m次幂等矩阵的等价条件

利用矩阵的秩和齐次线性方程组解空间的维数,给出了m(m≥2)次幂等矩阵的一些等价条件,推广了2,3次幂等矩阵的相应结果.此外,所获结果还给推广到了m次幂等线性变换中.     

一类带参数的半线性椭圆型方程边值问题的可解性

本文利用上、下解方法和不动点定理研究了一类带参数的半线性椭圆型方程边值问题，根据参数的不同情况，分别得出了解的存在性、唯一性和不存在性。     

Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems

We consider a general Euler-Korteweg-Poisson system in R ³, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-in-time weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which the Cauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Székelyhidi.     

A Coulomb-related family of potentials having zero-energy bound states

We propose here a new large class of singular central potentials having zero-energy bound states for many values of angular momenta. The potentials are shown to be closely related to the standard attractive Coulomb interaction. Some of them admit the E≠0$E\ne 0$ bound states as well. A quantum–classical correspondence is also discussed.     

Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.     

Case Studies With Mathematical Modeling of Free-Radical Multi-Component Bulk/Solution Polymerizations: Part 1

In part 1 of this series of two extensive overviews of multi-component polymerization case studies, we present mathematical modelling results with experimental confirmations. The case studies are from free-radical, bulk and/or solution polymerizations, covering the range from homo- to hexa-polymerization at both regular and elevated temperature levels, i.e., without and with possible depropagation steps. The model eventually tackles complex polymerization features, ranging from conversion-time histories to more esoteric multi-component composition and/or sequence length profiles. Part 2 of the series will describe more complicated situations with depropagation and composition control policies, all relying solely on a unique monomer/polymer database of physico-chemical properties and other characteristics, with no further parameter adjustment. These database items will be cited in tables in part 2 of the series.     

Synthesis of Stimuli-responsive Nanoparticles by Solution Polymerization

In this study, stimuli-responsive nanoparticles were prepared by solution polymerization. Two synthesis routes are proposed to synthesize the particles, the monomer route and the polymer/monomer route. For the monomer route, pH and thermal sensitive nanoparticles were synthesized from acrylic acid and N-isopropylacrylamide. For the polymer/monomer route, the pH sensitive nanoparticles were synthesized from chitosan and acrylic acid. The effect of reaction time, initiator concentration and agitation rate on the particle size and the size distribution were investigated. The stimuli-responsive nanoparticles could be directly blended with other polymers to prepare stimuli-responsive functional membranes.     

A New Polymer Flooding Agent Prepared Through Intermacromolecular Complexation

Abstract

This paper reports a new polymer flooding agent used for enhanced oil recovery (EOR), poly(acrylamide-acrylic acid) [P(AM-AA)]/poly(acrylamide-dimethyldiallylammonium chloride) [P(AM-DMDAAC)] polyelectrolyte complex. The solution viscosity of prepared P(AM-AA)/P(AM-DMDAAC) complex is enhanced due to the strong interaction between the two oppositely charged copolymers, i.e., P(AM-AA) and P(AM-DMDAAC), which were prepared through radical copolymerization. The ionic content could be controlled by changing the reaction conditions. The structures of the two copolymers were characterized through FT-IR, ¹H NMR, and acidic and precipitation titration. The formation as well as the factors affecting the P(AM-AA)/P(AM-DMDAAC) polyelectrolyte complex were investigated by means of viscosity measuring and light transmittance testing. The experimental results show that the composition of the copolymers, the pH value, and the concentration of the polymer solutions have remarkable effects on the formation of P(AM-AA)/P(AM-DMDAAC) polyelectrolyte complex and the solution viscosity. When DMDAAC content in P(AM-DMDAAC) is 3.2 mol%, AA content in P(AM-AA) is 48–58 mol%, the weight ratio of P(AM-AA) to P(AM-DMDAAC) is 70/30–30/70, the pH value of the solution is 6–10, and the concentration of solution is 1000–3500 ppm, then a homogeneous solution of P(AM-AA)/P(AM-DMDAAC) poly-electrolyte complex could be obtained which exhibits a much higher solution viscosity compared with its components.     

Effect of pH on Poly(acrylic acid) Solution Polymerization

The free-radical redox-initiated aqueous solution polymerization of fully and partially neutralized acrylic acid was carried out at room temperature under full exposure to air. The effect of neutralization degree on the polymerization rate and product properties was studied. Increasing neutralization of the reaction mixture with sodium hydroxide resulted in greater conversion of acrylic acid to sodium acrylate. The rate of polymerization, determined from a gravimetric off-line water removal technique, was shown to decrease significantly with decreasing degree of neutralization. Molecular weight also decreased with decreasing degree of neutralization. The glass transition temperature and hydrophilicity of the polymer product decreased with increasing degree of neutralization. In-line infrared monitoring was also used to monitor the reaction progress and was shown to be an effective tool for this purpose.     

Nanoalloy Based on Clays: Intercalated‐Exfoliated Layered Silicate in High Performance Elastomer

A novel method is described for the preparation of nanocomposites comprising a high performance rubber for tire application and layered silicates clay. In this work nanocomposites of solution‐styrene butadiene rubber (S‐SBR) with montmorillonite layered silicate were prepared with carboxylated nitrile rubber (XNBR), a polar rubber, as a compatibilizer. A sufficient amount of organomodified layered silicate was loaded in carboxylated nitrile rubber (XNBR) and this compound was blended as a master batch in the S‐SBR. Mixed intercalated/exfoliated morphologies in the nanocomposite are evinced by X‐ray diffraction measurements and transmission electron microscopy. Dynamic mechanical analysis also supports the compatibility of the composites. A good dispersion of the layered silicate in the S‐SBR matrix was reflected from the physical properties of the nanocomposites, especially in terms of tensile strength and high elongation properties.