The Feynman–Kac formula for Schrödinger operators on vector bundles over complete manifolds

Methods from stochastic analysis are combined with functional analytic methods in order to prove a Feynman–Kac formula för Schrödinger type operators with nonnegative locally square integrable potentials on vector bundles over complete Riemannian manifolds. In particular, we obtain a Feynman–Kac–Itô formula on manifolds for Schrödinger operators with magnetic fields.     

某类算子的加权Lorentz模不等式

关于算子Tf(x)=integral from n=0 to x (φ(t/x))f(t)dt的双权Lorentz模不等式,我们给出了充分和必要条件,其中φ:(0,1)→(0,∞)是非增且满足φ(ab)≤D(φ(a)+φ(b))0相似文献   

LEGENDRE SERIES SOLUTIONS FOR TIME-VARIATION DYNAMICS

In this topic, a new approach to the analysis of time-variation dynamics is proposed by use of Legendre series expansion and Legendre integral operator matrix. The theoretical basis for effective solution of time-variation dynamics is therefore established, which is beneficial to further research of time-variation science. Supported by Shanghai Key Project Research Foundation.     

在量子力学里先有算符,还是先有态矢

论证了在量子力学中,描写系统状态的态矢即即概率幅的概念是最根本的概念,它比描写动力学变量的算符的对易关系等性质更为重要。还举出了一般教材中常见的几个问题做例子来说明这一点。     

KdV-Burgers方程的级数解

给出ＫｄＶ－Ｂｕｒｇｅｒｓ方程的有界行波解的精确级数解,采用Ａｄｏｍｉａｎ算子分解法分别求行二个区域ζ〈０和ζ〉０的级数解,然后利用对接连续条件构成整体级数解。所得级数解能精确满足对接连续条件,并由此得到确定级数的系数递推公式,无需解非红性高阶代数方程组。与某些精确解及其它方法比较,计算简捷具在对接点处是收剑的。对某些非线性波动现象的研究,可作为计算和分析的数学依据。     

脉冲梯度场增强的DQF-COSY实验t1噪声研究

脉冲相位的不稳定性是导致二维谱中的t₁噪声的原因之一.本文从理论上和实验上对脉冲相位不稳定性所引起的t₁噪声进行了研究.从角动量算符I_x,I_y和I_z推导中发现,由于磁化矢量在P型和N型DQF-COSY实验的脉冲梯度场中进动方向的内在差异,一部分脉冲相位误差在P型DQF-COSY实验会被重聚掉,在N型DQF-COSY实验中却会被加重.因此P型DQF-COSY实验的t₁噪声比N型小.理论推导还得到t₁噪声在P型和N型中的理论比值为√3:√11.以上理论结果得到我们实验结果的支持.     

Rellich type inequalities related to Grushin type operator and Greiner type operator

We prove some sharp Hardy inequality associated with the gradient ? _?? = (? _x ,|x| ^?? ? _y ) by a direct and simple approach. Moreover, similar method is applied to obtain some weighted sharp Rellich inequality related to the Grushin operator in the setting of L ^p . We also get some weighted Hardy and Rellich type inequalities related to a class of Greiner type operators.     

利用LiDAR系统对飞机残骸进行分析的新方法

飞机失事的事故率较低,但损失一般较为严重.对飞机残骸现场的有效记录,能够帮助我们了解失事场景,并进行后续分析,但国内外相关研究较少.本文利用一套LiDAR系统对事故现场进行测绘和三维尺度图像信息保存.并结合改进的ICP算法实现了更高精度的点云拼接,从而对失事前后的同一部件进行对比分析,以确定其受力和变形情况,进而帮助确定失事原因.与其他飞机失事场景记录方法相比,该系统三维重现效果更好.     

Analogy between real irreducible tensor operator and molecular two-particle operator

. Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry. We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases. A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used. Received: 3 September 1996 / Accepted: 19 December 1996