Showing papers by "Chung Yuan Christian University published in 1983"

Acoustic Parameters of Commercial Plastics

Abstract: 264-268,1977. . _ and piezomagnetic materials and their function in transducers,” in Physical Acoustics, Vol. l A , W. P. Mason, Ed. Academic Press, 1964,pp. 188-189. (71 L. N. Bui, H. J. Shaw, and L. T. Zitelli, “Study of acoustic wave resonance in piezoelectric PVF2 film,” IEEE Trans. Sonics Ultruson.,vol. SU-24, pp. 331-336, Sept. 1977. [S] B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 1. New York: Wiley-Interscience, 1973, pp. 324-340. [ 91 D. A. Berlincourt and H.H.A. Krueger, “Behavior of piezoelectric ceramics under various environmental and operation conditions of radiating sonar transducers,” US. Navy J. Underwater Acoust., vol. 15, no. 2, pp. 266-283, 1965. [ 101 W. P. Leung and K. K. Yung, “Internal losses in polyvinylidene fluoride (F’VF2) ultrasonic transducers,”J. Appl. Phys., vol. 50, pp. 8031-8033,1980.

On polynomials taking small values at integral arguments II

Abstract: where F ∈ Q[X,Y ] is a given polynomial and T ∈ N is a variable growing to infinity. For a fixed integer x0, the quantity miny∈Z |F (x0, y)| (which was investigated already in [DZ]) gives a measure of the distance of the roots of F (x0, Y ) = 0 from the integers; the function SF (T ) expresses the behaviour of this distance as the first variable grows. Actually, SF (T ) implicitly appears in the statement of Hilbert’s Irreducibility Theorem; in fact most proofs of it (see e.g. [S]) reduce to showing the following: If for every integer x0 the equation F (x0, Y ) = 0 has an integral solution y, then there exists a polynomial f(X) ∈ Q[X] such that F (X, f(X)) = 0 identically. Note that the assumption of this statement may be reformulated as SF (T ) = 0 for all positive T . Hence, Hilbert’s theorem proves that either F (X, f(X)) = 0 for some polynomial f ∈ Q[X] or we have a lower bound SF (T ) ≥ c > 0 for all large T . Note that it may happen that SF (T ) is bounded, e.g. when there exists a polynomial f(X) ∈ Q[X], taking integral values on Z, such that F (X, f(X)) is a constant. However, Tung proves, among other things, that this is essentially the only case when SF (T ) is bounded. In fact, Tung has a much sharper conclusion. To state it, we first define, for an infinite set A ⊂ N, the symbol A(T ) = A ∩ [1, T ],

The Chemical Constitutents of Coniogramme Japonica (Thunb.) Diels

Abstract: β-Sitosterol, β-sitosteryl palmitate, β-sitosteryl-β-D-glucoside and cyclolaudenol were isolated from the rhizomes, long chain aliphatic esters and an UV stabilizer, octabenzone, were isolated from the leaves of Coniogramme japonica.