从立方抛物线谈起(1)--余弦型振动,椭圆余弦型振动与双曲线型非周期运动

从立方抛物线的特性谈起 ,用较初浅的方法 ,借助于雅可比椭圆函数求椭圆方程的解来说明一大类一维保守系统的余弦振动、椭圆余弦型振动与双曲线型非周期运动 .并以杜芬振子、单摆、倒摆、转动圆环上的小环运动为典型实例作了详细讨论     

一类对称的Kolmogorov系统的定性研究（Ⅰ）

本文对一类对称的三次微分系统进行探讨，对每个奇点导出表示其鞍结性的型号公式。给出（Ｋ３）所有的六种全局相图。     

Differentiability of the Value Function of Nonclassical Optimal Growth Models

We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions.     

Thermodynamic derivative properties and densities for hyperbaric gas condensates: SRK equation of state predictions versus Monte Carlo data

The ability of Soave–Redlich–Kwong cubic equation of state (SRK EoS) to predict densities and thermodynamic derivative properties such as thermal expansivity, isothermal compressibility, calorific capacity, and Joule–Thompson coefficients, for two gas condensates over a wide range of pressures (up to 110 MPa) was studied. The predictions of the EoS were compared to Monte Carlo simulation data obtained by Lagache et al. [M.H. Lagache, P. Ungerer, A. Boutin, Fluid Phase Equilibr. 220 (2004) 221]. Two completely different alpha functions for the SRK EoS attractive term were used and their respective effects on the predictions of such properties were analyzed. Also, two different forms of the crossed terms of the attractive parameter, a_ij, and three expressions of the crossed terms of the repulsive parameter, b_ij, were combined in different ways, and predictions were carried out. Little sensitivity of the properties on the chosen alpha function, except for the calorific capacities, was found in the systems studied. The most commonly used combination rules to model phase behavior of reservoir fluids, i.e. geometric and arithmetic forms of a_ij and b_ij, respectively, predicted very deficient results for these fluids at extreme conditions, specially for density calculations.     

混凝土未测区域质量预测方法研究

文章针对桩基超声波测试评价桩身混凝土质量，提出了回归分析、灰色理论和三次样条函数三种方法在预测未知区域的应用。尤其三次样条法有较好的应用前景，为桩基可靠度评价提供了保证。     

临界等温线的推算──几个立方型状态方程的比较

对ＰＴ方程等几个立方型状态方程描述氩的临界等温线的能力作比较研究。在临界压力以下区域．ＰＴ方程、ＨＳ－ＳＲＫ方程和ＳＲＫ方程推算精度较好，ＡＡＤ＜０．４％。在临界压力以上区域，所讨论的五个方程都不能提供具有合理精度的描述。     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

关于三次素变数方程在算术数列中的解

In this paper, we give a necessary and sufficient solvable condition for diagonal cubic equation with prime variable in arithmetic progressions and the outline of the proof.     

Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.