Intrinsic gravitational regularization of quantum fields

One implication of maximal proper acceleration is an intrinsic regularization of quantum fields which depends on the universal gravitational constant. It also follows that the vacuum energy density, seen by any one observer, is finite.     

New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming

We give a new upper bound on the maximum size Aq(n,d) of a code of word length n and minimum Hamming distance at least d over the alphabet of q?3 letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in n using semidefinite programming. For q=3,4,5 this gives several improved upper bounds for concrete values of n and d. This work builds upon previous results of Schrijver [A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory 51 (2005) 2859-2866] on the Terwilliger algebra of the binary Hamming scheme.     

Existence of Solutions to General Quasiequilibrium Problems and Applications

A general quasiequilibrium problem is proposed including, among others, equilibrium problems, implicit variational inequalities, and quasivariational inequalities involving multifunctions. Sufficient conditions for the existence of solutions with and without relaxed pseudomonotonicity are established. Even semicontinuity may not be imposed. These conditions improve several recent results in the literature. This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. The authors are very grateful to Professor Schaible and the referees for their valuable remarks and suggestions which helped to improve remarkably the paper.     

A New Lower Bound Theorem for Combinatorial 2k-Manifolds

We prove a centrally-symmetric analogue of the generalized Heawood inequality, i.e. we prove a Lower Bound Theorem for combinatorial 2k-manifolds M whose convex hull is a centrally-symmetric simplicial polytope P under the additional assumptions that M is a subcomplex of the boundary complex of P and that M contains the k-skeleton of P. We also deduce a relation for the minimum number of vertices of a combinatorial 2k-manifold satisfying our Lower Bound. Received June 12, 1996 Revised June 9, 1997     

On the spread of the spectrum of a graph

Some new upper bounds and lower bounds are obtained for the spread λ₁−λ_n of the eigenvalues λ₁≥λ₂≥?≥λ_n of the adjacency matrix of a simple graph.     

Fixed points and quasi-equilibrium problems

A fixed-point theorem for compact acyclic maps defined on convex subsets of notnecessarily locally convex topological vector spaces is applied to the existence of solutions of quasi-equilibrium problems. Such existence theorems extend known ones which were used for unified approaches to quasi-variational inequalities in [1–5] and others.     

A Carleman Function and the Cauchy Problem for the Laplace Equation

We suggest an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit continuation formula and a regularization procedure for a solution to the Cauchy problem for the Laplace equation.     

Three-Loop β-Function of N=1 Supersymmetric Electrodynamics Regularized by Higher Derivatives

We calculate three-loop corrections to the effective action for N=1 supersymmetric electrodynamics regularized by higher derivatives. Using the obtained results, we investigate the anomaly problem in the considered model.     

空间声场全息重建的波叠加方法研究

提出了基于波叠加法的近场声场全息技术，并将其用于任意形状物体的声辐射分析.在声辐射计算问题中，边界元法是通过离散边界面上的声学和位置变量来实现，而波叠加方法则通过叠加辐射体内部若干个简单源产生的声场来完成.因而，基于波叠加法的声全息就不存在边界面上的参数插值和奇异积分等问题，而这些问题是基于边界元法的声全息所固有的.与基于边界元法的声全息相比较，基于波叠加法的声全息在原理上更易于理解，在计算机上更容易实现.实验结果表明：该种全息技术在重建声场时，具有令人满意的重建精度. 关键词： 声全息 逆问题 波叠加方法 正则化方法     

基于逆散射理论的地震波速度正则化反演

本文基于逆散射理论利用正则化有限差分对比源反演算法对地震波传播速度进行反演, 该方法是基于波动方程的频率域波形反演算法, 利用非线性共轭梯度法, 通过最小化目标优化函数不断迭代更新速度模型. 由于地球物理反演问题的病态性和不稳定性, 通过基于反演参数总变差的正则化处理, 使反演问题变为良性问题且算法具有较强的抗噪声干扰能力. 反演过程中使用了频率-空间域9点差分正演算子以及PML吸收边界条件. 与其他反演算法相比, 由于背景模型在反演迭代过程中保持不变, 可以避免在每次迭代过程中重新构造正演算子及矩阵分解等相关计算过程, 使得该算法非常适合于大规模三维反演计算. 此外, 本文采用基于MPI的并行计算, 进一步提高了反演计算的效率. 二维CSEG模型反演结果表明该方法可以反演得到高分辨率的地震波速度重建结果, 为地震勘探数据处理及解释提供准确的速度信息.