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251.
J. E. Colliander J.-M. Delort C. E. Kenig G. Staffilani 《Transactions of the American Mathematical Society》2001,353(8):3307-3325
The three bilinearities for functions are sharply estimated in function spaces associated to the Schrödinger operator . These bilinear estimates imply local wellposedness results for Schrödinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cubic nonlinear Schrödinger equation (and certain generalizations) are also obtained.
252.
Let t be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when t is in different states. This new process Zt is a hidden Markov process. We study the probability distribution of the first passage time for Zt.Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull). 相似文献
253.
In 1914 Bohr proved that there is an r (0,1) such that if apower series converges in the unit disk and its sum has modulusless than 1 then, for |z| < r, the sum of absolute valuesof its terms is again less than 1. Recently, analogous resultshave been obtained for functions of several variables. The aimof this paper is to place the theorem of Bohr in the contextof solutions to second-order elliptic equations satisfying themaximum principle. 2000 Mathematics Subject Classification: 35J15, 32A05, 46A35. 相似文献
254.
Suppose that { f(n), n N
0
} is a sequence of positive real numbers and suppose that the sequence { a(n), n N
0
} is given by a(0) = 0, and, for n 1, by the convolution equation nf(n) = a* f(n). The resulting sequence is denoted by a(n) =
f
(n) and is called the De Pril transform of { f(n), n N
0
} . In this paper, we consider first- and second-order asymptotic behavior of {
f
(n), n N
0
} for a large class of subexponential sequences { f(n), n N
0
} . We also discuss some applications. 相似文献
255.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
256.
关于调和映照的一个 Liouville型定理 总被引:2,自引:2,他引:0
张希 《浙江大学学报(理学版)》2000,27(2):124-127
本文证明了完备非紧 Riemann流形 M,若其上不存在非常数、具有限 Dirichlet积分的调和函数 , 则从 M出发到任何 C-H流形的具有限能量的调和映照必为常值映照. 相似文献
257.
利用单调迭代方法,在Banach空间研究了更为一般脉冲微分方程的初值问题的最小最大拟解的存在性及迭代逼近程序。 相似文献
258.
It is well known that in the non-depleted pump approximation, the efficiency of a second harmonic generation (SHG) of a guided mode in a non-linear optical waveguide increases quadratically with the interaction length (P
2 L
2), and linearly (P
2 L) in the erenkov regime. The efficiency of the erenkov SHG in the waveguide with a non-linear substrate and linear guiding layer is known to be strongly peaked at a particular pump wavelength and a particular waveguide thickness, with the erenkov angle approaching zero. The known theory predicts an infinite efficiency value at the peak, however. In this contribution, a simple integral expression for the SHG efficiency in the erenkov regime is derived. For large erenkov angles and interaction lengths it yields the expected P
2 L dependence, while in the limit of small erenkov angles the dependence is found to have the form of P L
3/2, possessing also a finite value at the efficiency peak. The condition determining the accurate position of the efficiency peak in the waveguide thickness–pump wavelength plane is given, too. 相似文献
259.
260.
针对六角密堆金属锂16个原子超晶胞(supercell)、填隙一个氢原子的周期单元,采用基于密度泛函理论的平面波-赝势方法,研究了零温条件下压力及填隙氢掺杂对体系弹性性质的影响.结果表明氢掺杂导致体系的体模量增加.常压下掺杂体系的弹性常数C11,C33,C66和C12高于单质体系,剪切模量C44有所下降,而C13则与单质体系持平.压力作用下C11,C33和C66一直大于单质体系,但C12的值低于单质体系.在2GPa—4GPa压力区间内,弹性常数C13呈反常变化,小于单质体系;在高压区掺杂体系的C44和C13则高于单质体系的相应量值,压力导致掺杂体系和单质体系之间剪切模的偏离加剧.掺杂体系在压力作用下依然保持压缩模的各向同性,具有和单质体系相似的特性.
关键词:
第一性原理
压力效应
弹性常数
金属锂 相似文献