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.     

ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.     

Critical points in the Bragg glass phase of a weakly pinned crystal of Ca3Rh4Sn13

New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJ _c(H)) in isothermalMH scans in a weakly pinned single crystal of Ca₃Rh₄Sn₁₃, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJ _c(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of Ca₃Rh₄Sn₁₃ has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb.     

Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition

This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L ₁-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C ₀-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given.     

A mathematical model of the ring-spinning process

This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example.     

改性壳聚精膜用于醇水混合液分离的研究──Ⅲ．超细粉末填充壳聚精膜

首次制备了用Ｓｉ３Ｎ４，ＳｉＯ２，ＴｉＨ４超细粉末填充的改性壳聚精膜，并将其用于乙醇／水混合液的分离中。实验表明壳聚糖膜经超细粉末填充后强度增大，溶胀度减小。用于乙醇／水混合液渗透蒸发分离时，分离因子和渗透通量都有提高，并在填充量为１６．７％附近出现极大值。随着料液中乙醇含量的增大，渗透通量减小，分离因子增大；随着料液温度的升高渗透通量显著增大，分离因子则稍有下降。并简单讨论了超细粉末在乙醇／水混合液分离中的作用。     

Reactions of mercury salts with benzo- and tetrafluorobenzobarrelenes

Regiochemistry and stereochemistry of the addition of mercury salts to benzobarrelene and tetrafluorobenzobarrelene have been studied in acetic acid and methanol. The effect of the substrate structure on the regiochemistry of the reaction is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1105–1108, June, 1994.     

Thermoanalytical procedures to identify the morphology of polycrystalline materials

Polypropylenes of differing morphologies were examined by differential thermal analysis. The problems of reordering during the programmed heating are discussed. Four potential procedures by which the reordering could be inhibited are considered, and three of these are experimentally assessed. Their advantages and deficiencies are identified. Two pretreatments, an etching and a crosslinking, are recognised as able to qualitatively characterise the initial morphology, with a preference for the former. A test to identify the occurrence of reordering is identified. In celebration of the 60^th birthday of Dr. Andrew K. Galwey     

高抗冲聚丙烯序列结构的综合表征

用高分辨＾１３Ｃ ＮＭＲ、ＦＴＩＲ等手段获得了高抗冲聚丙烯的组成和序列分布等链结构方面的信息。用ＤＳＣ、ＷＡＸＤ等方法研究了它们的结晶行为、熔融转变及晶体结构，多种方法相结合有效地表征了高抗冲聚丙烯的序列结构。