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11.
12.
The Hawking radiation of Dirac particles in an arbitrarily rectilinearly accelerating Kinnersley black hole with electromagnetic charge and cosmological constant is investigated by using the generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the time and the polar angle. The Hawking thermal radiation spectrum of Dirac particles is also derived. 相似文献
13.
Cai Kairen 《数学年刊B辑(英文版)》1991,12(3):267-271
The author gives an optimum estimate of the first eigenvalue of a compact Riemannian manifold. It is shown that let M be a compact Riemannian manifold, then the first eigenvalue λ_1 of the Laplace operator of M satisfies α_1+max{0,-(n-1)K}≥π~2/d~2 where d is the diameter of M and (n-1)K is the negative lower bound of the Ricci curvature of M. 相似文献
14.
Zi‐Cai Li Tzon‐Tzer Lu Hung‐Tsai Huang Alexander H.‐D. Cheng 《Numerical Methods for Partial Differential Equations》2007,23(1):93-144
In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
15.
The following results are proved in this paper. Let G be a 2k-edge-connected eulerian graph. (i) For every set {e1, e2, ?, e2k+1} ? E(G) there is an eulerian trail T of the form e1, e2, ?, e2k+1, ?. (ii) For every set E* = {e1, e2, ?, ek} ? E(G) there is an eulerian trail T = e1, ?, e2, ?, ek, ? in which the elements of E* are traversed in accordance with a prescribed orientation. © 1995 John Wiley & Sons, Inc. 相似文献
16.
Zhengqian Luo Guoyong Sun Zhiping Cai Miaoling Si Qibo Li 《Optics Communications》2007,277(1):118-124
In this paper, continuous wave Yb3+-doped double-clad fiber lasers (DCFLs) with linear-cavity are investigated theoretically and numerically using the rate equations. Under the steady state conditions, the simplified analytic solutions of Yb3+-doped DCFLs under considering the scattering loss are deduced in the strongly pump condition. Compared with the known analytic solutions in published literatures, our analytic solutions are more accurate, especially, at higher reflectivity of output mirror. In addition, a fast and stable algorithm based on the Newton-Raphson method is proposed to simulate numerically Yb3+-doped DCFLs. The results by simplified analytic solutions are in good agreement with those by the numerical simulation. Moreover, we have performed the optimization of an Yb3+-doped DCFL using the simplified analytic solutions and the numerical simulations, respectively. 相似文献
17.
Ping-xing Chen Jian-ming Cai Zheng-wei Zhou Guang-can Guo 《量子光学学报》2006,12(B08):72-73
The second law of thermodynamics is one of the most fundamental and for-reaching laws of physics. It teaches us that when a closed system undergoes a thermodynamic process the entropy of the system never decreases; it increases, or at least remains constant. If the entropy increases the thermodynamic process is irreversible, otherwise it is reversible. Only ideal thermal process is reversible. In classical world a great number of facts have proved the second law is true. But in quantum world since the quantum coherence and correlations exist we are not sure the second law is still true, at least in principle. This is because that: 1. on the microscopic level the irreversibility is conflict with the reversibility of all fundamental physical laws ; 2. there are not enough evidences to show it is true in quantum world. 相似文献
18.
The contrast of interference pattern formed by two circularly polarized waves and by a linearly polarized wave and a circularly polarized one is discussed. The results are compared with that by two linear beams. It shows that the use of circular light in holographic fabrication of three-dimensional periodic microstructures may remove the necessity of beam ratio and polarization optimization needed in the interference of three linear noncoplanar beams and improve the uniform contrast of resultant pattern simultaneously. 相似文献
19.
In the inverse scattering transform (IST), the reflectionless Jost solutions are combined by their analytic properties in the complex spectrum parameter plane, and then can be shown to satisfy the two Lax equations indeed by Liouville theorem. So the corresponding soliton solutions certainly satisfy the nonlinear equation by compatibility condition. Especially the multi-soliton solutions of DNLS equation can be demonstrated in this way.
PACS Numbers: 05.45.Yv, 02.30.-f, 11.10.Ef 相似文献
20.
Übersicht Die Simulation steifer Differentialgleichungssysteme sehr hoher Ordnung durch implizite Runge-Kutta-Verfahren (gelegentlich auch nach Padé benannt) ist global weitgehend theoretisch geklärt. Bei der konkreten Behandlung von Aufgaben der nichtlinearen Strukturdynamik ist man jedoch zu vielfältigen Zusatzüberlegungen genötigt, um zu vertretbaren Rechenzeiten zu gelangen. Anknüpfend an die bewährte gleichgradige quadratische Padé-Entwicklung oder auch kubische Interpolation am System 1. Ordnung wird die Konvergenzbeschleunigung durch Extrapolation der Nichtlinearitäten belegt. Weiterhin werden Phänomene der modalen Reduktion beim Zusammenwirken verschiedener Steifigkeiten aufgezeigt.
Finite elements in time with extrapolation in nonlinear structural dynamics
Summary Today the theory of integrating stiff differential equations of high order by implicit Runge-Kutta methods (sometimes called Padé approximations) is developed very well especially concerning global properties. Nevertheless, additional considerations must be done in order to minimize the numerical effort when special problems from nonlinear structural dynamics are to be solved. Using a quadratic Padé-approximation or a cubic interpolation for the first-order-system it is shown that the rate of convergence profits from extrapolating the nonlinearities. Some observations and comments on modal reduction for problems characterized by multiple stiffnesses are added.相似文献