Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

平面上随机级数的性质

研究了平面上系数{Xn,n≥0}为(?)-混合序列在满足,(q>1)等条件下的随机级数的增长性及值分布,得到了比较好的结果．     

Refractive index of standard oils as a function of wavelength and temperature

The refractive indices (n) of eight standard oils from Physikalisch Technische Bundesanstalt, Germany were determined with an accuracy of ±1×10⁻⁴ by using Abbe Refractometer. The measurements were performed at temperature 20°C in the spectral range 0.4–0.7 μm. The experimental data were fitted to the simple Cauchy dispersion formula and the results were found to be consistent within the limits of experimental error. In all cases, the refractive index decreased monotonically with increasing wavelength. The refractive indices (n) of these oils have been measured as a function of the temperature t (20°C up to 50°C) at λ=0.589 μm and were found to have linear temperature dependencies. The refractive indices of the studied oils and the uncertainty in their values are calculated at λ=0.589. The Lorentz–Lorenz (L–L) formula has been tested and it was found to be valid with a maximum deviation of 0.4% and was used to calculate the molecular polarizability θ.     

Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors

We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.     

Duffing方程的唯三周期解问题

考虑Duffing方程x+g(x,t)=h(t),在g(x,t)满足简单的凸凹性条件。以及g＇(x,t)跨越第一共振点时,本文指出,当强迫振动项h(t)充分小时,所讨论的Duffing方程的2π周期解恰有三个.     

Phase Transition in Vertex-Reinforced Random Walks on {\mathbb{Z}} with Non-linear Reinforcement

Vertex-reinforced random walk is a random process which visits a site with probability proportional to the weight w _k of the number k of previous visits. We show that if w _k ∼ k ^α, then there is a large time T ₀ such that after T ₀ the walk visits 2, 5, or ∞ sites when α < 1, = 1, or > 1, respectively. More general results are also proven.      

Semiconvergence in distribution of random closed sets with application to random optimization problems

The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence statements for suitable functions of random sets are proved and the results are employed to derive stability statements for random optimization problems where the objective function and the constraint set are approximated simultaneously. The author is grateful to two anonymous referees for helpful suggestions.     

Reconstruction of the Point-Spread Function of the Human Eye Using a New Phase-Retrieval Algorithm

The double-pass method is thought to obtain the point spread function (PSF) in human eyes based on two techniques: the symmetric double-pass method using the same pupil size and the asymmetric double-pass method using a different pupil size. The symmetric double-pass method provides autocorrelation of the retinal PSF and, thus, the modulation transfer function. The asymmetric double-pass method provides low-frequency partial-phase information and the partial phase-retrieval algorithm is applied to obtain the complete-phase information, and to estimate the PSF. The partial phase-retrieval algorithm is based on the iteration method proposed by Fineup and Kowalczyk and requires a lengthy computation. In this study, we propose a new high-speed phase-retrieval algorithm based on the property that the real and imaginary parts of optical transfer functions (OTFs) continuously change in value.     

随机环境中多物种分枝随机游动

引进了随机环境中多物种分枝随机游动的一般模型.在分枝过程非灭绝的情况下,讨论了系统的状态分类,得到了系统暂留及强常返的充要条件是存在k个定义在整数集上的函数分别满足某种性质.最后给出了系统强暂留的充分条件.     

Magnetic behavior of the bond random mixed compound FE(BR x I1−x )2(x = 0.9) with Mössbauer spectroscopy

The bond random mixed compound Fe(Br_0.9I_0.1)₂ has been studied by magnetization and Mössbauer measurements. Although the zero-field cooled and field-cooled magnetization variations are not like a typical spin glass one, the Mössbauer spectrum below Néel temperature shows a hyperfine field distribution. It implies that the 10% FeI₂ mixed in FeBr₂ can be induced by the bond random effect which causes the sample to exhibit a spin glass-like behavior.