Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

乙烯系单体自由基聚合的阻聚效应──XIX．取代哌啶羟胺和二叔丁基羟胺及其稳定自由基对苯乙烯－丙烯腈共聚合的影响

研究了二叔丁基羟胺（ＤＴＢＨＡ），二叔丁基氮氧自由基（ＤＴＢＮＯ·），２，２，６，６－四甲基－４－羟基哌啶羟胺（ＴＭＨＰＨＡ）和２，２，６，６－四甲基－４－羟基哌啶－１－氧自由基（ＴＭＨＰＯ·）对过氧化苯甲酰（ＢＰＯ）６０℃引发的苯乙烯（Ｍ１）－丙烯腈（Ｍ２）共聚合的阻聚行为．结果表明，这些阻聚剂对Ｓｔ－ＡＮ共聚均表现良好的阻聚行为，其中氮氧自由基优于相应羟胺．同时观察到Ｓｔ—ＡＮ竞聚率的改变，羟胺使ｒ１有所降低，ｒ２略有增大．但相应的氮氧自由基是相反结果．阻聚剂为２００ｐｐｍ时，共聚物中的恒比共聚点由对照实验的０．６１９变化为０．５３３，０．６４５，０．５８９和０．６９８相对于ＤＴＢＨＡ，ＤＴＢＮＯ·，ＴＭＨＰＨＡ和ＴＭＨＰＯ·．     

Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

Applicability of polymer theories to the thermodynamics of proteins at the air/water interface: example of β-lactoglobulin

Knowledge of the equation of state of adsorbed or deposited layers of proteins at the air/water interface is of fundamental interest in the understanding of the surface activity of these molecules. Using scaling laws of current polymer theories, it has been shown that the equation of state of the interfacial layer in the semi-dilute regime should relate the surface pressure to the surface concentration through a power law. The exponent of this power law should reflect the quality of the solvent and the conformation of the adsorbed polypeptide chain. In the case of β-lactoglobulin layers, in the range of surface concentrations that should correspond to the semi-dilute regime, the relationship between surface pressure and surface concentration is expressed as a power law. The exponent of this power law is strongly influenced by the nature of the aqueous substrate and by the net charge of the protein molecule. The use of scaling laws gives a coherent view of the expansion of the polypeptide chain in the interfacial layer and of the relationship between surface concentration and surface pressure in the semi-dilute regime. This result favours a strong similarity between β-lactoglobulin and a polymer chain in the interfacial layer. It is concluded that current theories of polymer adsorption could be applied to interfacial protein layers.     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

Substituent control in the diastereoselectivity of dipolar cycloadditions of nitrones and their Zn(II) complexes with N-arylmaleimides

The π-π stacking interactions between maleimide's and nitrone's aromatic rings during the 1,3-dipolar cycloaddition were assumed to control the exo-endo selectivity of the reaction. The exo-endo ratios change during the reactions until they reach a constant value, which depends on the substituent. Electron-withdrawing groups favour the exo adduct while electron-donating groups favour the endo adduct. The nitrone ZnBr₂ complexes react much more slowly than the free nitrone and the cycloaddition is exo selective in all cases independent of the substituents on the maleimide's aromatic ring. Thermal retrocycloaddition of the cycloadducts produce the corresponding nitrones. The ring opening in the presence of secondary amines did not induce imine formation. endo Adducts were shown for the first time to be the stable paramagnetic compounds.     

β-Tricarbonyl compounds. I. 2,4-Disubstituted 1,3-cyclopentanediones

Summary Stable enolic isomers of 2-aroyl-4-aracyl-1,3-cyclopentanediones such as3 and4 were prepared by condensation of aryl methyl ketones and diethyl maleate using an excess of sodium ethoxide (Aryl=C₆H₅, 4-C₆H₄CH₃, 4-C₆H₄Br and 4-C₆H₄Cl).

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-Tricarbonyl Verbindungen. I. 2,4-Disubstituierte 1,3-Cyclopentandione

Zusammenfassung Stabile Enol-Isomere von 2-Aroyl-4-aracyl-1,3-cyclopentandionen wie3 und4 wurden durch Kondensation von Arylmethylketonen und Diethylmaleat mit einem Überschuß von Natriumethoxid dargestellt (Aryl=C₆H₅, 4-C₆H₄CH₃, 4-C₆H₄Br und 4-C₆H₄Cl).

     

A review ofL=λW and extensions

A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.     

15-甲基-双环[10,3,0]十五碳-1(12)-烯-13-酮的晶体结构及分子稳定构象

15-甲基-双环[10,3,0]十五碳-1(12)-烯-13-酮的单晶属空间群P2_1/n,晶胞参数:a=0.4838(1)nm,b=1.3949(2)nm,c=2.1645(4)nm,β=92.07(1)°,Z=4.其中平面五员环呈刚性。另一个含烯十二员环的实际构象与分子力学计算的最稳定构象一致。     

Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi–Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.