高频超声中带退化记忆项的MGT方程解的衰减估计北大核心CSCD

研究了高频超声应用中带无穷退化记忆项的Moore-Gibson-Thompson方程τu_(ttt)+α(x)u_(tt)-c^(2)Δu-bΔu_(t)+∫^(∞)_(0)g(s)div[a(x)▽u(t-s)]ds=0解的适定性和衰减速率,其中非负函数a(x)和α(x)是可退化的并满足a(x)+α(x)≥δ>0.该系统是由黏性热松弛流体中波传播模型的线性化而得到的.通过使用Faedo-Galerkin逼近和能量估计,证明了解的适定性.在适当的假设下,通过构造适当的李雅普诺夫泛函,建立了能量的指数或一般衰减结果.     

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Book reviews

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Notices bibliographiques

     

NMR-Spektren vontrans—Chalcon-oxim,-semicarbazon und-thiosemicarbazon und ihren cyclischen Isomeren (3,5-Diphenyl-2-isoxazolin und 1-substituierte 3,5-Diphenyl-2-pyrazoline)

Zusammenfassung Frühere Strukturvorschläge für dastrans-Chalcon-oxim, semicarbazon und thiosemicarbazon¹ werden mit Hilfe von NMR-Spektren richtiggestellt: Die sauer katalysierte Reaktion führt zwar zum Oxim, Semicarbazon und Thiosemicarbazon destrans-Chalcons; basische Katalysatoren bewirken dagegen eine interne Cyclisierung zu 3,5-Diphenyl-2-isoxazolin bzw. zu 1-substituierten 3,5-Diphenyl-2-pyrazolinen. Die Zuordnungen in den NMR-Spektren wurden durch Vergleich mittrans-Dypnon und seinem Semicarbazon getroffen.

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NMR spectra of trans-chalcone oxime, semicarbazone and thiosemicarbazone and their cyclic isomers (3,5-diphenyl-2-isoxazoline and 1-substituted 3,5-diphenyl-2-pyrazolines)

Earlier tentatively assigned structures fortrans-chalcone oxime, semicarbazone and thiosemicarbazone, resp., have been corrected by means of NMR spectra: open-chain structures have been found for the title compounds formed in the acid catalyzed reaction, whereas basic catalysts lead to intramolecular cyclization with formation of 3,5-diphenyl-2-isoxazoline and 1-substituted 3,5-diphenyl-2-pyrazolines resp. Assignments in the NMR spectra were made by comparison with those from authentic samples oftrans-dypnone and its semicarbazone.

     

A system for defining reference materials applicable to all food matrices

Recently the subcommittee on Food Definition of the AOAC INTERNATIONAL Task Force on Methods for Nutrition Labeling proposed a Food Matrix Organizational System [4] to systematically judge the applicability of collaboratively studied methods over a range of food matrices. This system describes a food matrix by its location in one of nine sectors in a triangle, with each point of the triangle defined as representing 100% and the opposite side representing 0% of the normalized contents of each of three major components of FAT, PROTEIN and CARBOHYDRATE. Foods falling within the same sector would be chemically similar and thus should behave in a similar analytical manner. This same scheme can be used to select one or two food matrices representing each sector, for development of a series of reference materials representing all foods. The list of 5250 foods contained in the USDA Nutrient Data Base for Standard Reference has been sorted and matched to this schematic to determine the scope of the selection process. In addition the list of foods in the USDA Data Base for Food Consumption Surveys has been examined. Results and progress of this selection process are reported.     

Neue Näherungsgleichung zur einheitlichen Berechnung von Wärmeübertragern

Zusammenfassung Es wird eine für alle Stromführungen einheitliche Näherungsgleichung mit drei oder vier anpaßbaren Parametern zur Berechnung des Korrekturfaktors für die mittlere logarithmische Temperaturdifferenz angegeben. Die anpaßbaren Parameter wurden für etwa 50 verschiedene Stromführungen durch Ausgleichsrechnung bestimmt. Die Genauigkeit der Gleichung ist für die Berechnung im praktisch wichtigen Bereich mehr als ausreichend.

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New approximate equation for uniform heat exchanger design

An approximate equation with three or four empirical parameters for the uniform calculation of the LMTD-correction factor of all heat exchanger configurations is proposed. The empirical parameters have been determined for about 50 different flow configurations using least squares estimation. The accuracy of the equation is more than sufficient for practical design purposes.

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Formelzeichen A Übertragungsfläche - a, b, c, d Parameter der Näherungsgleichung - Wärmekapazitätsstrom - F Korrekturfaktor für die logarithmische mittlere Temperaturdifferenz - k Wärmedurchgangskoeffizient - m, n Zahl der Durchgänge oder Einzelapparate - NTU Anzahl der Übertragungseinheiten (number of transfer units); NTU_i=kA/ _i - P dimensionslose Temperaturänderung - R Wärmekapazitätsstromverhältnis;R ₁=₁/₂;R ₂=₂/₁ - relativer Fehler - Mittelwert von NTU₁ und NTU₂ Indizes 1, 2 Stoffstrom 1, 2 - G Gegenstrom - s Schätzwert Herrn Prof. Dr.-Ing. E.h. K. Stephan zum 65. Geburtstag gewidmet.     

The finite element approximation of a coupled reaction-diffusion problem with non-Lipschitz nonlinearities

Summary. A coupled semilinear elliptic problem modelling an irreversible, isothermal chemical reaction is introduced, and discretised using the usual piecewise linear Galerkin finite element approximation. An interesting feature of the problem is that a reaction order of less than one gives rise to a "dead core" region. Initially, one reactant is assumed to be acting as a catalyst and is kept constant. It is shown that error bounds previously obtained for a scheme involving numerical integration can be improved upon by considering a quadratic regularisation of the nonlinear term. This technique is then applied to the full coupled problem, and optimal and error bounds are proved in the absence of quadrature. For a scheme involving numerical integration, bounds similar to those obtained for the catalyst problem are shown to hold. Received May 25, 1993 / Revised version received July 5, 1994     

Real-time onboard wind and windshear determination,part 2: Detection

This paper is concerned with windshear detection in connection with real-time wind identification (Ref. 1). It presents a comparative evaluation of two techniques, one based on the shear/downdraft factor and one based on the wind difference index. The comparison is done with reference to a particular microburst, that which caused the 1985 crash of Flight Delta 191 at Dallas-Fort Worth International Airport.The shear/downdraft factor has the merit of combining the effects of the shear and the downdraft into a single entity. However, its effectiveness is hampered by the fact that, in a real situation, the windshear is accompanied by free-stream turbulence, which tends to blur the resulting signal. In turn, this results in undesirable nuisance warnings if the magnitude of the shear factor due to free-stream turbulence is temporarily larger than that due to true windshear. Therefore, proper filtering is necessary prior to using the shear/downdraft factor in detection and guidance. One effective way for achieving this goal is to average the shear/downdraft factor over a specified time interval . The effect of on the average shear/downdraft factor is studied.     

Real-time onboard wind and windshear determination,part 1: Identification

Standard wind identification techniques employed in the analysis of aircraft accidents are post-facto techniques; they are processed after the event has taken place and are based on the complete time histories of the DFDR/ATCR data along the entire trajectory. By contrast, real-time wind identification techniques are processed while the event is taking place; they are based solely on the knowledge of the preceding time histories of the DFDR/ATCR data.In this paper, a real-time wind identification technique is developed. First, a 3D-kinematic approach is employed in connection with the DFDR/ATCR data covering the time interval preceding the present time instant. The aircraft position, inertial velocity, and accelerometer bias are determined by matching the flight trajectory computed from the DFDR data with the flight trajectory available from the ATCR data. This leads to a least-square problem, which is solved analytically every seconds, with / small.With the inertial velocity and accelerometer bias known, an extrapolation process takes place so as to predict the inertial velocity profile over the subsequent -subinterval. At the end of this subinterval, the extrapolated inertial velocity and the newly identified inertial velocity are statistically reconciled and smoothed. Then, the process of identification, extrapolation, reconciliation, and smoothing is repeated. Subsequently, the wind is computed as the difference between the inertial velocity and the airspeed, which is available from the DFDR data. With the wind identified, windshear detection can take place (Ref. 1).As an example, the real-time wind identification technique is applied to Flight Delta 191, which crashed at Dallas-Fort Worth International Airport on August 2, 1985. The numerical results show that the wind obtained via real-time identification is qualitatively and quantitatively close to the wind obtained via standard identification. This being the case, it is felt that real-time wind identification can be useful in windhsear detection and guidance, above all if the shear/downdraft factor signal is replaced by the wind difference signal (Ref. 1).This paper and its companion (Ref. 1) are based on Refs. 2–4.This research was supported by the Aviation Research and Education Foundation and by Texas Advanced Technology Program, Grant No. TATP-003604020.     

A Ramification Formula for Poincare Series, and a Hyperplane Formula for Modular Invariants

Let (A) be the coefficient of the second term in the Laurentexpansion about T 1 of the Poincare series p(A, t) of a gradedring A. For a finite extension of integrally closed domains,we prove a formula relating if (B), if (A) and the differentialexponent of B over A. As an application, we prove a conjectureof Carlisle and Kropholler which computes for rings of modularinvariants of finite groups in terms of stabilizers of hyperplanes.     

Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights

A classic 1970 paper of B. Muckenhoupt established necessary and sufficient conditions for weightedL _p convergence of Hermite series, that is, orthogonal expansions corresponding to the Hermite weight. We generalize these to orthogonal expansions for a class of Freud weightsW ²:=e ^–2Q , by first proving a bound for the difference of the orthonormal polynomials of degreen+1 andn–1 of the weightW ². Our identical necessary and sufficient conditions close a slight gap in Muckenhoupt's conditions for the Hermite weight at least forp>1. Moreover, our necessary conditions apply whenQ(x)=|x|, >1 while our sufficient conditions apply at least for =2,4,6,....Communicated by Vilmos Totik.