Eu:Fe:LiNbO3晶体非简并四波混频的研究

用波长为623.8nm的He-Ne激光作信号光和一束泵浦光,用波长为488.0nm的Ar⁺激光作另一束泵浦光,在Eu:Fe:LiNbO₃晶体中实现了非简并四波混频,获得了波长为488.0nm的变频相位共轭光,同时还产生了波长为632.8nm的同频相位共扼光。本文对上述实验结果进行了定性分析。     

二次李三系的分解定理

有限维李三系称为二次的,如果它容许一个非退化的不变对称双线性型.无论是李三系分解为不可分解理想的直和,还是二次李三系分解为不可分解非退化理想的正交直和,证明了这两类分解在同构意义下都是唯一的.     

Kerr效应对非简并双光子J—C模型中光场相位的影响

应用Pegg-Barnett相位理论研究了高Q Kerr介质腔中的二能级原子与双模光场相互作用系统中光场相位的演化特性,通过计算光场的相位几率分布函数,频率漂移量以相位涨落,分析讨论了Kerr效应对光场相位性质的影响。     

A conjugate gradient method for the unconstrained minimization of strictly convex quadratic splines

In this paper, we show that an analogue of the classical conjugate gradient method converges linearly when applied to solving the problem of unconstrained minimization of a strictly convex quadratic spline. Since a strictly convex quadratic program with simple bound constraints can be reformulated as unconstrained minimization of a strictly convex quadratic spline, the conjugate gradient method is used to solve the unconstrained reformulation and find the solution of the original quadratic program. In particular, if the solution of the original quadratic program is nondegenerate, then the conjugate gradient method finds the solution in a finite number of iterations. This author's research is partially supported by the NASA/Langley Research Center under grant NCC-1-68 Supplement-15.     

Probabilistic solution of the American options

The existence and uniqueness of probabilistic solutions of variational inequalities for the general American options are proved under the hypothesis of hypoellipticity of the infinitesimal generator of the underlying diffusion process which represents the risky assets of the stock market with which the option is created. The main tool is an extension of the Itô formula which is valid for the tempered distributions on Rd and for nondegenerate Itô processes in the sense of the Malliavin calculus.     

A HOPF INDEX THEOREM FOR A REAL VECTOR BUNDLE

The authors generalize the works in [5] and [6] to prove a Hopf index theorem associated to a smooth section of a real vector bundle with non-isolated zero points.     

Numerical Approximation of Transcritical Simple Bifurcation Point of the Navier-Stokes Equations

The extended system of nondegenerate simple bifurcation point of the Navier-Stokes equations is constructed in this paper, due to its derivative has a block lower triangular form, we design a Newton-like method, using the extended system and splitting iterative technique to compute transcritical nondegenerate simple bifurcation point, we not only reduces computational complexity, but also obtain quadratic convergence of algorithm.     

Theoretical analysis and experimental scheme of QND measurement for intensity difference fluctuations

A feasible experimental scheme of QND measurement for intensity difference fluctuations is presented, in which a nondegenerate optical parametric amplifier is used as the nonlinear coupling device. Optimum behavior is obtained by appropriately choosing the operating parameters, which can provide design references for the measurement.     

Three-colour entanglement generated by an injection-seeded nondegenerate optical parametric oscillator

Three-colour continuous-variable (CV) entanglement can be directly generated by an injection-seeded nondegenerate optical parametric oscillator (INOPO). The quantum correlations among the pump, signal, and idler beams are calculated and discussed by applying sufficient inseparability criteria for CV entanglement. The results clearly show that strong three-colour CV entanglement can be produced by operating the pump above the oscillation threshold. The INOPO is easier to realize experimentally and more steady in comparison to that without an injected signal since the injected signal can increase the nonlinear conversion efficiency and the stability, as well as allow a large degree of tunability. This scheme can be very useful for the applications in quantum communication and computation networks.     

Reduced matrix of topological distances with a minimum number of independent parameters: distance vectors and molecular codes

Entries of the topological distance matrix are shown to be functions of entries of the reduced distance matrix, which has a smaller size. The latter entries are expressed through a minimum number m of independent parameters (m ≤ 2n − 3). The expanded distance matrices, whose sum constitutes the reduced matrix, are defined. The reduced vectors have lower degeneracy than the corresponding vectors proposed by Randić as molecular codes. Nondegenerate sets of reduced-matrix entries are proposed as molecular codes.