Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Quantitative study on selective stacking of zwitterions in large-volume sample matrix by moving reaction boundary in capillary electrophoresis

The paper advanced the theoretical procedures for quantitative design on selective stacking of zwitterions in full capillary sample matrix by a cathodic-direction moving reaction boundary (MRB) in capillary electrophoresis (CE) under control of electroosmotic flow (EOF). With the procedures, we conducted the theoretical computations on the selective stacking of two test analytes of L-histidine (His) and L-tryptophan (Trp) by the MRB created with 30 mM pH 3.0 formic acid-NaOH buffer and 2-80 mM sodium formate. The results revealed the following three predictions. At first, the MRB cannot stack His and Trp plugs if less than 12.5 mM sodium formate is used to form the MRB and prepare the sample matrix. Second, the MRB can stack His and/or Trp sample plugs completely if higher than 50 mM sodium formate is chosen to form the MRB. Third, the MRB can only focus His plug completely, but stack Trp plug partially if 20-50 mM sodium formate is used; this implied the complete MRB-induced selective stacking to His rather than Trp. All the three predictions were quantitatively proved by the experiments. With great dilution of sample matrix and control of EOF, controllable, simultaneous and MRB-induced selective stacking and separation of zwitterions were achieved. The theoretical results hold evident significances to the quantitative design of selective stacking conditions and the increase of detection sensitivity of zwitterions in CE. In addition, the control of EOF by cetyltrimethylammonium bromide (CTAB) can evidently improve the stacking efficiency to both His and Trp.     

Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

The interface of the Ising model and the Brownian sheet

We study the limit theorem related to the interface of the three-dimensional Ising model. Dobrushin proved that the interface does not fluctuate and becomes rigid for sufficiently large. We define the random fieldX ^L (t, s), 0t, s1, on the interface, and prove that X^L(t, s) converges to the Brownian sheet as L for sufficiently large, whereL denotes the size of the system. This result does not mean that the interface itself converges to the Brownian sheet.     

Note on the fractal dimension of hard sphere trajectories

Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations.     

(ClAlNH)n簇合物的结构与稳定性

用量子化学从头算方法（HF／6－31G）和密度泛函理论（DFT）的B3LYP方法，以6－31G标准基组加一个极化函数，对（ClAlNH)n(n=1-10)簇合物的几何构型，电子结构和红外光谱进行了优化，并讨论了聚合反应（ClAlNH)m→(ClAlNH)n的热力学效应，结果表明，（ClAlNH)n系列簇合物的基态稳定结构为Cs(n=1),D2h(n=2),D3h(n=3),Td(n=4),Cs(n=5),D3d(n=6),Cs(n=7),S4(n=8),D3h(n=9),C2h(n=10,n=2,4,6,8,10等偶数对应的（ClAlNH)n簇化合物的结构比n等于奇数量更稳定。     

Mathematical studies of Kekulé structures

The perfect matching vector and forcing and the Kekulé-vector of cata-benzenoids are defined. Two theorems are given which set the sufficient and necessary conditions for HKZ-vector (Harary et al. J Math Chem 6:295, 1991) and Kekulé-vector in cata-benzenoids. Additional two theorems are obtained which give sharp bounds for the modules of HKZ- and Kekulé vectors. Dedicated to Professor Tadeusz Marek Krygowski on the happy occasion of his 70th birthday.     

Structural and magnetic properties of the Kagomé antiferromagnet YbBaCo4O7

The mixed-valent compound YbBaCo₄O₇ is built up of Kagomé sheets of CoO₄ tetrahedra, linked in the third dimension by a triangular layer of CoO₄ tetrahedra in an analogous fashion to that found in the known geometrically frustrated magnets such as pyrochlores and SrCr_9xGa_12−9xO₁₉ (SCGO). We have undertaken a study of the structural and magnetic properties of this compound using combined high-resolution powder neutron and synchrotron X-ray diffraction. YbBaCo₄O₇ undergoes a first-order trigonal→orthorhombic phase transition at 175 K. We show that this transition occurs as a response to a markedly underbonded Ba²⁺ site in the high-temperature phase and does not appear to involve charge ordering of Co²⁺/Co³⁺ ions in the tetrahedra. The symmetry lowering relieves the geometric frustration of the structure, and a long-range-ordered 3-D antiferromagnetic state develops below 80 K.     

On a double degenerate fourth-order parabolic equation

The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit.     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.