On Globally Periodic Solutions of the Difference Equation x n + 1 = f ( x n )/ x n − 1

We study the second-order difference equation x n +1 = f ( x n ) x n m 1 where f ] C 1 ([0, X ),[0, X )) and x n ] (0, X ) for all n ] Z . For the cases p h 5, we find necessary and sufficient conditions on f for all solutions to be periodic with period p . We answer some questions and conjectures of Kulenovi ' and Ladas.     

On the Global Character of the Difference Equation X n + 1 =

We investigate the global stability, the periodic character, and the boundedness nature of solutions of the difference equation x n +1 = f + n x n m (2 k +1) + i x n m 2 l A + x n m 2 l , n =0,1,… where k and l are non-negative integers, the parameters f , n , i , A are non-negative real numbers with f + n + i >0, and the initial conditions are non-negative real numbers. We show that the solutions exhibit a trichotomy character depending upon the parameters n , i and A .     

一个非线性色散-耗散方程的显式精确解

本文通过直接代数方法与假设方法的一种结合求出了一个用于描述由冷离子和热电子组成的等离子体弱非线性离子声波演化的非线性色散－耗散方程的几类显式精确行波解。这里的结果包含已有文献的结果作为特例,本文的方法也适用于高维非线性发展方程。     

Effect of gamma irradiation on the thermal,mechanical and structural properties of chlorinated polyvinyl chloride

Non isothermal studies were carried out using thermogravimetry (TG) and differential thermogravimetry (DTG) to obtain the activation energy of decomposition for chlorinated polyvinyl chloride (CPVC) before and after exposure to gamma doses at levels between 5.0 and 50.0 KGy. Thermal gravitational analysis (TGA) indicated that the CPVC polymer decomposes in one main breakdown stage and a decrease in activation energies was observed followed by an increase on increasing the gamma dose. The variation of melting temperatures with the gamma dose has been determined using differential thermal analysis (DTA). Also, mechanical and structural property studies were performed on all irradiated and non-irradiated CPVC samples using stress-strain relations and X-ray diffraction. The results indicated that the exposure to gamma doses at levels between 27.5 and 50 KGy leads to further enhancement of the thermal stability, tensile strength and isotropic character of the polymer samples due to the crosslinking phenomenon. This suggests that gamma radiation could be a suitable technique for producing a plastic material with enhanced properties that can be suitable for high temperature applications and might be a suitable candidate for dosimetric applications.     

带多余参数的回归方程系统的两步估计

研究了带多余参数的回归方程系统,得到了参数的两步估计是某一特定形式的一个充要条件,并讨论了两步估计的有限样本性质。     

Set Differential Equations and Flow Invariance

The study of Set Differential Equations is initiated in the metric space of nonempty, compact, convex subsets of , endowed with the Hausdorff metric. The existence of a generalized solution for the associated initial value problems is proved when the function involved does not satisfy any continuity assumptions. Utilizing the ideas of nonsmooth analysis, a proximal aiming condition is employed to investigate the weak and strong invariance for these solutions.     

On the periodic solution of N–Dimensional Stochastic Population Models *

Two n species stochastic population models with periodic coefficients are studied. Some sufficient conditions for the existence of asymptotically stable periodic solution process are obtained respectively     

Moving in and out of contexts in collaborative reasoning about equations

This case study investigates how a group of 12-year-old pupils contextualizes a task formulated as an equation expressed in a word problem. Of special interest is to explore in detail the phenomenon of pupils working with manipulative-based equation-solving methods in a task involving another real world context. The pupils’ small group discussions were videotaped and analyzed in terms of how the pupils contextualized the task in their attempts to arrive at an answer. The results highlight the importance of giving pupils opportunities to realize the particular position of symbolic mathematical representations when dealing with mathematical concepts. While an abstract concept describes something general, concrete representations and specific real-world examples always describe something specific. No one particular example incorporates the rich meaning of an abstract concept. This central distinction needs to be included in teaching practices.     

Analytic Solutions for a Class of Nonlinear Ordinary Differential Equations

In this article, existence and uniqueness of analytic solutions to a class of problems of the form $ zG^{prime prime }(z)+J(z)G^{prime }(z)+F(G(z))=0, G(0)=G_0 $ are considered, where J is analytic in some neighborhood about 0 and F is analytic in some neighborhood of G 0 . This is a generalization of a class of problems considered by Rothe (F. Rothe (1997). A variant of Frobenius' method for the Emden-Fowler equation. Applicable Analysis , 66 , 227-245).     

Differential Operator Solutions of the Bauer-Peschl Equation

In this paper new solutions of the Bauer-Peschl equation represented by differential operators are derived. A relation to the solutions of Bauer is given. Furthermore, it will be said in which new way Bauer's solutions can be obtained. Also three other ways for obtaining the solutions of the Bauer-Peschl equation are sketched.