Discrete Compound Poisson Process with Curved Boundaries: Polynomial Structures and Recursions

This paper provides a review of recent results, most of them published jointly with Ph. Picard, on the exact distribution of the first crossing of a Poisson or discrete compound Poisson process through a given nondecreasing boundary, of curved or linear shape. The key point consists in using an underlying polynomial structure to describe the distribution, the polynomials being of generalized Appell type for an upper boundary and of generalized Abel–Gontcharoff type for a lower boundary. That property allows us to obtain simple and efficient recursions for the numerical determination of the distribution.      

Orthogonal partitions in designed experiments

A survey is given of the statistical theory of orthogonal partitions on a finite set. Orthogonality, closure under suprema, and one trivial partition give an orthogonal decomposition of the corresponding vector space into subspaces indexed by the partitions. These conditions plus uniformity, closure under infima and the other trivial partition give association schemes. Examples covered by the theory include Latin squares, orthogonal arrays, semilattices of subgroups, and partitions defined by the ancestral subsets of a partially ordered set (the poset block structures).Isomorphism, equivalence and duality are discussed, and the automorphism groups given in some cases. Finally, the ideas are illustrated by some examples of real experiments.Dedicated to Hanfried Lenz on the occasion of his 80th birthday.     

Energy level crossings in quantum mechanics

From the eigenvalue equationH \ _n () =E _n ()\ _n () withH H ₀ +V one can derive an autonomous system of first order differential equations for the eigenvaluesE _n () and the matrix elementsV _mn () where is the independent variable. To solve the dynamical system we need the initial valuesE _n ( = 0) and \ _n ( = 0). Thus one finds the motion of the energy levelsE _n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H ₀ +V ₁ + ² V ₂ and give an application to a supersymmetric Hamiltonian.     

The singlet and triplet states of phenyl cation. A hybrid approach for locating minimum energy crossing points between non-interacting potential energy surfaces

The phenyl cation is known to have two low-energy minima, corresponding to ¹ A ₁ and ³ B ₁ states, the first of which is more stable by ca. 25 kcal/mol. The minimum energy crossing point between these two surfaces, located at various levels including a hybrid method first described here, lies just above the minimum of the triplet, 0.12 kcal/mol at the CCSD(T)/cc-pVDZ//B3LYP/SV level, and there is significant spin-orbit coupling between the surfaces at this point. On the basis of these results, the lifetime of the triplet is expected to be very short. Received: 24 October 1997 / Accepted: 25 November 1997     

比光谱导数-零交点法同时测定铜、锌、镍

在ｐＨ＝８的硼砂－ＨＣｌ缓冲溶液中，以乳化剂ＯＰ作增溶剂，Ｃｕ＾２＋，Ｚｎ６２＋，Ｎｉ＾２＋分别与５－Ｂｒ－ＰＡＤＡＰ形成稳定的配合物，用比光谱导数－零交点法同时测定铜，锌，镍，合成试样６次测定的相对标准偏差小于５％，铜，锌，镍的回收率分别为９７．０％－１０３．２％，９６．３５－１０４．８％和９５．２％－１０１．９％。     

Ab initio studies for the photodissociation mechanism of hydroxyacetone

The reaction pathways for CH(3)COCH(2)OH (hydroxyacetone) photodissociation on the low-lying electronic states have been studied with use of the CASSCF energy gradient techniques. The S(0)/S(1) and S(1)/T(1) intersection points were determined by the state-average CASSCF method. Two main reaction pathways, which are possible to the photodissociation, have been studied. It has been found that the mechanism is stepwise, and belongs to Norrish type-I reaction. The n --> pi* excitation leads to the first excited singlet state, followed by the intersystem crossing from S(1) to T(1). On the T(1) potential energy surface, the system can dissociate adiabatically to CH(3)(x) +COCH(2)OH( x) and CH(3)CO(x)+CH(2)OH(x). The COCH(2)OH(x) and CH(3)CO(x) radicals can further dissociate into CO, OH, and other fragments. Our calculated results are in good agreement with recent experimental results.     

非高斯结构首次超越分析的概率模型

利用Fleishman近似,通过非高斯结构动力响应的前四阶中心矩,将分布未知的结构响应过程变换为标准高斯随机过程,提出非高斯结构动力响应的平均穿越率计算公式,并考虑初始条件和群穿尺寸的影响,修正平均穿越率的计算,在此基础上,利用传统Poisson模型,建立非高斯结构首次超越分析的概率模型.算例分析表明,本文提出的概率模型可以在结构随机振动分析或试验与检测数据的基础上,分析非高斯结构的首次超越问题,并克服了传统高斯模型所固有的诸多缺点.     

交会测量中具有自适应权因子的最优无偏方法

在利用多台测量站对空中运动物体进行交会测量过程中，测量站两两交会得到的测量结果并不会完全一致，有时甚至会有很大差别。讨论了具有自适应权的最优无偏方法：首先利用最小二乘法的原理，推导出了最小二乘解的表达式。在求解最优无偏解的过程中，通过求条件极值的方法导出了最优无偏解的权因子。由于权因子中的某些因素与目标像在CCD像面上的位置有关，提出了“自适应权”的思想，即权因子随目标像点位置的不同而自动调整。与传统的方法相比，具有自适应权的最优无偏方法，在一定程度上更充分地利用了不同情况下来自不同测量站的测量信息，从而提高了测量精度。经实际计算表明，在低空目标定位时，具有自适应权的最优无偏方法的平均偏差为传统方法平均偏差的40％左右。     

Flashlamp Pumped Emulsion Dye Laser

Results of experimental study of flashlamp pumped cc-NPO emulsion dye laser are reported. Superior quality α-NPO emulsion over α-NPO solution in n-hexane is found.     

Efficient calculation of Franck–Condon factors and vibronic couplings in polyatomics

We present a technique for the calculation of Franck–Condon factors and other integrals between vibronic wave functions belonging to different electronic states. The technique is well suited for the determination of the nonadiabatic or spin‐orbit couplings related to radiationless decays in polyatomics. Rigorous or approximate partitions of the internal coordinate space are exploited to achieve better efficiency and/or to go beyond the harmonic approximation. The technique is tested by computing the Internal Conversion and InterSystem Crossing rates of (CH₃)₃CNO in its ¹(n→π*) state. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 968–975, 2001