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201.
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 .
202.
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
203.
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
204.
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.
205.
Zeng -Gui Chen 《International Journal of Infrared and Millimeter Waves》1993,14(2):197-211
A cylindrical waveguide gyro-peniotron amplifier is analysed theoretically in this paper. By a ballistic method and directly using the energy conservation in the beam-wave system, a set of interaction equations for the cylindrical waveguide gyro-peniotron amplifier is derived. Computer simulation shows that under defined conditions an interaction efficiency of 47%, an output power of 240kW at a gain of 22. 5 dB and a 3 dB-instantaneous bandwidth of 1. 9% for a central frequency of 35GHz, TE03 mode gyro-peniotron amplifier could be achieved. The influence of the operation parameters on the amplifier performance is also presented. 相似文献
206.
George Adomian 《Foundations of Physics Letters》1993,6(6):603-605
In mathematical approaches to elementary particle theory, the equation [2 -
2/t2]=m2
;+g
3 has been of interest [1,2]; it describes a quartically self-coupled neutral scalar meson field. This paper applies the decomposition method [3-6] to obtain accurate non-perturbative timedevelopment of the field for this equation, or variations involving other nonlinear interactions, without the use of cutoff functions or truncations. 相似文献
207.
We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 1030, are measured). 相似文献
208.
A. G. Schlijper 《Journal of statistical physics》1985,40(1-2):1-27
A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf
n on the free energy per lattice sitef and thatf
n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states. 相似文献
209.
210.
严继民 《中国科学B辑(英文版)》1990,(7)
An ab initio calculation of the hydrogen bond complex (HF)_2 is given with the 6-311 G~(**) basis set, according to which the potential surface around the balance point of the distancès and the orientations between two HF molecules is obtained. The atomic charges in the system are calculated with the PD/LSF method (potential-derived/least-square-fitting method) and then an analysis of the hydrogen bond interaction between two HF molecules is given with the (exp-6-1) potential function, by means of which it is shown that the main interaction between them is not an electro-static but a charge transfer one. The potential curve between two HF molecules is like a Morse function. 相似文献