DARBOUX POLYNOMIALS FOR LOTKA–VOLTERRA SYSTEMS IN THREE DIMENSIONS

We consider Lotka–Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.     

Effect of long-period stacking ordered phase on thermal stability of refined grains in Mg-RE-based alloys

The refined grains in both as-cast Mg-10Y-1Zn-2Zr (WZ101?K, wt.%) and Mg-10Y-1Al (WA101, wt.%) alloys have been found to have superior thermal stability after solution treatment. Plate-shaped, but different polytypes of long-period stacking ordered (LPSO) phases distributed along grain boundaries are considered as the predominant inhibitors of grain growth. Based on the plate-shaped features of the LPSO phases, a modified Zener’s model is established and the predicted limiting grain sizes are in a good agreement with the experimental results. Therefore, this model has strong potential for designing advanced Mg-RE-based alloys with high strength and high creep resistance at high temperatures.     

厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

A new representation of permittivity versus temperature for alkanols of the same chain length

The alkanols of three carbon length have been studied by dielectric methods during many years and they do not obey any theoretical model. These substances have the same chain length and have one, two or three dipoles per molecule, so their ability to form hydrogen bridges changes from one substance to other, and one can obtain information by comparative studies. In previous works, we have measured the thermal dependence of permittivity of these substances and analysed the results with an empirical modification of the Onsager equation. Now we shall analyse and compare the results using a different representation. In this representation, the data shows straight lines, whose slopes depend on the quantity of dipoles of each molecule encouraging the high quality of the fittings obtained with the three substances, and also that they behave in the same dielectric way with the rise of temperature.     

Röntgenographische Strukturuntersuchung geschmolzener Magnesium-Blei Legierungen

Abstract

Um Aufschluß über die Atomanordnung in geschmolzenen Magnesium-Blei Legierungen zu erhalten, wurden rontgenographische Strukturuntersuchungen durchgeführt.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

Lifshitz tails for periodic plus random potentials

We prove that the integrated density of states () for a potentialW =V _per +V has Lifshitz tails where V_per is a periodic potential with reflection symmetry andV is a random potential, e.g., of the formV =q _i ()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).