ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

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Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.

     

Effect of induced shielding current transmission in longitudinal direction on levitation force of melt grown single-domain YBa_2Cu_3O_(7-x) cylindrical superconductor

YBa2Cu3O7-x (YBCO) bulk is one of the most important high temperature superconducting materials for magnetic levitation applications, because it has a high magnetic irreversibility field Hirr at liquid nitrogen temperature, and can grow into large grains. The levitation force of YBCO bulk is proportional to the critical current density (Jc) and grain radius (r)[1], so higher Jc and r are appreciated for YBCO bulks to achieve higher levitation force. Now single-domain YBCO bulks up to s…     

A Triangle Inequality for Measurement

We introduce the triangle inequality for measurement. This is a property that when satisfied by a measurement enables one to construct a metric on the set of elements with measure zero that yields the relative Scott topology. The naturality of this construction permits a categorical solution to the model problem in domain theory for locally compact metric spaces. The first time such a solution has been achieved.     

Substructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions

This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell's equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddle-point systems so that they can be solved by some existing preconditioned iterative methods. Then some substructuring preconditioners are proposed, with very simple coarse solvers, for the augmented saddle-point systems. With the preconditioners, the condition numbers of the preconditioned systems are nearly optimal; namely, they grow only as the logarithm of the ratio between the subdomain diameter and the finite element mesh size.

     

Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.     

Effects of poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] on the charge distributions of low‐density polyethylene/polystyrene blends

The effect of the triblock copolymer poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] (SEBS) on the formation of the space charge of immiscible low‐density polyethylene (LDPE)/polystyrene (PS) blends was investigated. Blends of 70/30 (wt %) LDPE/PS were prepared through melt blending in an internal mixer at a blend temperature of 220 °C. The amount of charge that accumulated in the 70% LDPE/30% PS blends decreased when the SEBS content increased up to 10 wt %. For compatibilized and uncompatibilized blends, no significant change in the degree of crystallinity of LDPE in the blends was observed, and so the effect of crystallization on the space charge distribution could be excluded. Morphological observations showed that the addition of SEBS resulted in a domain size reduction of the dispersed PS phase and better interfacial adhesion between the LDPE and PS phases. The location of SEBS at a domain interface enabled charges to migrate from one phase to the other via the domain interface and, therefore, resulted in a significant decrease in the amount of space charge for the LDPE/PS blends with SEBS. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2813–2820, 2004     

X波段六腔渡越管振荡器的高频特性研究

 从麦克斯韦方程出发，采用时域有限差分法（FDTD）和离散傅里叶变换（DFFT）相结合的方法，通过数值计算得出了六腔开放式谐振腔中前四个谐振频率和场分布，计算出的谐振频率与实验测量结果基本相同。比较了开放腔和封闭腔谐振频率，验证了TEM波吸收边界条件，并在实际编程计算中得以应用。计算结果为六腔渡越管振荡器的机理研究提供了依据。     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.