Complex point sources in probe-corrected cylindrical near-field scanning

A probe-corrected theory based on complex point sources is presented for computing the acoustic field of an arbitrary finite source from measurements of the near field on a cylindrical scanning surface. The complex point sources are used both as basis functions for the expansion of the field outside the scan cylinder and for the representation of the probe. The resulting probe-corrected formulas are considerably simpler than the standard probe-corrected formulas based on cylindrical waves. The new formulation makes simulations of near-field scanning systems much less computationally intensive than simulations based on standard theory. The complex point-source theory is validated through numerical examples involving a baffled circular piston transducer probe.     

Boundaries for algebras of holomorphic functions

Let A_u(B_G) be the Banach algebra of all complex valued functions defined on the closed unit ball B_G of a complex Banach space G which are uniformly continuous on B_G and holomorphic in the interior of B_G, endowed with the sup norm. A characterization of the boundaries for A_u(B_G) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129-151. The non-existence of the Shilov boundary for A_u(B_G) is also proved.     

复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.     

On the field of definition for modularity of CM elliptic curves

The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

Three-dimensional steady supersonic duct flow using Lagrangian formulation

In this paper, numerical simulation of three-dimensional supersonic flow in a duct is presented. The flow field in the duct is complex and can find its applications in the inlet of air-breathing engines. A unique streamwise marching Lagrangian method is employed for solving the steady Euler equations. The method was first initiated by Loh and Hui (1990) for 2-D steady supersonic flow computations and then extended to 3-D computation by the present authors Loh and Liou (1992). The new scheme is shown to be capable of accurately resolving complicated shock or contact discontinuities and their interactions. In all the computations, a free stream of Mach numberM=4 is considered.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

抗坏血酸同顺磁离子Mn~(2+)、Gd~(3+)络会的~(13)C NMR研究

该文用顺磁离子对其近邻~(13)C核的NMR吸收增宽效应,系统地研究了抗坏血酸在不同溶剂中对金属离子Mn~(2+)、Gd~(3+)的配合行为.在水溶液中,抗坏血酸可通过两种配合方式与Mn~(2+)作用,但与Gd~(3+)的作用只有一种稳定的结构.在水中抗坏血酸对金属的配位活性部位分别是1位羟基氧,3位离解的羟基氧和6位羟基氧.在DMSO中,3位羟基由于H~+对该基团的静电遮蔽而变得对金属离子Mn~(2+)表现为配位惰性,同时6位羟基配位活性较大增强.对Gd~(3+)来说,此时没有优势配位活性部位存在.文章还讨论了抗坏血酸在H_2O-DMSO混合溶剂中的~(13)C NMR谱及在DMSO中NaOH对其~(13)C NMR谱及其与金属络合结构的影响.     

Macroscopic non-equilibrium thermodynamics in dynamic calorimetry

What is really measured in dynamic calorimetric experiments is still an open question. This paper is devoted to this question, which can be usefully envisaged by means of macroscopic non-equilibrium thermodynamics. From the pioneer work of De Donder on chemical reactions and with other authors along the 20th century, the question is tackled under an historical point of view. A special attention is paid about the notions of frequency dependent complex heat capacity and entropy production due to irreversible processes occurring during an experiment. This phenomenological approach based on thermodynamics, not widely spread in the literature of calorimetry, could open significant perspectives on the study of macro-systems undergoing physico-chemical transformations probed by dynamic calorimetry.     

A hybrid-Trefftz element containing an elliptic hole

Much work on special elements that simplify geometrical modelling of structures containing holes, cracks and/ or inclusions has been reported extensively in the literature. This paper presents a hybrid-Trefftz element containing elliptic hole formulated using Hellinger–Reissner principle by employing trial functions based on the mapping technique and the Cauchy integral method. The element presented in this paper could be regarded as an improved formulation over Piltner [Special finite elements with holes and internal cracks, Int. J. Numer. Methods Eng. 21 (1985) 1471–1485] element because the chosen trail functions in this paper have provided relatively more stable solutions. The use of the element with other ordinary displacement-based finite elements has also yielded very accurate solutions even when very coarse meshes relative to the size of the elliptic hole have been used.     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.