Transfer activity coefficient of the proton in water-pyridine mixtures. A comparison of some extrathermodynamic assumptions

Various water-pyridine mixtures have been selected in order to compare several of the most popular extrathermodynamic assumptions involved in the determination of the transfer activity coefficient of the proton, _t(H⁺). Two techniques have been utilized for this purpose: voltammetry [study of the ferrocene, ferricyanide, or thallium(1) systems] and potentiometry at equilibrium (emf measurements of various galvanic cells, including liquid junctions and hydrogen electrode or silver electrode as a test electrode). The assumptions have been classified into various groups [e.g., _t(Z^p+)=_t(Z^q+) or _t(X^–)=_t(Y⁺)], and the values of _t(H⁺) have been experimentally determined in each case. The results vary depending upon the basic assumption (several pH units); less important differences (e.g., 0.5 pH unit) occur within a given group, and this may be assigned to the nature of the reference species chosen. A simple model of solvation has been also examined; the application of the law of mass action to the corresponding equilibrium provides results close to the _t(X^–) =_t(Y⁺)type of assumptions which ultimately leads to most self-consistent results.     

Stationary queues with one autonomous server

Given a stationary stochastic continuous demand of service σ(θ_tω) dt with ∫ σ(ω)P(dω) < 1, we construct real stationary point processes $\text{(T}{}_{\mathrm{n}}\text{, n ∈}\text{Z}\text{)[T}{}_{\mathrm{n}}\text{< T}{}_{\mathrm{n}}\text{+1, lim}{}_{\mathrm{\pm \infty }}\text{T}{}_{\mathrm{n}}\text{= ±∞]}$ such that

for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [T_n, T_n+1[ the demand of service accumulated during the proceding intervals [T_n?1, T_n[ and take a rest of fixed duration D.     

Some Logical Implications of the Two Einstein Assumptions Used in His Analysis of Geometry on a Relativistically Rotating Disc

We show that with the help of the two well known Einstein assumptions used by him in the treatment of geometry on relativistically rotating disc, and elementary logical analysis only, two different and opposite models of rotating discs can be constructed: In one of them the disc, set rotating from the stationary state, changes neither its radius nor circumference, as measured from stationary inertial frame; while in the other both the radius and the circumference contract by the same Lorentz factor. We also show that one can construct discs whose contraction factors vary continuously from unity (no contraction) to the full Lorentz factor.     

Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions

In this paper, a new class of Runge–Kutta methods is introduced. Some basic properties of this subgroup of algebraically stable methods are presented and a complete parametric representation is given. Necessary and sufficient order conditions for lower order methods as well as sufficient order conditions for higher order methods are derived yielding a significantly reduced number of conditions when compared with general Runge–Kutta methods. Design examples conclude this paper.     

Existence of Equilibria in Economies with Externalities and Nonconvexities

We consider a general equilibrium model of an economy in which the production possibilities, the consumption sets and the preferences of the consumers are represented by set-valued mappings which depend on the environment to take into account the possibility of external effect. In order to encompass all kinds of nonconvexities, we do not put any convexity assumption either on the graph of the set-valued mapping which describes the technological possibilities or on the production set for a given environment. The firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other producers and on consumption plans.We report an existence result of general equilibria. As in the model without external effects, the key hypotheses are bounded loss and survival assumptions. Nevertheless, we also assume that the set-valued mappings which describe the fundamentals of the economy are lower semi-continuous and have a closed graph.Our framework is sufficiently large to generalize previous works on the existence of competitive equilibria with externalities when the firms have convex production sets and on the existence of equilibria with general pricing rule without externality.     

不用Kirchhoff-Love假设的三维弹性板二级近似理论及其边界条件

前文[1]给出了不用Kirchhoff-Love假设的三维弹性板的一级近似理论及其边界条件。这个理论有6个微分方程求解6个待定平面函数,即u₀,u_α,A₍₀₎,S_(2)α,其中有3个方程为一组求解3个待定平面函数u₀,S_(2)α,而另一组3个方程求解另外3个待定平面函数u_α,A₍₀₎.它们的边界条件和这些方程一样,可以从本问题的广义变分原理的泛函变分的驻值条件求得,当板厚h和板宽α之比h/α很小时,这种解接近于经典薄板解,当h/α值较大时(如h/α≈0.3),这种解和经典薄板解,就有较大差别。但这种差别在h/α值的什么范围内是合理的这一问题,并不清楚,为了解决这一问题,我们必须研究本问题的二级近似理论。本文是前文的继续,我们将用本问题的广义变分原理的泛函变分驻值条件,导出9个微分方程和有关边界条件,用以求解9个二级近似解的待定平面函数u₀,u_α,A₍₀₎,A₍₁₎,S_(2)α,S_(3)α,把二级近似理论解和一级近似理论以及经典理论的解相比较,就能明确一级近似理论的适用范围,这里必须指出,二级近似理论也可以分成两组方程求解,求解过程也并不过分复杂。有关符号和前文相同,这里必须指出,二级近似理论也可以分成两组方程求解,求解过程也并不过分复杂.有关符号和前文相同,这里将不再重复。     

关于克劳修斯方法对可逆和不可逆过程(循环)的处理

介绍了克劳修斯方法对可逆和不可逆过程(循环)的处理,提出了处理不可逆过程的方法,论证了处理方法与克劳修斯方程的一致性,论述了克劳修斯方法的实质和意义;简单介绍了熵的另一个导出方法,比较了两种方法对绝热过程的处理,指出克劳修斯方法存在一个假设条件.     

Comparison and bounds for functionals of future lifetimes consistent with life tables

We derive a new crossing criterion of hazard rates to identify a stochastic order relation between two random variables. We apply this crossing criterion in the context of life tables to derive stochastic ordering results among three families of fractional age assumptions: the family of linear force of mortality functions, the family of quadratic survival functions and the power family. Further, this criterion is used to derive tight bounds for functionals of future lifetimes that exhibit an increasing force of mortality with given one-year survival probabilities. Numerical examples illustrate our findings.