一类与凸函数有关的不等式的概率证法

通过构造随机变量的方法,并结合凸函数的性质,证明了数学分析中的一些著名不等式,证明方法简明、独特.     

Ferromagnetic Properties of Bond-Dilution and Random Positive or Negative Uniaxial Anisotropy Blume-Capel Model

We study the ferromagnetic properties of spin-1 system, which is considered in the frame of the bond dilution and random positive or negative anisotropy Blume-Capel model in the effective field theory and a cutting approximation. The investigation of phase diagrams displays some rich properties of the trajectory of tricritical point, reentrant henomena at low temperatures. Under certain both bond concentrations and random negative anisotropy, there are new transition lines of double tricritical points. So special emphasis is placed on the influence of the bond dilution and random anisotropy on phase diagrams. The magnetizations of the system are also discussed. Some results have not been evealed in previous reports.     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

Phase-Only Encryption and Single Path Decryption System Using Phase-Encoded Exclusive-OR Rules in Fourier Domain

A phase-only encryption scheme using phase-encoded exclusive-OR (XOR) rules in a Fourier plane and a single path decryption system are presented. To generate phase-only encrypted data, a zero-padded original image, multiplied by a random phase image, is Fourier transformed and its real-valued data is encrypted with key data by using phase-encoded XOR rules. Since the original information is encrypted on the Fourier plane, the proposed encryption is more tolerant to loss of key information by scratching or cutting than previous XOR encryption in a space domain. A decryption is simply performed based on 2-f setup with spatial filter by Fourier transform for multiplication phase-only encrypted data with phase-only key data. Due to single path architecture without a reference wave, the proposed system is resistant to mechanical vibrations and fluctuation. Numerical simulations have confirmed the validity of the proposed encryption scheme and simple decryption architecture.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

频率受随机过程调制的体系中的光谱扩散

通过在Bloch方程中增加描述对频率微扰的随机过程项{ω(t)},我们讨论了系统在窄谱带的光激发后的光谱扩散。特别是以下两种情况:1)如果ω以相同的概率变化为系综中的任一ω’,光谱是一个指数式衰减的定域峰和指数式增长的动态非均匀背底的叠加。2)如果ω'到ω的概率仅与|ω’-ω|有关,非定域峰随时间变宽。作为一个例子,我们讨论了频率受多个独立随机电报过程调制的系统中的光谱扩散。     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Let _l be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ₂=0.6240±0.0005±0.0011 and ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ₂=5/8 and ₃=35/24.