SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition :　　　　εx″(t) =f(t,x(t) ,x(t-ε) ,ε) ,　　t∈(0 ,1 ) ,(1 )　　　　x(t) =φ(t,ε) ,　t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1～5] .Butthosestudiespossessedanesse…     

Synthesis and Characterization of Silicone Modified Polyurethane Surfactant Useable at High Temperature

A series of novel silicone modified polyurethane (Si-PU) surfactants were successfully synthesized by using hydroxypropyl-terminated polydimethylsiloxane (HPMS), polyethylene glycol (PEG), dimethylolpropionic acid (DMPA) and isophoronediisocyanate (IPDI). The chemical structure of the surfactant was confirmed by FTIR and ¹H-NMR. TEM photographs showed that the micelles of the Si-PU surfactants dispersed in aqueous solution were spherical with the particle size in the range of 100–400 nm. Surface tension measurements indicated that these surfactants had low surface tension to 29.9 mN·m^?1and a definite critical micelle concentration to, approximately 5.0×10^?4–7.5×10^?4mol·L^?1. When the content of HPMS was 20 wt%, the surfactant's, emulsifying performance was superior to the traditionally available Span80/Tween80 mixed emulsifiers. In addition to that, no phase transition temperature was detected from 20°C to 90°C by fluorescence probe and DSC measurements, confirming the high thermal stability of the micelles.     

Clique-cutsets beyond chordal graphs

Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (eg, the class of perfect graphs and the class of even-hole-free graphs), appearing both as excluded configurations, and as configurations around which graphs can be decomposed. In this paper, we study the structure of graphs that contain (as induced subgraphs) no Truemper configurations other than (possibly) universal wheels and twin wheels. We also study several subclasses of this class. We use our structural results to analyze the complexity of the recognition, maximum weight clique, maximum weight stable set, and optimal vertex coloring problems for these classes. Furthermore, we obtain polynomial -bounding functions for these classes.     

Ideal Free Distribution in Two Patches

In this paper, the formats of Julia sets for a class of nonlinear complex dynamic systems with variable coefficients were studied under certain conditions. For the complex dynamic systems in piecewise cases, we proposed some methods to control the forms of their Julia sets and stable domains analytically. What’s more, we illustrated that our methods worked well by computational simulations. Our work provides a better understanding about how to control the Julia sets of certain complex dynamic systems.     

纯奇点范畴中的Buchweitz定理

我们定义纯奇点范畴D_(psg)~b(R)为有界纯导出范畴D_(pur)~b(R)与纯投射模构成的有界同伦范畴K~b(■)的Verdier商,得到了纯奇点范畴D_(psg)~b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴■的一个充分必要条件.同时,还给出三角等价D_(psg)~b(R)≌D_(psg)~b(S)的充分条件,这里R和S都是环.     

多对一双方匹配市场中的最优化

在双方市场中定义的博弈概念，可以使市场同方参与者的收益同时达到最大．这种最优化存在的理论依据是选择匹配的稳定性．用博弈论的分析与证明方法研宄多对一双方匹配市场中的最优化．在替代偏好和LAD（Law of Aggregate Demend）偏好下，证明由企业作选择的选择函数一定是个稳定匹配，由工人做选择的选择函数也是一个稳定匹配．     

Multiple attractors in a Leslie–Gower competition system with Allee effects

We investigate asymptotic dynamics of the classical Leslie–Gower competition model when both competing populations are subject to Allee effects. The system may possess four interior steady states. It is proved that for certain parameter regimes both competing populations may either go extinct, coexist or one population drives the other population to extinction depending on initial conditions.     

Influence of Earthworms on the Sulfur Turnover in the Soil

Abstract

The effects of earthworm activity on the concentration and isotopic composition of total sulfur in soils was investigated using batch experiments. Two ecologically different lumbricid species, the anecic Lumbricus terrestris and the endogeic Aporrectodea caliginosa, were used. The earthworms were fed birch leaves, beech leaves, cattle manure or mixed plant litter. All food sources differed isotopically (δ³⁴S) from the soil (Parabraunerde). As a reference, one experiment was carried out without additional food.

The experimental results show, that both earthworm species influence the total S-content and the δ³⁴S-values in the soil by digestion of the different food sources. The differences in the total S-content of the earthworm tissues and in the S-isotopic composition of the casts can be attributed to the ecological differences between the earthworm species.     

Strategic measures in optimal control problems for stochastic sequences

Controlled discrete–time stochastic processes axe studied using the convex–analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.