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21.
We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series. 相似文献
22.
本文考虑广义C-R组^[1](H)的解f=u iv jw∈C^2的一些性质,提出与之相关的两个边值问题,用积分方程方法和调和函数性质证明了边值问题解的存在唯一性,并写出解的积分表达式. 相似文献
23.
V. S. Gorelik P. P. Sverbil' A. B. Fadyushin V. V. Vasil'ev 《Journal of Russian Laser Research》2004,25(1):54-63
A possibility of application of semiconductor lasers of the visible range as exciting sources for Raman spectroscopy is studied. An experimental set-up for measuring Raman spectra of polycrystalline dielectrics and broad-gap semiconductors excited by a semiconductor laser with a wavelength of 640 nm was created. The conditions under which the spectral width of the lasing line of a semiconductor laser was within 10-3 cm-1 in the continuous mode with a power of 10 mW are realized. The characteristics of various types of exciting sources used in Raman spectroscopy are compared. The results of studies of the characteristic Raman spectra excited with a semiconductor laser in polycrystalline sulfur are presented. 相似文献
24.
Yuri M. Boiko Anders Bach Jørgen Lyngaae-Jørgensen 《Journal of Polymer Science.Polymer Physics》2004,42(10):1861-1867
Films of amorphous polystyrene (PS) with a weight-average molecular weight (Mw) of 225 × 103 g/mol were bonded in a T-peel test geometry, and the fracture energy (G) of a PS/PS interface was measured at the ambient temperature as a function of the healing time (th) and healing temperature (Th). G was found to develop with (th)1/2 at Th = Tg-bulk − 33 °C (where Tg-bulk is the glass-transition temperature of the bulk sample), and log G was found to develop with 1/Th at Tg-bulk − 43 °C ≤ Th ≤ Tg-bulk − 23 °C. The smallest measured value of G = 1.4 J/m2 was at least one order of magnitude larger than the work of adhesion required to reversibly separate the PS surfaces. These three observations indicated that the development of G at the PS/PS interface in the temperature range investigated (<Tg-bulk) was controlled by the diffusion of chain segments feasible above the glass-transition temperature of the interfacial layer, in agreement with our previous findings for fracture stress development at several polymer/polymer interfaces well below Tg-bulk. Close values of G = 8–9 J/m2 were measured for the symmetric interfaces of polydisperse PS [Mw = 225 × 103, weight-average molecular weight/number-average molecular weight (Mw/Mn) = 3] and monodisperse PS (Mw = 200 × 103, Mw/Mn = 1.04) after healing at Th = Tg-bulk − 33 °C for 24 h. This implies that the self-bonding of high-molecular-weight PS at such relatively low temperatures is not governed by polydispersity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1861–1867, 2004 相似文献
25.
Wolfgang Knirsch 《Mathematische Nachrichten》2004,265(1):15-23
On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
26.
Clemens Heuberger 《Periodica Mathematica Hungarica》2004,49(2):65-89
We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bases q, similar results are given which complement those given in [6]. 相似文献
27.
Tracing is a method of assigning flows in an electricity network to particular generators and loads, assuming perfect mixing at each node. It can be used to assign costs to transmission users. We show that the resulting allocation is equal to the Shapley value of an equivalent co-operative game. 相似文献
28.
The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be zero. The value function is shown to be solution to the Bellman equation in a weak sense; however the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls. 相似文献
29.
30.
汪更生 《数学物理学报(B辑英文版)》2005,25(1):7-22
This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper. 相似文献