Initial-boundary value problem for the two-component nonlinear Schrödinger equation on the half-line

We present a 3×3 Riemann-Hilbert problem formalism for the initial-boundary value problem of the two-component nonlinear Schrödinger (2-NLS) equation on the half-line. And we also get the Dirichlet to Neuemann map through analysising the global relation in this paper.     

Influence of a Longitudinal Magnetic Field on the Hall Effect in the Plasma Accelerator Channel

An analytic model of steady-state two-dimensional flows in coaxial plasma-accelerator channels in the presence of a longitudinal magnetic field is proposed. The solution of the problem is found in the smooth channel approximation for the MHD equations of an ideal two-component plasma. An example of the developing axisymmetric flows is given and the features of the plasma-dynamic processes are investigated. It is found that the Hall effect and the anode flow zone can be reduced using a longitudinal field and plasma rotation.     

Gradient model in the problem of stress-concentration around a circular hole in two-component stochastic composites

The gradient model of stochastically inhomogeneous media is used to study the stress concentration around a circular hole in a two-component elastic composite. The study is based on a general solution of the system of equilibrium equations expressed in terms of harmonic functions and functions that satisfy the Helmholtz equation. This solution is used to solve problems for an infinite plane with a circular hole under uniform and uniaxial tension. The results obtained are compared with the solutions found using the theory of effective moduli, which is simpler __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 41–53, December 2007.     

Cytokinin signal transduction： Known simplicity and unknown complexity

Cytokinin plays a critical role in plant growth and development by regulating cell divisions and cell differentiation. Recent studies suggest that cytokinin signaling is presumably mediated by a two-component system analogous to those found in bacteria and fungi, which transduces an external signal via a phosphorelay from the plasma membrane-anchored receptors to downstream effectors and regulators. Moreover, cytokinin signaling is highly interactive with other pathways, and many components of the pathway appear to be functionally redundant. Proper address of these questions will be crucial for our further understanding on this important network.     

Global periodic conservative solutions of a periodic modified two-component Camassa-Holm equation

In the paper, we first show the existence of global periodic conservative solutions to the Cauchy problem for a periodic modified two-component Camassa-Holm equation. Then we prove that these solutions, which depend continuously on the initial data, construct a semigroup.     

Ideas of relativistic quantum chemistry

The basic ideas of relativistic quantum chemistry are highlighted, with the most important ingredients summarised as follows. (1) The restricted kinetic balance (RKB) condition, being both necessary and sufficient, serves as the cornerstone for the matrix representation of the Dirac-based Hamiltonian. (2) The concept of matrix transformation plays the key role in formulating two-component relativistic theories. Some popular ones, albeit presented as operators, are de facto matrix formulations in terms implicitly of the RKB condition. They merely make simple things complicated as a one-step block-diagonalization of the matrix Dirac equation can do the whole job. (3) The computational efficiency for both four- and two-component relativistic theories can be gained by means of the simple chemical idea of ‘from atoms to molecule’ without recourse to mathematical tricks. The two branches of relativistic theories have thus been made fully equivalent in all the aspects of simplicity, accuracy, and efficiency. It is concluded that the best relativistic electrons-only Hamiltonian has been found, which can be combined with any know-how correlation methods for electronic structure calculations of all the atoms in the Periodic Table. Most amazingly, the new quantum mechanical equation serves as a seamless bridge between the Schrödinger and Dirac equations. In short, the ‘relativity problem’ in chemistry has been solved.     

Stability of Solitary Waves and Global Existence of a Generalized Two-Component Camassa–Holm System

We study here the existence of solitary wave solutions of a generalized two-component Camassa–Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped solitary waves. We also demonstrate that all smooth solitary waves are orbitally stable in the energy space. We finally give a sufficient condition for global strong solutions to the equation in some special case.     

Yb、YbO电子激发态的相对论含时密度泛函理论研究

本文用基于精确二分量哈密顿（exact two—component Hamiltonian）的相对论含时密度泛函理论（time-dependent relativistic density functional theory）计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认．     

Relativistic calculations of AuSi+ and AuSi−

Theoretical calculations of the electronic structure of the ground state and a series of excited states of the AuSi⁺ and AuSi⁻ molecules are presented. The calculations were carried out with the spin-free relativistic infinite-order two-component (IOTC) method and high-level complete active space self-consistent field/complete active space perturbation theory correlated methods. The spin-orbit (SO) coupling was introduced via the restricted active space state interaction method with the use of the atomic mean-field SO integrals. The work presents the spectroscopic parameters of calculated states and full potential energy curves of the ionic AuSi⁺ and AuSi⁻ structures for the first time. Electrostatic potential maps projected on the electron density surface illustrate the significant relativistic effects on going from nonrelativistic to scalar relativistic treatments.