Estimates for the Rapid Decay of Concentration Functions of n-Fold Convolutions

We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov–Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n ^–1/2). On the other hand, Esseen⁽³⁾ has shown that this rate is o(n ^–1/2) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.⁽⁹⁾ Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n ^–1/2).     

The <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/∞ system revisited: finiteness,summability, long range dependence,and reverse engineering

We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated. We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied to various examples, including ones with infinite queues and non-summable workloads. AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10     

L1-optimal estimates for a regression type function in R

Let X₁, X₂, …, X_n be random vectors that take values in a compact set in R^d, d ≥ 1. Let Y₁, Y₂, …, Y_n be random variables (“the responses”) which conditionally on X₁ = x₁, …, X_n = x_n are independent with densities f(y | x_i, θ(x_i)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θ_q,d of real valued functions, an optimal L₁-consistent estimator of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θ_q,d.     

Convexity Bias in the Pricing of Eurodollar Swaps

The traditional use of LIBOR futures prices to obtain surrogates for the Eurodollar forward rates is proved to yield a systematic bias in the pricing of Eurodollar swaps when one assumes that the yield curve is well described by the Heath-Jarrow-Morton model. The resulting theoretical inequality is consistent with the empirical observations of Burghardt and Hoskins (1995), and it provide a theoretical basis for price anomalies that are suggested by more recent empirical data.     

Deconvolving compactly supported densities

This paper addresses the statistical problem of density deconvolution under the condition that the density to be estimated has compact support. We introduce a new estimation procedure, which establishes faster rates of convergence for smooth densities as compared to the optimal rates for smooth densities with unbounded support. This framework also allows us to relax the usual condition of known error density with non-vanishing Fourier transform, so that a nonparametric class of densities is valid; therefore, even the shape of the noise density need not be assumed. These results can also be generalized for fast decaying densities with unbounded support. We prove optimality of the rates in the underlying experiment and study the practical performance of our estimator by numerical simulations.      

Rate processes on fractals: Theory,simulations, and experiments

Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A products we show that the diffusion-limited reaction rate is proportional tot ^– h[A]² or to [A]^x, whereh=1- d _s/2, X=1+2/d _s =(h-2)(h-1), andd _s is the effective spectral dimension. We note that ford = d _s =1, h =1/2 andX = 3, for percolating clustersd _s = 4/3,h = 1/3 andX = 5/2, while for dust ds <1, 1 >h > 1/2 and >X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates.     

Heating rate effect on the DSC kinetics of oil shales

This research was aimed to investigate the combustion and kinetics of oil shale samples (Mengen and Himmetoğlu) by differential scanning calorimetry (DSC). Experiments were performed in air atmosphere up to 600°C at five different heating rates. The DSC curves clearly demonstrate distinct reaction regions in the oil shale samples studied. Reaction intervals, peak and burn-out temperatures of the oil shale samples are also determined. Arrhenius kinetic method was used to analyze the DSC data and it was observed that the activation energies of the samples are varied in the range of 22.4–127.3 kJ mol⁻¹ depending on the oil shale type and heating rate.     

Thermal behaviour and slow molecular mobility in two isomers of biphenylmethanol

This research was aimed to investigate the role of clay on the combustion and kinetic behavior of crude oils in limestone matrix. For this purpose, simultaneous TG (thermogravimetry) and DTA (differential thermal analysis) experiments were performed at three different heating rates as 10–15 and 20°C min^–1, respectively. A uniform trend of decreasing activation energies was observed with the addition of clay. It was concluded that clays surface area affects the values of Arrhenius constant, while it is the catalytic properties of clay, which lower the activation energies of all the reactions, involved in the combustion process.     

二水草酸锌脱水的热分解动力学研究

提出一种多升温速率-等温法确定机理函数g(α)的新方法;并用迭代的等转化率法求出较为可靠的活化能Ea;在Ea和g(α)的基础上计算出指前因子A.用该法对二水草酸锌（ZnC2O4•2H2O）脱水反应的热分解动力学三因子进行了求算,得出Ea为87.22 kJ•mol－1, A为4.2120×108～7.2328×108 s－1;以及随机成核和随后生长型机理函数Am（Avrami-Erofeer）,其积分形式g(α)=[－ln(1－α)] 1/m和微分形式f(α)=m(1－α)•[－ln(1－α)](1－1/m),调节因子m=1.85～2.00.     

用~(13)C NMR弛豫研究星形聚苯乙烯在溶液中的分子运动(Ⅱ)

对不同支化度和不同支链链长的20％(W/V)星形聚苯乙烯溶液测定了~(13)C NMR弛豫参数,用1g-x~2分布、Cole-Cole分布和构象跳跃模型对主链的分子运动进行了分析讨论,并对芳环侧基的内旋转运动也进行了分析,求出了活化能和跳跃速率。结果表明,轻度化学交联对相关时间分布有一定影响,对链段运动的势垒没有明显影响。支链链长对~(13)C NMR弛豫的影响和对线形聚合物的影响是类似的。