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991.
It is known that at the critical temperature the Curie-Weiss mean-field model has non-Gaussian fluctuations and that internal fluctuations can be Gaussian. Here we compute the distribution of theq-mode magnetization fluctuations as a function of the temperature, the wave vectorq, and a fading out external field. We obtain new classes of probability distributions generated by this external field as well as new critical behavior in terms of its rate of fading out. We discuss also the susceptibility as the limitq tending to zero. 相似文献
992.
993.
994.
Joseph R. Lakowicz Zakir Murtaza Wayne E. Jones Jr. Kihan Kim Henryk Szmacinski 《Journal of fluorescence》1996,6(4):245-249
We report the first observation of polarized emission from a rhenium-phenanthroline complex, Re(CO)3(phen)Cl. Highly luminescent rhenium complexes are known, with quantum yields near 0.5 and lifetimes in excess of 10 s. The detection of polarized emission suggests the use of rhenium complexes as probes of the hydrodynamics of large macromolecular complexes and for use in fluorescence polarization immunoassays with gated detection. 相似文献
995.
Let be complex numbers, and consider the power sums , . Put , where the minimum is over all possible complex numbers satisfying the above. Turán conjectured that , for some positive absolute constant. Atkinson proved this conjecture by showing . It is now known that , for . Determining whether or approaches some other limiting value as is still an open problem. Our calculations show that an upper bound for decreases for , suggesting that decreases to a limiting value less than as .
996.
For the multidimensional heat equation in a parallelepiped, optimal error estimates inL
2(Q) are derived. The error is of the order of +¦h¦2 for any right-hand sidef L
2(Q) and any initial function
; for appropriate classes of less regularf andu
0, the error is of the order of ((+¦h¦2
), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996. 相似文献
997.
Xiao-Qing Jin 《BIT Numerical Mathematics》1996,36(1):101-109
We study methods for solving the constrained and weighted least squares problem min
x
by the preconditioned conjugate gradient (PCG) method. HereW = diag (1, ,
m
) with 1
m
0, andA
T
= [T
1
T
, ,T
k
T
] with Toeplitz blocksT
l
R
n × n
,l = 1, ,k. It is well-known that this problem can be solved by solving anaugmented linear 2 × 2 block linear systemM +Ax =b, A
T
= 0, whereM =W
–1. We will use the PCG method with circulant-like preconditioner for solving the system. We show that the spectrum of the preconditioned matrix is clustered around one. When the PCG method is applied to solve the system, we can expect a fast convergence rate.Research supported by HKRGC grants no. CUHK 178/93E and CUHK 316/94E. 相似文献
998.
Nahid Emad 《Numerical Algorithms》1996,11(1):159-179
We make use of the Padé approximants and the Krylov sequencex, Ax,,...,A
m–1
x in the projection methods to compute a few Ritz values of a large hermitian matrixA of ordern. This process consists in approaching the poles ofR
x()=((I–A)–1
x,x), the mean value of the resolvant ofA, by those of [m–1/m]Rx(), where [m–1/m]Rx() is the Padé approximant of orderm of the functionR
x(). This is equivalent to approaching some eigenvalues ofA by the roots of the polynomial of degreem of the denominator of [m–1/m]Rx(). This projection method, called the Padé-Rayleigh-Ritz (PRR) method, provides a simple way to determine the minimum polynomial ofx in the Krylov subspace methods for the symmetrical case. The numerical stability of the PRR method can be ensured if the projection subspacem is sufficiently small. The mainly expensive portion of this method is its projection phase, which is composed of the matrix-vector multiplications and, consequently, is well suited for parallel computing. This is also true when the matrices are sparse, as recently demonstrated, especially on massively parallel machines. This paper points out a relationship between the PRR and Lanczos methods and presents a theoretical comparison between them with regard to stability and parallelism. We then try to justify the use of this method under some assumptions. 相似文献
999.
L. Hatvani 《Proceedings of the American Mathematical Society》1996,124(2):415-422
The equation is considered under the assumption . It is proved that is sufficient for the asymptotic stability of , and is best possible here. This will be a consequence of a general result on the intermittent damping, which means that is controlled only on a sequence of non-overlapping intervals.
1000.
The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large . 相似文献