电路暂态过程的教学研究

从解法、解的形态和时间常数三个方面研究了电路暂态过程的教学。     

Exact solution of external tangential contact problem for a transversely isotropic elastic half-space

Summary  The following mixed boundary-value problem for a transversely isotropic elastic half-space is considered. Arbitrary tangential displacements are prescribed at the exterior of a circle, while the interior of the circle is free of tangential stress, and the normal stress vanishes all over the boundary. The governing integral equation is solved exactly, in closed form, and in terms of elementary functions. The method of continuation of solutions previously published by the author has been used here. Several examples are considered. No similar results has been reported before, even in the case of an isotropic body. Received 8 May 2000; accepted for publication 20 July 2000     

A new rational auxiliary equation method and exact solutions of a generalized Zakharov system

A new rational auxiliary equation method for obtaining exact traveling wave solutions of constant coefficient nonlinear partial differential equations of evolution is proposed. Its effectiveness is evinced by obtaining exact solutions of a generalized Zakharov system, some of which are new. It is shown that the G^′/G and the generalized projective Ricatti expansion methods are special cases of the auxiliary equation method. Further, due the solutions obtained, four other new and practicable rational methods are deduced.     

A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.     

Comment on the paper: “Forced oscillation of certain neutral hyperbolic equations with continuous distributed deviating arguments” [Math. Comput. Modeling 49 (2009) 1211–1220]

In recent years, many results on oscillation criteria of second-order nonlinear neutral delay differential equations with distributed deviating argument have been obtained, but some of these criteria are incorrect due to a mistake in a crucial auxiliary result. We give two counterexamples.     

THE ANALYTICAL SOLUTION FOR SEDIMENT REACTION AND DIFFUSION EQUATION WITH GENERALIZED INITIAL-BOUNDARY CONDITIONS

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Service stage Petri net models with product form solution

A class of service stage Petri net models whose equilibrium probabilities satisfy local balance equations is presented. Examples of their applicability include bus oriented multiprocessor interconnections, the classical dining philosophers problem and the alternating bit protocol. The natural topological space for embedding the state transition lattice for this class of SSPN is shown to be a multidimensional toroidal manifold.     

Thallium(III) coordination compounds: chemical information from 205Tl NMR longitudinal relaxation times

²⁰⁵Tl longitudinal relaxation rate measurements were performed on several thallium(III) complexes with the composition Tl(OH)_n(H₂O)_6?n^(3?n)+ (n = 1,2), Tl(Cl)_n(H₂O)_m?n^(3?n)+, Tl(Br)_n(H₂O)_m?n^(3?n)+ (m = 6 for n = 1–2, m = 5 for n = 3, m = 4 for n = 4), Tl(CN)_n(H₂O)_m?n^(3?n)+ (m = 6 for n = 1–2, m = 4 for n = 3–4) in aqueous solution, at different magnetic fields and temperatures. ¹³C and ²D isotopic labelling and ¹H decoupling experiments showed that the contribution of the dipolar relaxation path is negligible. The less symmetric lower complexes (n < 4) had faster relaxation rate dominantly via chemical shift anisotropy contribution which depended on the applied magnetic field: T₁ values are between 20 and 100 ms at 9.4 T and the shift anisotropy is Δσ = 1000–2000 ppm. The tetrahedral complexes, n = 4, relax slower; their T₁ is longer than 1 s and the spin–rotation mechanism is probably the dominant relaxation path as showed by a temperature dependence study. In the case of the TlCl₄^? complex, presumably a trace amount of TlCl₅^2? causes a large CSA contribution, 300 ppm. Since the geometry and the bond length for the complexes in solution are known from EXAFS data, it was possible to establish a correlation between the CSA parameter and the symmetry of the complexes. The relaxation behaviour of the Tl–bromo complexes is not in accordance with any known relaxation mechanism. Copyright © 2002 John Wiley & Sons, Ltd.     

Novel method for simultaneous measurement of film thickness and mass fraction of urea–water solution

Quantitative knowledge of the film thickness and mass fraction of the urea-water solution is very crucial in many practical applications. Film thickness or mass fraction can only be determined individually by conventional measurement techniques. We develop a novel measurement method to measure the film thickness and mass fraction of ure~water solution simultaneously. The absorption coefficients of urea-water solution （5 50 wt%） are measured, a pair of optimized wavelengths is then chosen to achieve high measurement sensitivity. Cross validation is also performed and uncertainties of the technique are smaller than 0.68% for thickness measurements and 1.86% for mass fractions.     

High‐mobility solution‐processed zinc oxide thin films on silicon nitride

A high effective electron mobility of 33 cm² V^–1 s^–1 was achieved in solution‐processed undoped zinc oxide (ZnO) thin films. The introduction of silicon nitride (Si₃N₄) as growth substrate resulted in a mobility improvement by a factor of 2.5 with respect to the commonly used silicon oxide (SiO₂). The solution‐processed ZnO thin films grown on Si₃N₄, prepared by low‐pressure chemical vapor deposition, revealed bigger grain sizes, lower strain and better crystalline quality in comparison to the films grown on thermal SiO₂. These results show that the nucleation and growth mechanisms of solution‐processed films are substrate dependent and affect the final film structure accordingly. The substantial difference in electron mobilities suggests that, in addition to the grain morphology and crystalline structure effects, defect chemistry is a contributing factor that also depends on the particular substrate. In this respect, interface trap densities measured in high‐κ HfO₂/ZnO MOSCAPs were about ten times lower in those fabricated on Si₃N₄ substrates. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)