PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.     

Symmetry of the Barochronous Motions of a Gas

We study the system of nonlinear differential equations which expresses the constancy of the algebraic invariants of the Jacobian matrix for smooth vector fields in three-dimensional space. This system is equivalent to the equations of gas dynamics which describe the barochronous motions of a gas (the pressure and density depend only on the time). We present the results of computation of the admissible local Lie group and construction of the general solution of the system. We mention a few new problems that arise here.     

第二类Fredholm积分方程的泰勒展开解法

本进一步发展了用Taylor公式求解第二类Fredholm积分方程的方法，并给出了近似解的误差精度分析．     

集值映射的切导数与向量优化问题的最优性条件

利用集值映射切导数与半可微概念，给出了无约束与具约束的集值向量优化问题局部真有效解与局部强有效解的最优性条件。     

广义拟变分不等式解集的稳定性及本质连通区的存在性

在赋范线性空间下．讨论广义拟变分不等式解集的稳定性，证明了满足一定连续性和凸性条件的广义拟变分不等式问题构成的空间M中，大多数(在Baire分类意义下)广义拟变分不等式问题的解集是稳定的，并证明了M中每一个广义拟变分不等式的解集至少存在一个本质连通区。     

Periodic solutions of a second order forced sublinear differential equation with delay

In this paper, existence criteria are established for the existence of periodic solutions of a second order sublinear differential equation with delay and forcing function. Our method is based on careful a priori estimation and continuation theorems, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

Three Types of Expression in Dark-Soliton Perturbation Theory Based on Squared Jost Solutions

Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of perturbagion on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.     

等厚双层涂层材料受集中力作用的平面问题理论解

界面应力的正确评价是分析薄膜涂层材料力学特性的难题之一。利用镜像点法和Dirichlet等值性原理，本文推导了等厚双层薄膜涂层材料受表面集中力作用的平面问题理论解。该显式理论解是以固定在各镜像点上的局部坐标系下的Goursat应力函数的形式给出的。对应于高阶镜像点的应力函数，可通过递推的方法，从对应于低阶镜像点的应力函数求得，而且也易于计算机编程。随着镜像点阶数的增大，它与界面的距离也越来越大，因而相对应的应力函数对界面应力的影响越来越小。最后的算例表明，只需考虑前面有限个镜像点，便可获得足够精度的解。该理论解可作为格林函数，以求解复杂问题的理论解，也可用作边界元法的基本解，提高数值计算的精度和效率。     

Petrographic/geochemical studies of primary and alteration–weathering minerals in garnetiferous ultramafic xenoliths–basanite, Tartous Province, NW Syria

Kimberlitic–pyropic peridotite–xenolites, probably of Jurassic–Cretaceous age, were found mixed with a younger Upper Tertiary basanitic diabase, as flow texture of plagioclase laths and ilmenite rods around those xenoliths indicated. Mafic–ultramafic rocks were crushed, sheared, and cropped along a creek about 15–18 km NE of the town of Dreikeesh, NW Syria. ⁴⁰K–⁴⁰Ar isotopic dating of a pure fresh black cpx sample, collected from the peridotite xenoliths, yielded an age of about 70 Ma. This age is concurrent to the time when Africa, Eurasia, and America were part of the super continent Pangaea. It also suggests that kimberlite–pyropic peridotitic rocks were located within a cratonic pipe prior to their 2000-km eastward journey (starting from the Mid-Atlantic Rift). Sampled outcrops were located within a ring of about 40 km diameter, considered to be a dome consisting of one or more clusters of kimberlitic pipes. The dome structure, mostly covered with Upper Jurassic–Cretaceous carbonate beds, was tilted westward, and rifted and sheared along its eastern edge. Tilting and crushing were accomplished after the opening of the Red Sea in the Miocene, and the counterclockwise movements of the Arabian plate, which folded the carbonate beds to form the N–S-trending Alawite mountain range along the Syrian coast. Olivine, cpx, and pyrope were the major phases in peridotite. Pyrope, including its Cr–Ni-contents, was found to be the best indicator to decipher the temperature–pressure (T–P) conditions for the system. The inferred temperature was found to be about 1460 °C, at a pressure of 62 kb (around 207 km-depth). Petrographic studies revealed many zoned, resorbed, octahedral and non-metasomatized tiny grains, associated with partly to wholly metasomatized and iddingsitized olivines.     

Stationary Distributions of GI/M/c Queue with PH Type Vacations

We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies.