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391.
Ohne Zusammenfassung 相似文献
392.
393.
394.
Ohne Zusammenfassung 相似文献
395.
396.
Ohne Zusammenfassung 相似文献
397.
We consider the differential operators Ψ
k
, defined by Ψ1(y) =y and Ψ
k+1(y)=yΨ
k
y+d/dz(Ψ
k
(y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ
k
F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z
2+β
z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ
k
(F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ
k
(f
′/f) =f
(k)/f, we deduce in particular that iff andf
(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f
′/f :f ∈F} is normal.
The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999,
and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank
Günter Frank for helpful discussions. 相似文献
398.
399.
Fundamentals of the direct measurement of sound intensity and practical applications 总被引:1,自引:0,他引:1
Sound intensity is a measure of the magnitude and direction of the flow of sound energy. Developments in sound intensity measurement capabilities in the last quarter century have occurred because of several reasons. The main ones include the derivation of the cross-spectral formulation for sound intensity and developments in digital signal processing. This paper begins with a brief historical introduction of sound intensity measurements. Then elementary theory for sound intensity is presented. A section on sound intensity measurements is then included. The next section of the paper discusses sources of measurement error; the major sources of error are described in some detail. The paper continues with a discussion of the main applications of sound intensity measurements: sound power determination, noise source identification, and transmission loss measurements. The paper concludes with a discussion of ISO and ANSI intensity related standards and relevant references. 相似文献
400.
Pascher W. Den Besten J. H. Caprioli D. Leijtens X. Smit M. van Dijk R. 《Optical and Quantum Electronics》2003,35(4-5):453-464
Based on a rigorous vectorial analysis, a fast travelling-wave Mach–Zehnder modulator is modelled and designed. The cross-section of the semiconductor layer stack and the lossy electrodes are carefully modelled using the method of lines in order to investigate propagation characteristics, velocity and losses. This yields an accurate microwave and optical field distribution to explain the behaviour of the component. In order to enhance the modulation efficiency, design curves are derived and the cross-sectional dimensions for minimum microwave loss are determined. The loss of the optimized modulator agrees very well with small-signal measurements up to 40 GHz and HFSS simulations. The layerstack of the fabricated device is suitable for integration with InP multi-wavelength lasers. 相似文献