On Gibbs measures of P-adic Potts model on the cayley tree

We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ? _p) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ? p and p ≥ 3 (resp. q ? 2², p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ? p if p ≥ 3 and q ? 2² if p = 2.     

Elliptic fibers over non-perfect residue fields

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néron list. We describe these new types and extend Tate's algorithm to deal with all discrete valuation rings. Specifically, we show how to translate a Weierstrass equation into a form where the reduction type may be easily determined. Having determined the special fiber type, we construct the regular model of the curve with explicit blow-up calculations. We also provide tables that serve as a simple reference for the algorithm and which succinctly summarize the results.     

Lower Bound for the Interatomic Distance in Lennard-Jones Clusters

We prove in this article lower bounds and upper bounds for the interatomic distance in cluster of atoms minimizing the Lennard-Jones energy. Our main result is in dimension three, but we also prove it in the two-dimensional case, since it seems interesting from a theoretical point of view.     

Exact Anomalous Dimensions of Composite Operators in the Obukhov–Kraichnan Model

We consider two stochastic equations that describe the turbulent transfer of a passive scalar field (x)(t,x) and generalize the known Obukhov–Kraichnan model to the case of a possible compressibility and large-scale anisotropy. The pair correlation function of the field (x) is characterized by an infinite collection of anomalous indices, which have previously been found exactly using the zero-mode method. In the quantum field formulation, these indices are identified with the critical dimensions of an infinite family of tensor composite operators that are quadratic in the field (x), which allows obtaining exact values for the latter (the values not restricted to the -expansion) and then using them to find the corresponding renormalization constants. The identification of the correlation function indices with the composite-operator dimensions itself is supported by a direct calculation of the critical dimensions in the one-loop approximation.     

Linear Versus Quadratic Estimators in Linearized Models

In nonlinear regression models an approximate value of an unknown parameter is frequently at our disposal. Then the linearization of the model is used and a linear estimate of the parameter can be calculated. Some criteria how to recognize whether a linearization is possible are developed. In the case that they are not satisfied, it is necessary to take into account either some quadratic corrections or to use the nonlinear least squares method. The aim of the paper is to find some criteria for an ordering linear and quadratic estimators.     

上市公司资本成本面板数据模型与实证分析

本文利用我国上市公司1997至2002年的有关财务数据,建立了我国上市公司资本成本面板数据模型,运用该模型分析了我国上市公司资本成本与财务杠杆、企业规模的关系.结果表明,财务杠杆的提升、企业规模的扩大将使资本成本下降.该结论对我国上市公司优化资本结构、提高企业价值具有一定的参考价值.     

高压水射流作用下岩石破碎机理及过程的数值模拟研究

根据连续介质力学和有限元理论,给出了高压水射流破岩系统中流体和岩石的控制方程,并建立了相应的有限元列式．运用连续损伤力学和细观损伤力学理论,建立了适用于水射流破岩全过程分析的岩石损伤模型以及宏细观损伤的耦合模式．数值计算的结果较真实地反映了水射流破岩过程中,岩石的动态响应以及水射流动力学特性的演化过程,普通连续水射流破碎岩石主体所用的时间为毫秒量级,破岩的主要形式是卸载及射流冲击所产生的拉伸破坏,并呈“阶跃式”发展．数值计算与相关试验结果基本吻合,表明该分析方法是可行的,可用来指导高压水射流破岩理论的进一步研究及应用．     

Structures of（ΩΩ）0＋and（[1]Ω）1＋in Extended Chiral SU（3） Quark Model

The structures of (ΩΩ)0 and ([1]Ω)1 are studied in the extended chiral SU(3) quark model in which vector meson exchanges are included. The effect from the vector meson fields is very similar to that from the one-gluon exchange (OGE) interaction. Both in the chiral SU(3) quark model and in the extended chiral SU(3) quark model,di-omega (ΩΩ)0 is always deeply bound, with over one hundred MeV binding energy, and ([1]Ω)1 ‘s binding energy is around 20 MeV. An analysis shows that the quark exchange effect plays a very important role for making di-omega (ΩΩ)0 deeply bound.     

The algebraic Bethe ansatz for the Izergin–Korepin model with open boundary conditions

We present the procedure of exactly solving the Izergin–Korepin model with open boundary conditions by using the algebraic Bethe ansatz, which include constructing the multi-particle state and achieving the eigenvalue of the transfer matrix and corresponding Bethe equations. We give a proof about our conclusions on the multi-particle state based on an assumption. When the model is U_q(su(2)) quantum invariant, our results agree with that obtained by analytic Bethe ansatz method.