BOOK REVIEWS a fluid-filled tube in which the tube can be elastic or viscoelastic but the fluid is assumed to be incompressible and inviscid. All articles are very mathematically and analytically oriented. Nevertheless, the articles cover a fairly wide range of wave propagation phenomena in viscoelastic media. In view of the fact that there are not many books available on viscoelasticity and even fewer on wave propagation in viscoelastic media, the appearance of this volume is welcome. It would serve as a useful reference for those who want to venture into this field.
The equations relating the magnetic anomalies to the shape and susceptibility of a body are nonlinear with respect to the coordinates describing the shape. Therefore, iterative procedures must be used to obtain least‐squares estimates of the body coordinates. One method in general use for obtaining nonlinear least‐squares estimates is the Gauss method. This method often fails when the initial values for the structures and susceptibilities do not adequately account for the magnetic anomalies. Another method known as the steepest descent method generally converges to a solution; however, a large number of iterations are required. A method suggested by Marquardt (1963) incorporates the best features of the previous methods. In this paper the Marquardt method is applied to the interpretation of magnetic anomalies. For this purpose the two‐dimensional formulas derived by Talwani and Heirtzler (1964) are used to relate the geometry of a body to the resulting magnetic anomalies. The procedure efficiently controls the amount of change made to an interpreted structure at each iteration, assuring rapid convergence to a solution which satisfies the observed data better in the least‐squares sense than does the initial solution. The method is applied to representative problems.
In recent years there has been considerable interest in the effect of variations in activities of xenobiotic-metabolizing enzymes on cancer incidence. This interest has accelerated with the characterization of human enzymes, both those involved in activation and detoxication, and the development of methods for analyzing genetic polymorphisms. However, progress in epidemiology has been slow and the contributions of polymorphisms to risks from individual chemicals and mixtures are often controversial. A series of studies is presented to show the complexities encountered with a single chemical, aflatoxin B1 (AFB,). AFB1 is oxidized by human cytochrome P450 enzymes to several products. Only one of these, the 8,9-exo-epoxide, appears to be mutagenic and the others are detoxication products. P450 3A4, which can both activate and detoxicate AFB1, is found in the liver and the small intestine. In the small intestine, the first contact after oral exposure, epoxidation would not lead to liver cancer. The (nonenzymatic) half-life of the epoxide has been determined to be approximately 1 sec at 23°C and neutral pH. Although the half-life is short, AFB1-8,9-exo-epoxide does react with DNA and glutathione S-transferase. Levels of these conjugates have been measured and combined with the rate of hydrolysis in a kinetic model to predict constants for binding of the epoxide with DNA and glutathione S-transferase. A role for epoxide hydrolase in alteration of AFB1 hepatocarcinogenesis has been proposed, although experimental evidence is lacking. Some inhibition of microsome-generated genotoxicity was observed with rat epoxide hydrolase; further information on the extent of contribution of this enzyme to AFB, metabolism is not yet available. Environ Health Perspect 1 04(Suppl 3): 557-562 (1996)
Abstract. The Chow variety is a parameter space for effective algebraic cycles on P n (or A n ) of given dimension and degree. We construct its analog for differential algebraic cycles on A n , answering a question of [12]. The proof uses the construction of classical algebro-geometric Chow varieties, the theory of characteristic sets of differential varieties and algebraic varieties, the theory of prolongation spaces, and the theory of differential Chow forms. In the course of the proof several definability results from the theory of algebraically closed fields are required. Elementary proofs of these results are given in the appendix.
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