Skew Brownian motion-type of extensions

We consider a class of possible extensions of a given symmetric Feller processZ _t fromR{0} to the entire real lineR, depending on a parameter [0, 1]. It is proved that the proposed extension exists if =1/2; for 1/2, exists if and only ifZ _t does not jump over 0 (e.g., ifZ _t is a diffusion).     

Small ball probabilities for a Wiener process under weighted sup-norms,with an application to the supremum of bessel local times

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup_0<11(t ^–p R(t)) and sup _t 0(e ^–1 R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.     

The difference between Newtonian and relativistic forces

This paper discusses a new turn in the 148-year old electrodynamic force law controversy between the 1822 Ampère force law of the Newtonian electrodynamics and Grassmann's 1845 law which has become the electrodynamic force law of relativistic electromagnetism. Faced with the infallibility of Ampère's empirical law, defenders of relativity theory now argue that Ampère's law is equivalent to the relativistic law. This paper demonstrates that, far from being equivalent, the laws require two different mechanics of solid bodies, disagree on internally generated stresses, and predict different force distributions.     

Transient flow towards a well in an aquifer including the effect of fluid inertia

Transient propagation of weak pressure perturbations in a homogeneous, isotropic, fluid saturated aquifer has been studied. A damped wave equation for the pressure in the aquifer is derived using the macroscopic, volume averaged, mass conservation and momentum equations. The equation is applied to the case of a well in a closed aquifer and analytical solutions are obtained to two different flow cases. It is shown that the radius of influence propagates with a finite velocity. The results show that the effect of fluid inertia could be of importance where transient flow in porous media is studied.List of symbols b Thickness of the aquifer, m - c ₀ Wave velocity, m/s - k Permeability of the porous medium, m² - n Porosity of the porous medium - p( ,t) Pressure, N/m² - Q Volume flux, m³/s - r Radial coordinate, m - r _w Radius of the well, m - s Transform variable - S Storativity of the aquifer - S _d(r, t) Drawdown, m - t Time, s - T Transmissivity of the aquifer, m²/s - ( ,t) Velocity of the fluid, m/s - Coordinate vector, m - z Vertical coordinate, m - Coefficient of compressibility, m²/N - Coefficient of fluid compressibility, m²/N - Relaxation time, s - (r, t) Hydraulic potential, m - Dynamic viscosity of the fluid, Ns/m² - Dimensionless radius - Density of the fluid, Ns²/m⁴ - (, ) Dimensionless drawdown - Dimensionless time - , x Dummy variables - ₀, ₁ Auxilary functions     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

Kinetics of thermal decomposition of alkaline phosphates

Summary The thermal behavior of KH₂PO₄, NaH₂PO₄ and Na₂HPO₄ under non-isothermal conditions using TG method with different heating rates was studied. The values of the reaction rate were processed by means of Friedmans differential-isoconversional method. A dependence of the activation energy vs. conversion was observed. Therefore a procedure based on the compensation effect (suggested by Budrugeac and Segal) was applied. A less speculative data processing protocol was offered by the non-parametric kinetics method suggested by Serra, Nomen and Sempere. Three steps were observed by non-isothermal heating: a dehydration, a dimerization and a polycondensation. The differences in the intimate reaction mechanism are determined by the initial number of water molecules.     

Dielectric behaviour of a side-chain-bearing liquid-crystalline polysiloxane

The relaxation of electric field-induced polar orientation in a side-chain-bearing liquid-crystalline polysiloxane was measured by means of thermally stimulated depolarization currents. Different relaxation mechanisms were identified and characterized: the glass transition cooperative relaxation exhibits compensation behaviour. On the other hand, lowerT _g and upperT _g discharges were observed and their molecular nature is discussed.     

光度分析中协同系数补偿方法的研究──三次标准加入法同时测定钼、钨和钛

本文在两次标准加入法[1]的基础上，提出了三组份同时测定的三次标准加入法，并应用于钼、钨和钛的流动注射同时测定。测定条件：［水杨基荧光酮（SAF）］＝1．25　×10-4mol／L，［溴化＋六烷基三甲基铵（CTMAB）」＝2．5×10－3mol／L，pH1．35，25℃，采样、进样时间分别为10s和18s，进样频率128次／h。为消除组份间协同作用引起的吸光度加合性的偏离，定义了三组份协同系数。将其引入三组份同时测定方法，补偿了吸光度对线性的偏离。补偿后钼、钨和钛的测定范围分别为0．05～0．35，0．25～1．00，0．025～0．30mg／L。测定了钢样及模拟样品中钼、钨和钛含量，结果较好。     

The Kissinger law and isokinetic effect: Part II. Experimental analysis

On the basis of copper sulphate pentahydrate thermal dissociation, for analyzed reactions I to IV, 6 thermokinetic equations was discussed. Arrhenius law parameters were determined and the isokinetic effect (IE) and Kissinger law appearing was analyzed. It was found that only dependence resulting from isokinetic effect, in the form k _m=q/T _m, relates to the suitable thermokinetic Eq. (2) and Kissinger law in modified form (14). The confirmation was made that the possibility of determining the averaged activation energy from thermokinetic equations using suitable correction coefficients exists.This revised version was published online in November 2005 with corrections to the Cover Date.     

Compensation effect in the electrical conduction process in a series of pyrenyl polyenes

The semiconductive properties of a series of pyrenyl polyenes of the type R-(CH=CH)_n-R, are studied as a function of the adsorption of different amount of a vapour. With regard to the compensation temperature (T ₀) the compounds are divided into two groups. For compounds which have odd number of double bonds,T ₀ is infinite and in compounds having even number double bonds,T ₀ is finite.T ₀ for II₂ is higher while that of II₄ is lower than the experimental temperature. DifferentT ₀ for the compounds having odd or even number of double bonds suggests a physical basis for the compensation rule, which we believe, is related to the molecular and crystalline structure of the compounds