一个增算子不动点定理及其在Banach 空间非线性方程的应用

给出了Banach空间的一个增算子不动点定理,将这一定理应用到Banach空间的积分-微分方程,给出了一类积分-微分方程的连续可微最大解和连续可微最小解的存在性定理.     

A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.     

Poincaré-Hopf inequalities

In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.

     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

A parallel cell‐based DSMC method on unstructured adaptive meshes

A parallel DSMC method based on a cell‐based data structure is developed for the efficient simulation of rarefied gas flows on PC‐clusters. Parallel computation is made by decomposing the computational domain into several subdomains. Dynamic load balancing between processors is achieved based on the number of simulation particles and the number of cells allocated in each subdomain. Adjustment of cell size is also made through mesh adaptation for the improvement of solution accuracy and the efficient usage of meshes. Applications were made for a two‐dimensional supersonic leading‐edge flow, the axi‐symmetric Rothe's nozzle, and the open hollow cylinder flare flow for validation. It was found that the present method is an efficient tool for the simulation of rarefied gas flows on PC‐based parallel machines. Copyright © 2004 John Wiley & Sons, Ltd.     

Polyelectrolyte complexes. VI. Polycation structure,polyanion molar mass,and polyion concentration effects on complex nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate)

The formation and characterization of some interpolyelectrolyte complex (IPEC) nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate) (NaPAMPS), as a function of the polycation structure, polyanion molar mass, and polyion concentration, were followed in this work. Poly(diallyldimethylammonium chloride) and two polycations (PCs) containing (N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride) units in the backbone (PCA₅ and PCA₅D₁) were used as starting polyions. The complex stoichiometry, (n^?/n⁺)_iso, was pointed out by optical density at 500 nm (OD₅₀₀), polyelectrolyte titration, and dynamic light scattering. IPEC nanoparticle sizes were influenced by the polycation structure and polyanion molar mass only before the complex stoichiometry, which was higher for the more hydrophilic polycations (PCA₅ and PCA₅D₁) and for a higher NaPAMPS molar mass, and were almost independent of these factors after that, at a flow rate of the added polyion of about 0.28 mL × (mL PC)^?1 × h^?1. The IPEC nanoparticle sizes remained almost constant for more than 2 weeks, both before and after the complex stoichiometry, at low concentrations of polyions. NIPECs as stable colloidal dispersions with positive charges in excess were prepared at a ratio between charges (n^?/n⁺) of 0.7, and their storage colloidal stability, as a function of the polycation structure and polyion concentration (from 0.8 to ca. 7.8 mmol/L), was demonstrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2495–2505, 2004     

Large melting point depression of 2–3‐nm length‐scale nanocrystals formed by the self‐assembly of an associative polymer: Telechelic,pyrene‐labeled poly(dimethylsiloxane)

Large melting point depressions for organic nanocrystals, in comparison with those of the bulk, were observed in an associative polymer: telechelic, pyrene‐labeled poly(dimethylsiloxane) (Py‐PDMS‐Py). Nanocrystals formed within nanoaggregates of pyrenyl units that were immiscible in poly(dimethylsiloxane). For 5 and 7 kg/mol Py‐PDMS‐Py, physical gels resulted, with melting points exceeding 40 °C and with small‐angle X‐ray scattering peaks indicating that the crystals were nanoconfined, were 2–3 nm long, and contained roughly 18–30 pyrenyl dye end units. In contrast, 30 kg/mol Py‐PDMS‐PY was not a gel and exhibited no scattering peak at room temperature; however, after 12 h of annealing at ?5 °C, multiple melting peaks were present at 5–30 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3470–3475, 2004     

半自由声场的全息重建和预测实验研究

半自由声场环境下的声源重建和声场预测研究对声全息技术走向实际应用具有非常重要的意义.在提出基于分布源边界点法的半自由声场全息重建和预测方法的基础上，对此展开了实验研究.并将重建和预测的结果与常规方法重建和预测的结果进行了比较和讨论，说明了重建预测过程中反射声压的影响和考虑反射声压的必要性，证明了所提出方法在解决半自由声场环境下存在地面反射时的声源重建和声场预测时的有效性和准确性.还提出了采用奇异值截断滤波和Tikhonov正则化方法来削弱测量误差的影响，从而进一步优化了重建结果，提高了全息成像的可信度. 关键词： 声全息 半自由场 边界点 声辐射 反射声     

强流四脉冲电子束源实验研究

 为了进行强流多电子束源研究，对现有2MeV LIA 注入器进行了四脉冲改造，二极管脉冲电压约500kV。实验研究了天鹅绒阴极在四脉冲条件下的发射能力、传导电流负载效应以及阴极等离子体运动对阴极电子发射和束能量的影响。利用空间电荷限制流模型推算出阴极等离子体膨胀速率在1 ~4cm/μs之间。     

The Isoelectric Point and the Points of Zero Charge of Fe-Al-Mg Hydrotalcite-like Compounds

The relation of the isoelectric point (IEP) and the point of zero net charge (PZNC) of the hydrotalcite-like compounds was discussed. It was found that the IEP does not equal to the PZNC and the IEP is higher than the PZNC. The structural positive charges existing in the HTlc,which cause the difference between the IEP and the PZNC. The effects of the structural positive charges of the HTlc on its IEP and PZNC are the same as the specific adsorption of metal cations.