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1.
In this work we study nonnegativity and positivity of a discrete quadratic functional with separately varying endpoints. We introduce a notion of an interval coupled with 0, and hence, extend the notion of conjugate interval to 0 from the case of fixed to variable endpoint(s). We show that the nonnegativity of the discrete quadratic functional is equivalent to each of the following conditions: The nonexistence of intervals coupled with 0, the existence of a solution to Riccati matrix equation and its boundary conditions. Natural strengthening of each of these conditions yields a characterization of the positivity of the discrete quadratic functional. Since the quadratic functional under consideration could be a second variation of a discrete calculus of variations problem with varying endpoints, we apply our results to obtain necessary and sufficient optimality conditions for such problems. This paper generalizes our recent work in [R. Hilscher, V. Zeidan, Comput. Math. Appl., to appear], where the right endpoint is fixed. 相似文献
2.
Grishin D. F. Semyonycheva L. L. Telegina E. V. Smirnov A. S. Nevodchikov V. I. 《Russian Chemical Bulletin》2003,52(2):505-507
Organometallic compounds Cp2TiCl2, (EtC5H4)2NbCl2, and (PriC5H4)2WCl2 were assessed as additives that control polymer chain growth in the polymerization of methyl methacrylate. In the presence of compounds mentioned in amounts comparable with that of the initiator, a uniform process with no gel-effect occured and respective linear increase in the molecular weight of the polymer up to high degrees of the monomer conversion was observed. 相似文献
3.
The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions.
In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation
solutions.
Accepted 27 February 1996 相似文献
4.
5.
In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128. 相似文献
6.
Ming-Chieh Lin Der-San Chuu 《Physica E: Low-dimensional Systems and Nanostructures》2003,18(4):421-428
A simple time-dependent model is presented to investigate lifetimes of the quasibound states in coupled quantum wells (CQWs). The transfer matrix approach is employed to discretize the conduction-band profile of the heterostructure and form a dispersion equation whose zeros correspond to the complex eigenenergies. Both the bound and quasibound states are extracted numerically in the complex plane by Newton's method. The lower and higher well subbands are found to have negative and positive energy shift, respectively, as following the no level crossing theorem. Besides, the decay rate of the quasibound state is approximately proportional to the absolute energy shift. The quasibound states, which have larger energy shift, have shorter lifetime and decay more quickly. Furthermore, the differences in lifetime between the quasibound states in CQWs can be easily realized as all the wave functions are specially adjusted to form the relative probability density distributions. 相似文献
7.
教学质量的时齐马尔可夫链评估法 总被引:1,自引:0,他引:1
本文研究了教学质量评估中的一种定量分析方法──时齐马尔可夫链评估法.阐明了这种方法的理论依据及其实施程序、并指出它较之其他教学质量评估法更显合理. 相似文献
8.
Transfer matrix approach of vibration isolation analysis of periodic composite structure 总被引:1,自引:0,他引:1
Wang Yong Huang Qibai Zhou Minggang Xu Zhisheng 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(7):461-471
The transmission properties of elastic waves propagating in a three-dimensional composite structure embedded periodically
with spherical inclusions are analyzed by the transfer matrix method in this paper. Firstly, the periodic composite structures
are divided into many layers, the transfer matrix of monolayer structure is deduced by the wave equations, and the transfer
matrix of the entire structure is obtained in the case of boundary conditions of displacement and stress continuity between
layers. Then, the effective impedance of the structure is analyzed to calculate its reflectivity and transmissivity of vibration
isolation. Finally, numerical simulation is carried out; the experiment results validate the accuracy and feasibility of the
method adopted in the paper and some useful conclusions are obtained.
Project (No. 50075029) supported by the National Natural Science Foundation of China. 相似文献
9.
Generalized KKM Type Theorems in FC-Spaces with Applications (I) 总被引:1,自引:0,他引:1
Xie Ping Ding 《Journal of Global Optimization》2006,36(4):581-596
The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper. 相似文献
10.
Due to the Meissner effect, a permanent magnet is levitated, when released above a high temperature superconductor. When there is an inhomogeneous temperature field around the magnet, the magnet might start to oscillate with increasing amplitude until it remains in a continuous rotation. A mathematical model for the described effect is presented which couples heat transfer and electromagnetic forces with the equation of motion, yielding to a multiphysics task. In a detailed analysis it is found, that the torque which drives the rotation of the magnet, is explicitly given in terms of Bessel functions and the Fourier coefficients of order zero and one of the temperature field of the surrounding air. 相似文献