Phase Equilibria in the Ni–Al–W System at 900°C

Summary. Multicomponent Ni-base alloys exhibit good mechanical properties even at elevated temperatures and they are widely used for industrial production of exertion-resistive parts of engines. These properties are mainly determined by the coexistence of a disordered γ matrix with a face centred cubic lattice and cuboidal domains of its ordered γ′ structure. Therefore it is useful to study phase equilibria in Ni-base systems, namely in the regions involving both mentioned phases. One of the conclusions of our recent work on Ni–Al–Cr–W system was a necessity of modification of selected thermodynamic parameters of the ternary Ni–Al–W subsystem in order to achieve a better agreement of our experimental observations with theoretical modelling. This involves new measurements of the microstructure of selected samples of the Ni–Al–W system at 900°C and the comparison of the results with existing literature data in order to confirm our conclusions on higher order system investigated before. It is a first step on the way to an assessment of the Ni–Al–W system, which has not been done before.     

Crystal structure, phase transition and anisotropic thermal expansion of barium zirconium diorthophosphate, BaZr(PO4)2

The crystal structure of BaZr(PO₄)₂ at 298 K was determined from conventional X-ray powder diffraction data using direct methods, and it was further refined by the Rietveld method. The structure was monoclinic (space group C2/m, Z=2) with , , , β=93.086(1)° and . Final reliability indices were R_wp=8.21%, R_p=5.64% and R_B=2.92%. The atom arrangement is similar to that of yavapaiite (KFe(SO₄)₂), however, these crystal structures differ distinctly in the coordination numbers of barium and potassium atoms; the former is tenfold coordinated, whereas the latter is sixfold coordinated. The powder specimens were also examined by high-temperature XRD and DTA to reveal the occurrence of a phase transition from monoclinic to orthorhombic at 732 K during heating. Upon cooling the reverse transition occurred at 710 K. The monoclinic crystal expanded almost one-dimensionally along [503] during the heating process. The orthorhombic phase also showed a tendency to expand one-dimensionally along the c-axis above 732 K.     

Periodic solutions and oscillation of discrete non-linear delay population dynamics model with external force

^** Email: emelabbasy{at}mans.edu.eg^*** Email: shsaker{at}mans.edu.eg In this paper, we consider the discrete non-linear delay populationdynamics model [graphic: see PDF] where m is a positive integer, p(n), Q(n) and (n) are positiveperiodic sequences of period . By the method that involves theapplication of the Gaines and Mawhins coincidence degree theory,we prove that there exists a positive -periodic solution (n). We prove that every positive solutionof (*) which does not oscillate about (n)satisfies lim_t[y(n)–(n)]=0.We establish some necessary and sufficient conditions for theoscillation of every positive solution about (n), and finally, we establish the lower and upperbounds of the oscillatory solutions.     

Problems with one quarter

In this paper two sequences of oscillation criteria for the self-adjoint second order differential equation (r(t)u(t)) + p(t)u(t) = 0 are derived. One of them deals with the case dt/r(t) = , and the other with the case dt/r(t) < .This work was supported by the grant VGA of Slovak Republic No. 1/7466/20.     

Geometry of quadratic differential systems in the neighborhood of infinity

In this article we give a complete global classification of the class QS_ess of planar, essentially quadratic differential systems (i.e. defined by relatively prime polynomials and whose points at infinity are not all singular), according to their topological behavior in the vicinity of infinity. This class depends on 12 parameters but due to the action of the affine group and re-scaling of time, the family actually depends on five parameters. Our classification theorem (Theorem 7.1) gives us a complete dictionary connecting very simple integer-valued invariants which encode the geometry of the systems in the vicinity of infinity, with algebraic invariants and comitants which are a powerful tool for computer algebra computations helpful in the route to obtain the full topological classification of the class QS of all quadratic differential systems.     

时标上二阶广义Emden-Fowler型动态方程的振荡性

研究了时标上的一类具有阻尼项的二阶广义Emden-Fowler型泛函动态方程的振荡性,利用时标上的微积分理论和广义的Riccati变换及不等式技巧,建立了该方程振荡的若干判别准则, 推广且改进了一些已有的结果,并用具体实例来说明本文的主要结论。     

A first-order phase transition between crystal phases in the shift model

We describe rigorously a many-body model of interacting classical particles exhibiting the following behavior at zero temperature: as the pressure varies through a critical value, the system goes through a first-order phase transition between different crystal phases. Moreover, at the critical pressure the system is demonstrably a mixture of the two phases.Supported in part by NSF Grant No. MCS81-01596.     

一类三阶非线性分布时滞动力方程的振动结果

研究一类三阶非线性分布时滞动力方程的振动性,通过构造广义Riccati变换得到一类新的广义Riccati不等式,利用积分平均技巧等方法,建立了保证该方程一切解均振动或收敛于0的若干新的振动结果,推广和改进了近期文献的相关结论,并给出了若干例子。     

吸收型双稳半导体激光器的起振波长

从双稳半导体激光器上跳阈值处的谐振波长是所需阈值电流最低的波长这个物理事实出发，利用双稳半导体激光器的速率方程组，本文对双稳半导体激光器上跳阈值处的谐振波长进行了研究。文中还就一些器件参量对双稳半导体激光器上跳阈值处谐振滤长的影响进行了讨论。     

2，5─哌嗪二酮与α，β─不饱和醛反应研究

综合运用了多种波谱学方法及化学手段确证并归属了２，５－哌嗪二酮与α，β－不饱和醛在超声波分散金属钾及双季铵盐作用下反应产物的立体化学与核磁共振信号，为研究这个反应提供了有用的信息．