimental step, five groups of forces were identified, two of hydrogen bonding and three of Van der Waals: 1) dispersion (London), 2) orientation or polarity strictly speaking (Keesom), and 3) induction-polarizability (Debye). At this stage, an attempt of characterization the solvent parameters via the SMT procedure has been limited to those related to the Van der Waals forces, those related to the hydrogen bonding being for now left aside.展开更多
Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potenti...Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.展开更多
The electrical properties of magnetic sensing devices fabricated from anisotropic materials are not easily extracted. Here we present a method for determining the resistance matrix for an anisotropic device with multi...The electrical properties of magnetic sensing devices fabricated from anisotropic materials are not easily extracted. Here we present a method for determining the resistance matrix for an anisotropic device with multiple electrical contacts placed in a perpendicular magnetic field. By using the methods developed by Van der Pauw and Wasscher, the analysis for the anisotropic system is reduced to the equivalent problem for an isotropic sample, which can then be solved using methods developed previously. As a result, the method works in the case of structures with an arbitrary number of asymmetric extended contacts at large magnetic field strength. In addition to the extraction of nonisotropic resistivities, the resistance matrix can be used to analyze the Hall effect for anisotropic plates.展开更多
研究了冲击噪声环境中波束域波达方向(direction of arrival,DOA)估计问题。在冲击噪声环境下,基于共变和分数低阶矩的ROC-MUSIC和FLOM-MUSIC方法稳健性较差。为了改进空间谱估计性能,首次将波束空间处理应用于共变系数矩阵和分数低阶...研究了冲击噪声环境中波束域波达方向(direction of arrival,DOA)估计问题。在冲击噪声环境下,基于共变和分数低阶矩的ROC-MUSIC和FLOM-MUSIC方法稳健性较差。为了改进空间谱估计性能,首次将波束空间处理应用于共变系数矩阵和分数低阶矩矩阵中,定义了新的波束域共变系数矩阵和波束域分数低阶矩矩阵,提出了新的波束域ROC-MUSIC(BROC-MUSIC)算法和波束域FLOM-MUSIC(BFLOM-MUSIC)算法。理论分析表明,可以通过波束域共变系数矩阵和波束域分数低阶矩矩阵的特征分解来估计噪声子空间,从而实现对信源的DOA估计。计算机仿真结果证明了算法的有效性和正确性。展开更多
基金Supported by National Natural Science Foundation of China(10471048)Research Foundation of Hubei Education Committee(B20092809)Research Foundation of Xianning University(Bk0714)
基金supported by the National Natural Science Foundation of China(No.12271334).
文摘This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.
文摘It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present study is limited to those of solutes, and among them the three ones are involved in the Van der Waals forces, whereas the two ones involved in the hydrogen bonding are left aside at this stage. These three studied parameters, which we call δ, ω and ε, respectively reflect the three types of Van der Waals forces: dispersion, orientation or polarity strictly speaking, and induction-polarizability. These parameters have been experimentally obtained in previous studies for 121 Volatile Organic Compounds (VOC) via an original Multiplicative Matrix Analysis (MMA) applied to a superabundant and accurate GLC data set. Then, also in previous studies, attempts have been made to predict these parameters via a Simplified Molecular Topology procedure (SMT). Because these last published results have been somewhat disappointing, a promising new strategy of prediction is developed and detailed in the present article.
文摘Innovative viewpoint on the older topic of the van der Waals forces, is of interesting and significant issue to be concerned in both the fields related to the fundamental investigation and thus valuable in guiding the new physiochemical phenomena and processes for both academic research and practical applications. The intermolecular Van der Waals forces involved in solutions have been recently deeply reconsidered as far as the solute side is concerned. More precisely, the solute descriptors (or parameters) experimentally established, have been accurately related to molecular features of a Simplified Molecular Topology. In the present study, an equivalent result is reached on the solvent side. Both experimental parameters have been obtained simultaneously in previous Gas Liquid Chromatographic studies for 121 Volatile Organic Compounds and 11 liquid stationary phases, via an original Multiplicative Matrix Analysis. In that experimental step, five groups of forces were identified, two of hydrogen bonding and three of Van der Waals: 1) dispersion (London), 2) orientation or polarity strictly speaking (Keesom), and 3) induction-polarizability (Debye). At this stage, an attempt of characterization the solvent parameters via the SMT procedure has been limited to those related to the Van der Waals forces, those related to the hydrogen bonding being for now left aside.
文摘Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.
文摘The electrical properties of magnetic sensing devices fabricated from anisotropic materials are not easily extracted. Here we present a method for determining the resistance matrix for an anisotropic device with multiple electrical contacts placed in a perpendicular magnetic field. By using the methods developed by Van der Pauw and Wasscher, the analysis for the anisotropic system is reduced to the equivalent problem for an isotropic sample, which can then be solved using methods developed previously. As a result, the method works in the case of structures with an arbitrary number of asymmetric extended contacts at large magnetic field strength. In addition to the extraction of nonisotropic resistivities, the resistance matrix can be used to analyze the Hall effect for anisotropic plates.
文摘研究了冲击噪声环境中波束域波达方向(direction of arrival,DOA)估计问题。在冲击噪声环境下,基于共变和分数低阶矩的ROC-MUSIC和FLOM-MUSIC方法稳健性较差。为了改进空间谱估计性能,首次将波束空间处理应用于共变系数矩阵和分数低阶矩矩阵中,定义了新的波束域共变系数矩阵和波束域分数低阶矩矩阵,提出了新的波束域ROC-MUSIC(BROC-MUSIC)算法和波束域FLOM-MUSIC(BFLOM-MUSIC)算法。理论分析表明,可以通过波束域共变系数矩阵和波束域分数低阶矩矩阵的特征分解来估计噪声子空间,从而实现对信源的DOA估计。计算机仿真结果证明了算法的有效性和正确性。
