Law of the iterated logarithm for perturbed empirical distribution functions evaluated at a random point for nonstationary random variables

We consider perturbed empirical distribution functions , where {Ginn, n1} is a sequence of continuous distribution functions converging weakly to the distribution function of unit mass at 0, and {X _{i, i}1} is a non-stationary sequence of absolutely regular random variables. We derive the almost sure representation and the law of the iterated logarithm for the statistic whereU _n is aU-statistic based onX ₁,...,X _n . The results obtained extend or generalize the results of Nadaraya,⁽⁷⁾ Winter,⁽¹⁶⁾ Puri and Ralescu,^(9,10) Oodaira and Yoshihara,⁽⁸⁾ and Yoshihara,⁽¹⁹⁾ among others.Research supported by the Office of Naval Research Contract N00014-91-J-1020.     

Interpretation of an exactly solvable two-component plasma

The interpretation of the exact calculation of the partition function and correlations of a two-component plasma obtained earlier is considered. The system has species of charge ratio 12 which are constrained to lie on a circle and interact via the two-dimensional Coulomb potential. By studying the exact results we gain an understanding of why the excess thermodynamic quantities of the two component system can be well approximated by the sum of the appropriate excess thermodynamic quantities of the one-component systems.     

The molecular anvil model of an enzyme taking into consideration the flexibility of enzyme molecules

The concept of a molecular anvil model of an enzyme, assuming a rigid enzyme molecule, is introduced. Two distinct features of enzymes, high catalytic power and high specificity, are reasonably and consistently explained. The dynamic nature of molecular anvil action is stressed. The origin of the high catalytic power is the spontaneous creation of a high energy state at the anvil site. The origin of the high specificity is a high sensitivity of the maximum accessible potential energy to the relatively extruded distance of the molecular anvil. The flexible model is developed by assuming a flexible enzyme molecule. It is deduced from this flexible model that enzyme activity shows a maximum with a wide range of monotonous change of the configuration of the enzyme molecule. This is the origin of the general property of enzymes that enzyme activity shows a maximum with monotonous variation of environmental parameters such as pH, temperature, pressure or some times concentration of chemical substances. The induced fit theory of Koshland is reasonably explained. The relation and differences between individual theories of enzymes are discussed. The enzymological basis of the complex regulation of biological organisms is discussed. The inversion of the sign of control of effectors is predicted when environmental parameters are varied. This concept may be useful in designing artificial enzymes or high specificity catalysts.Presented at the Fourth International Symposium on Inclusion Phenomena and the Third International Symposium on Cyclodextrins, Lancaster, U.K., 20–25 July 1986.     

Ergodic properties of infinite-dimensional stochastic systems

The ergodic properties of two stochastic models _I and _II are investigated. Each model is described by a fieldx(t),t > 0, on the lattice =Z ^d,d < . For _I,x(t) evolves according to the equations wherex _s (t) R for eachs eF. Here the {w_s(t): s } are independent, one-dimensional Wiener processes, ₂ is a bounded interaction between adjacent lattice sites, and the potentials ₁ and ₂ satisfy appropriate regularity conditions. It is shown that for each model,x(t) is a Markov process on an infinite-dimensional phase spaceX. The probability measures onX that satisfy the Dobrushin-Lanford-Ruelle (DLR) conditions are stationary for this process and have a mixing property. Moreover, for _I any stationary, time-reversal-invariant probability measure that has certain regularity properties must satisfy the DLR conditions.This paper is based on a portion of the author's Ph.D. thesis.⁽²⁾     

On the Circulation Structure and Formation Mechanism of the Cold Water Mass of the Yellow Sea (Ⅰ)——Zero-order Solution and Circulation Structure

A series of studies have been made on the circulation structure and the responsible mechanisms related to the Cold Water Mass of the Yellow Sea. From the present model governing the nonlinear thermally driven circulation in shallow seas, some complete analytical solutions of temperature and velocity components have been obtained in this paper by solving the coupled equations of motion and heat conduction. The results demonstrate that the wind-induced stirring and the tidal mixing are all responsible for the termal structure formation of Cold Water Mass. The computed vertical convection (u-w) develops only within a thin layer (called "a current shell" here) in the vicinity of thermocline while the deeper layer remains almost motionless. This current structure represents well the maintenance mechanisms of thermocline or the Cold Watermass during the summer.     

Excess properties of aqueous mixtures of methanol: Simulation versus experiment

We report molecular simulation results for both the excess mixing and partial molar properties of water–methanol mixtures over the entire concentration range with the particular emphasis on the low concentration ends. It is shown that the mixing properties are very sensitive to potential models and that the used realistic potentials (TIP4P for water and OPLS for methanol) give a reasonably good agreement with experiment only for volumetric properties although the qualitative trend of the partial molar volume at low concentrations is not reproduced. As regards excess enthalpy, the results are rather bad and only its sign is predicted correctly.     

Thermodynamics of the system H2O−NaCl−Na2SO4−MgSO4 to the saturation limit of NaCl at 25°C

Isopiestic results are reported for the quaternary system H₂O–NaCl–Na₂SO₄–MgSO₄. The excess free energies for mixing the double salt Na₂ Mg(SO₄)₂ with NaCl are fairly large and negative, as also are the free energies for mixing the three salts to form the quaternary aqueous system.     

Enthalpies of the urea-tert-butanol-water system at 25°C

The enthalpies of solution of urea (U) in water (W)-tert-butanol (TBA) mixtures and of TBA in W-U mixtures, the enthalpies of dilution of TBA in W, and the enthalpies of mixing of U and TBA aqueous solutions were measured with a solution calorimeter and a flow microcalorimeter. Enthalpies of transfer of U and TBA to the mixed solvents were derived. Also, pair and triplet interaction parameters between the various solutes were derived from the mixing and dilution experiments. The enthalpic pair parameter h_U-TBA is positive, suggesting that the main contribution to this parameter is the decrease in hydrophobic hydration of TBA in the presence of U.     

Thermodynamics of mixed electrolyte solutions. IX. Calculation of the osmotic and activity coefficients in a pseudoternary system (NaCl−nKCl)−MgCl2-H2O at 298.15°K

The equation of Reilly, Wood, and Robinson was used to predict the osmotic coefficient of a pseudoternary system (NaCl–nKCl)–MgCl₂–H₂O over a molal ionic strength range of 1.0 to 5.0 moles-kg^–1. The results are in close agreement with experimental data at most ionic strengths. The standard deviation in the osmotic coefficients over the entire concentration range lies within 0.0035. The predicted values of the mean activity coefficients are in good agreement with those obtained by the treatments of both Scatchard and Friedman. Mean activity coefficients for the other components were also predicted.     

基于制冷机的高温超导谐波混频

我们分别选用了小型脉冲管制冷机以及小型G-M制冷机设计了高温超导混频测量系统,对亚毫米波段谐波混频进行了实验研究.采取了一些抑制系统噪声的措施后,在脉冲管制冷机上我们成功实现了100GHz混频,最高谐波次数达60次,在G-M制冷机上我们实现了300GHz混频,最高谐波次数达100次.