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991.
The semi-infinite Toda lattice is the system of differential equations d
n
(t)/dt =
n
(t)(b
n+1(t) – b
n
(t)), db
n
(t)/dt = 2(
n
2(t) –
n–1
2(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences
n
(t), b
n
(t) which satisfy the conditions
n
(0) =
n
,, b
n
(0) = b
n
, where
n
> 0 and b
n
are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences
n
and b
n
are bounded. When at least one of the known sequences
n
and b
n
is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences
n
and b
n
such that the system has a unique solution. The results are illustrated with a typical example where the sequences
i
(t), b
i
(t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d2/dt
2 log h
n
= h
n+1 + h
n–1 – 2h
n
, n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation. 相似文献
992.
In this Letter we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights ,, three scalar parameters q,,k, and spectral parameters z
1,...,z
N
, which may be regarded as q-analogs of conformal blocks of the Wess–Zumino–Witten model on an elliptic curve. It is expected that in the rank 1 case they essentially coincide with the elliptic hypergeometric functions defined by Felder and Varchenko. Our main result is that after a suitable renormalization the traces satisfy four systems of difference equations – the Macdonald–Ruijsenaars equation, the q-Knizhnik–Zamolodchikov–Bernard equation, and their dual versions. We also show that in the case when the twisting automorphism is trivial, the trace functions are symmetric under the permutation , k . Thus, our results generalize those of Etingof and Schiffmann, dealing with the case q=1, and Etingof, Varchenko, and Schiffmann, dealing with the finite-dimensional case. 相似文献
993.
Marco Matone 《Foundations of Physics Letters》2002,15(4):311-328
We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton–Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may generate the gravitational potential. The investigation, related to the formulation of quantum mechanics based on the equivalence postulate, is based on the analysis of the reduced action. A consequence of this approach is that the quantum potential is always non-trivial even in the case of the free particle. It plays the role of intrinsic energy and may in fact be at the origin of fundamental interactions. We pursue this idea, by making a preliminary investigation of whether there exists a set of solutions for which the quantum potential can be expressed with a gravitational potential leading term which alone would remain in the limit 0. A number of questions are raised for further investigation. 相似文献
994.
设计了3套针对“神光-Ⅱ”倍频激光直接驱动的透镜阵列均匀辐照系统,并对冲击波的平面性进行了实验研究。结果表明,冲击波的平面性与透镜阵列参数、平面靶厚度、靶面位置等有关,采用列阵元数为121的透镜阵列进行激光束匀滑驱动的冲击波平面性最好,间接说明它在靶面的激光辐照是最均匀的;另外,随着靶厚的增加,冲击波平面性变差,平面区变小;而且冲击波平面性随靶面离焦位置的变化成一定的周期性变化,第2套透镜阵列焦点处的冲击波平面性最好。 相似文献
995.
A new nonlinear three-wave equation of the sixth order for pressure in a polydisperse gas-liquid mixture with bubbles of two
sizes is obtained, and its stationary solutions are analyzed. The equation includes two nonlinear quadratic terms of different
derivative orders. These terms are of fundamental importance for obtaining good correspondence between the solutions to this
equation and the experimentally observed solitary waves in the form of two coupled solitons. 相似文献
996.
高聚物PMMA的受力变形行为与粘弹-塑性本构理论模型 总被引:1,自引:0,他引:1
对高聚物PMMA实验测定了不同(T,ε)的单轴加卸载循环的应力-应变曲线。讨论了应力促进热激活塑性变形的活化粘壶理论和塑性变形的发展规律。提出由SLS或MS与活化粘壶作串联耦合的粘弹-塑性本构理论模型,给出了微分和积分形式的本构方程组,用于拟合求解加卸载循环的应力-应变曲线,获得良好吻合的结果。详细讨论了PMMA在加载过程中的受力变形行为,包括起始加载的粘弹性变形,ε_v和ε_p的互相挤占,屈服点,以及屈服后应变软化和硬化的抗衡过程。对应变软化-硬化效应提出一种新的起因于粘弹变形内禀滞后效应的理论解释,并定名为粘弹软化-强化效应。对所包含的粘弹变形成分,从E_v的移位因子和归一化应力-应变主曲线两方面,讨论了可能存在的率温等效关系。 相似文献
997.
Z. Xiancheng N. Zhaodong X. Yan Z. Yuanqin Z. Honglin 《Journal of Thermal Analysis and Calorimetry》1999,58(2):279-285
The power-time curves of two species of bacteria, Vibro metschnikovii, Vibro bollisae were determined calorimetrically by using a 2277 bioactivity monitor. The power-time curve equation of bacterial growth in the log phase can be expressed as
. A self-function recursion equation, fi=b1fi+1+b2fi+2, was obtained through the perfect non-linear function
. A linear equation, i/i+1=b1+b2i+2/i+1, was obtained by using the self-function recursion equation. The rate constants of bacterial growth k1, the time constant of the calorimeter k, the generation times G, and the pre-exponential factors A were obtained from the power—time curve equations.Power—time curve equations of bacterial growth in the log phase are expressed for V.metschnikovii as =1.05(e0.0228t–e–0.0175t), and for V. bollisae as =1.58(e0.0278t–e–0.0170t).This revised version was published online in November 2005 with corrections to the Cover Date. 相似文献
998.
环上矩阵的Moore-Penrose逆的注记 总被引:1,自引:0,他引:1
崔雪芳 《宁波大学学报(理工版)》1999,12(2):9-13
讨论带有对合反自同构的环上矩阵的广义逆,给出了矩阵存在Mooore-Penrose逆的条件及Moore-Penrose逆的一些性质和显式. 相似文献
999.
研究一类三阶自治系统的积分方法,证明了在一定条件下,这类系统的积分问题归结为求解由该方程的系数所确定的Riccati方程 相似文献
1000.
一阶时滞微分方程解的零点分布 总被引:3,自引:0,他引:3
Abstract. The paper gives two estimates of the distance between adjacent zeros of solutions 相似文献