Theory of the Domino Dynamics Via Nonadiabatic Transitions

Photoinduced nucleation processes, called photoinduced domino processes, via excited electronic states are discussed theoretically for a one-dimensional arrangement of deformable molecules using a model composed of localized electrons and lattices. We show that the global structural transition by photoexcitation only at a molecule (site) is possible in the adiabatic and diabatic limits. An intermediate regime between these limits is investigated; an analytical treatment and a numerical calculation are presented taking into account the nonadiabatic electronic transition, i . e ., the Landau-Zener-type transition. In this regime, the domino dynamics can be terminated halfway ( i . e ., a finite - size domain appears) in contrast to the "all-or-nothing" domino dynamics ( i . e ., a photoinduced domain vanishes or grows up to the system size) in the adiabatic and diabatic limits.     

A-dependence of φ-meson production in p + A collisions

A systematic analysis of the A-dependence of φ-meson production in proton-nucleus collisions is presented. We apply different formalisms for the evaluation of the φ-meson distortion in nuclei and discuss the theoretical uncertainties of the data analysis. The corresponding results are compared to theoretical predictions. We also discuss the interpretation of the extracted results with respect to different observables and provide relations between frequently used definitions. The perspectives of future experiments are evaluated and estimates based on our systematical study are given.     

Epigraphical nesting: A unifying theory for the convergence of algorithms

In an earlier paper, the authors introduced epigraphical nesting of objective functions as a means to characterize the convergence of global optimization algorithms. Epigraphical nesting of objective functions may be looked upon as a relaxation of epigraphical convergence of objective functions, whereby one ensures that epigraphs of the approximations contain asymptotically the epigraph of the objective function of the original optimization problem. In this paper, we show that, for algorithms which seek only a stationary point, convergence can be assured by objective function approximations whose directional derivatives attain an epigraphical nesting property. We demonstrate that epigraphical nesting provides a unifying thread that ties together a number of different algorithms, including those for the solution of variational inequalities and smooth as well as nonsmooth optimization. We show that the Newton method and its variants for unconstrained optimization, successive quadratic programming methods for constrained optimization, and proximal point algorithms (deterministic and stochastic) all construct approximations in which the directional derivatives attain an epigraphical nesting property, even though the approximations themselves fail to attain such a property.This work was supported in part by Grants NSF-DDM-89-10046 and NSF-DDM-91-14352 from the National Science Foundation.     

General Full Implicit Strong Taylor Approximations for Stiff Stochastic Differential Equations

In this paper, we present the backward stochastic Taylor expansions for a Ito process, including backward Ito-Taylor expansions and backward Stratonovich-Taylor expansions. We construct the general full implicit strong Taylor approximations (including Ito-Taylor and Stratonovich-Taylor schemes) with implicitness in both the deterministic and the stochastic terms for the stiff stochastic differential equations (SSDE) by employing truncations of backward stochastic Taylor expansions. We demonstrate that these schemes will converge strongly with corresponding order $1,2,3,\ldots$ Mean-square stability has been investigated for full implicit strong Stratonovich-Taylor scheme with order $2$, and it has larger mean-square stability region than the explicit and the semi-implicit strong Stratonovich-Taylor schemes with order $2$. We can improve the stability of simulations considerably without too much additional computational effort by using our full implicit schemes. The full implicit strong Taylor schemes allow a larger range of time step sizes than other schemes and are suitable for SSDE with stiffness on both the drift and the diffusion terms. Our numerical experiment shows these points.     

Deformed foam structure and transitions in a tube

The “staircase” (2,1,1) foam structure in an ordered foam under expansion in a cylindrical tube and the structural transition to the “bamboo” (1,1,0) structure are studied experimentally, analytically, and numerically using the Surface Evolver minimization program. An analytical expression of the oblique interface in the (2,1,1) structure, a minimal surface, but curved by stretching of the foam, is given as a classic example of singular perturbation (boundary layer) theory. The structural transition from staircase structure to bamboo structure takes place at a considerable dilation. The transition is not due to an edge length tending to zero continuously with dilation, but results from the equilibrium (2,1,1) solution losing its stability due to a saddle node bifurcation. Received 3 August 2000     

Notes on the diamond-α dynamic derivative on time scales

Various dynamic derivative formulae have been proposed in the development of a time scales calculus, with the goal of unifying continuous and discrete analysis. Recent discussions of combined dynamic derivatives, in particular the α_? derivative defined as a linear combination of the Δ and the ∇ derivatives, have promised improved approximation formulae for computational applications. This paper presents an equivalent definition of the α_? functions without reference to the existing Δ and ∇ derivatives, examines the status of the α_? as a dynamic derivative and its properties relative to the Δ and ∇ derivatives, and compares data obtained using the various dynamic derivatives as approximation formulae in computational experiments. A α_? integral case is investigated.     

Efficient option valuation using trees

An algorithm is proposed for the discrete approximation of continuous market price processes that uses trees instead of lattices. It is shown that it is convergent when used for pricing both European and American options and that it is more efficient, for some models, than the usual recombining schemes.     

2-周期整(m1,…,mp;m1′,…,mq′)插值的逼近性质

研究了一类等距结点上的2-周期整(m1,…,mp;m1′,…,mq′)插值算子的逼近性质,通过引入辅助算子得到了该插值算子在Lp(R)(1≤p＜∞)空间的饱和阶与饱和类.     

Best estimates of the generalized Stirling formula

The aim of this paper is to introduce an approximations family of the factorial function that contains Stirling’s formula, Burnside’s formula and Gosper’s formula. The parameters which provide the best approximations are indicated. Finally, numerical computations are made to show the superiority of our formulas over other known formulas.