Subdifferential representation of homogeneous functions and extension of smoothness in Banach spaces

In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke＇s subdifferentials of locally Lipschitzian functions defined on Banach space respectively, and obtain the generalized Euler identity of homogenous functions. Then, by introducing a multifunction F, we extend the smoothness of sphere and differentiability of norm function in Banach space.     

Computation of collective modes and acoustic investigations at different temperatures of vitrous silica

This paper is mainly concerned with elastic and acoustic properties of vitrous silica besides the computation of phonon frequencies. Thus the phonon frequencies of vitrous silica have been calculated assuming the electronic bulk modulus,K _e, as equal to zero. New equations have been derived to relate the pressure derivatives of second order elastic constants to the acoustic Gruneisen’s parameters using both Bhatia-Singh’s parameters and Schofield’s equations. The calculated longitudinal and transverse Gruneisen’s parameters and the predicted absorption band spectra from Nagendranath’s equation and Bhatia Singh’s parameters are in good agreement with experiment. The calculated mean acoustic mode Gruneisen’s parameter evaluated from the pressure derivative of Nagendranath’s equation is also in good agreement with experiment. An erratum to this article is available at .     

The Wigner Function as Distribution Function

Some entangled states have nonnegative Wigner representative function. The latter allow being viewed as a distribution function of local hidden variables. It is argued herewith that the interpretation of expectation values using such distribution functions as local hidden variable theory requires restrictions pertaining to the observables under study. The reasoning lead to support the view that violation of Bell’s inequalities that is always possible for entangled states hinges not only on the states involved but also whether the dynamical variables have their values defined even when they cannot be measured.     

SPME-GC-MS快速分析炼油厂废水中痕量VOCs

采用固相微萃取-气相色谱-质谱联用(SPME-GC-MS)对炼油厂废水中痕量挥发性有机化合物(VOCs)进行了定性分析,简化了预处理过程,总分析时间为1h左右.对比处理前后的废水样品的MS定性结果,为废水处理工艺的评价以及有机物降解机理提供了依据.     

The catecholamine system in health and disease —Relation to tyrosine 3-monooxygenase and other catecholamine-synthesizing enzymes—

Catecholamines [dopamine, noradrenaline (norepinephrine), and adrenaline (epinephrine); CAs] are neurotransmitters in the central and peripheral nervous systems as well as hormones in the endocrine system. CAs in the brain play a central role in versatile functions as slow-acting neurotransmitters functioning in synaptic neurotransmission, modulating the effects of fast-acting neurotransmitters such as glutamate and γ-aminobutyric acid (GABA). In this review, I focus on recent advances in the biochemistry and molecular biology of the CA system in humans in health and disease, especially in neuropsychiatric diseases such as Parkinson’s disease (PD), in relation to the biosynthesis of CAs regulated by a pteridine-dependent monooxygenase, tyrosine 3-monooxygenase (tyrosine hydroxylase, TH) and its pteridine cofactor, tetrahydrobiopterin (BH4).     

High-Order Hamilton＇s Principle and the Hamilton＇s Principle of High-Order Lagrangian Function

In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton＇s principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton＇s principle. Finally, the Hamilton＇s principle of high-order Lagrangian function is given.     

非线性函数耦合的Chen吸引子网络的混沌同步

利用非对称非线性函数耦合混沌同步方法,讨论了Chen吸引子的混沌同步问题,数值模拟分析初始值和耦合强度因子的选择对于实现混沌同步的影响. 将非对称非线性函数耦合同步方法进一步推广发展到完全连接网络和由星形子网络构成的复杂大网络混沌同步的研究中. 提供了确定网络中神经元之间混沌同步状态稳定性的误差发展方程,并讨论各个耦合强度因子对网络同步稳定性过程的影响,给出了相应的稳定性范围. 通过数值模拟证明利用非线性函数作为耦合函数,实现完全连接网络、星形子网络构成大网络的混沌同步是有效的. 可以预测在网络的混沌同步 关键词： 非线性耦合函数 Chen吸引子 混沌同步 网络     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

For the first time we introduce an operator Δ _h (γ,ε;κ) for studying Husimi distribution function in phase space (γ,ε) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ | representation we find that Δ _h (γ,ε;κ) is just a pure squeezed coherent state density operator | γ,ε〉 _{κ κ} 〈γ,ε |, which brings much convenience for studying Husimi distribution, so we name Δ _h (γ,ε;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution. Work supported by the National Natural Science Foundation under the grant: 10775097.     

Nucleon charge exchange on the deuteron: A critical review

The existing experimental data on the d(n, p)nn and d(p, n)pp cross-sections in the forward direction are reviewed in terms of the Dean sum rule. It is shown that the measurement of the ratio of the charge exchange on the deuteron to that on the proton might, if taken together with other experimental data, allow a direct construction of the np → np scattering amplitude in the backward direction with few ambiguities. Communicated by T. Hennino