ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD

The author gives an optimum estimate of the first eigenvalue of a compact Riemannian manifold. It is shown that let M be a compact Riemannian manifold, then the first eigenvalue λ_1 of the Laplace operator of M satisfies α_1+max{0,-(n-1)K}≥π~2/d~2 where d is the diameter of M and (n-1)K is the negative lower bound of the Ricci curvature of M.     

Influence of preparation methods on structure and properties of PA6/PA66 blends: A comparison of melt‐mixing and in situ blending

The blends composed of polyamide 6 (PA6) and polyamide 66 (PA66) were obtained using two different preparation methods, one of which was the melt‐mixing through a twin‐screw extruder and the subsequent injection molding; and the other, the in situ blending through anionic polymerization of ε‐caprolactam in the presence of PA66. For the former, there existed a remarkable improvement in toughness but a drastic drop in strength and modulus; however, for the latter, a reverse but less significant trend of mechanical properties change appeared. Various characterizations were conducted, including the analyses of crystalline morphology, crystallographic form, and crystallization and melting behaviors using polarized optical microscopy (POM), wide‐angle X‐ray diffraction (WAXD), and differential scanning calorimetry (DSC), respectively; observation of morphology of fractured surface with scanning electron microscope (SEM); measurement of glass transition through dynamic mechanical analysis (DMA); and the intermolecular interaction as well as the interchange reaction between the two components by Fourier transform infrared spectrometry (FT‐IR) and ¹³C solution NMR. The presence and absence of interchange reaction was verified for the in situ and melt‐mixed blends, respectively. It is believed that the transreaction resulted in a drop in glass transition temperature (T_g) for the in situ blends, contrary to an increase of T_g with increasing PA66 content for the melt‐mixed ones. And the two kinds of fabrication methods led to significant differences in the crystallographic form, spherulite size and crystalline content and perfection as well. Accordingly, it is attempted to explain the reasons for the opposite trends of changes in the mechanical properties for these two blends. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1176–1186, 2007     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

General Information

In this paper, we propose and analyze an SQP-type method for solving linearly constrained convex minimization problems where the objective functions are too complex to be evaluated exactly. Some basic results for global convergence and local superlinear convergence are obtained according to the properties of the approximation sequence. We illustrate the applicability of our approach by proposing a new method for solving two-stage stochastic programs with fixed recourse.     

The solution existence of general variational inclusion problems

We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.     

热等离子体裂解天然气制备C2烃

采用氮气热等离子体来裂解天然气制备乙炔乙烯,着重研究了天然气转化率和乙炔、乙烯收率随氮气流量和天然气流量的变化.结果表明,天然气流量与氮气流量之比为11时,可得到较好的结果.当等离子体功率为15kW、天然气流量为3Nm3*h-1、氮气流量为3Nm3*h-1时得到最好的结果.这时天然气转化率为57%,乙炔、乙烯的收率分别为34%和9%;乙炔在反应气中的体积浓度为7.5%,与部分氧化法相似;扣除不参加反应的氮气,乙炔在气相产品中的体积浓度为13.2%,与热力学平衡计算结果基本符合.     

High-performance liquid chromatographic detection of hydroxylated benzoic acids as an indirect measure of hydroxyl radical in heart: its possible link with the myocardial reperfusion injury.

The present report describes a method suitable for the indirect assay of hydroxyl radical (OH.), which is likely to be produced during reperfusion of ischemic myocardium. Isolated rat heart perfused by the Langendorff technique was subjected to 30 min of ischemia, followed by 30 min of reperfusion. Salicylic acid (2 mM) was added to the perfusion circuit to trap any OH. radical generated during the experiment. 2,5- and 2,3-dihydroxybenzoic acids (hydroxylated products of salicylic acid) were identified by authentic standards as well as by pure OH.-generating system using high-performance liquid chromatography with electrochemical detection. In addition to serving as a chemical trap for the detection of OH., salicylate attenuated myocardial reperfusion injury as evidenced by reduced formation of creatine kinase, decreased lipid peroxidation, and improved myocardial contractile functions during reperfusion. These results thus provide direct evidence for the presence of OH. in heart and link it to the myocardial reperfusion injury.     

An eulerian trail traversing specified edges in given order

The following results are proved in this paper. Let G be a 2k-edge-connected eulerian graph. (i) For every set {e₁, e₂, ?, e_2k+1} ? E(G) there is an eulerian trail T of the form e₁, e₂, ?, e_2k+1, ?. (ii) For every set E* = {e₁, e₂, ?, e_k} ? E(G) there is an eulerian trail T = e₁, ?, e₂, ?, e_k, ? in which the elements of E* are traversed in accordance with a prescribed orientation. © 1995 John Wiley & Sons, Inc.     

Simplified analytic solutions and a novel fast algorithm for Yb-doped double-clad fiber lasers

In this paper, continuous wave Yb³⁺-doped double-clad fiber lasers (DCFLs) with linear-cavity are investigated theoretically and numerically using the rate equations. Under the steady state conditions, the simplified analytic solutions of Yb³⁺-doped DCFLs under considering the scattering loss are deduced in the strongly pump condition. Compared with the known analytic solutions in published literatures, our analytic solutions are more accurate, especially, at higher reflectivity of output mirror. In addition, a fast and stable algorithm based on the Newton-Raphson method is proposed to simulate numerically Yb³⁺-doped DCFLs. The results by simplified analytic solutions are in good agreement with those by the numerical simulation. Moreover, we have performed the optimization of an Yb³⁺-doped DCFL using the simplified analytic solutions and the numerical simulations, respectively.