A potentiometric investigation of the hydrolysis of chromate (VI) ion in NaCl media to 175°C

The hydrolysis of chromate ion was studied potentiometrically in a concentration cell fitted with hydrogen electrodes by titrating basic NaCl–Na₂CrO₄ solutions with standardized HCl against a NaOH reference solution. The temperature was varied from 25 to 175°C at 25° intervals at the following ionic strengths (I): 0.1140, 0.2346, 0.5337, 0.9988, 2.940, and 5.239 (NaCl). Depending on the ionic strength, the molality of total chromium was varied from 0.001 to 0.100. The resulting titration curves could be resolved best in terms of three equilibria involving the formation of HCrO ₄ ^– (aq), Cr₂O^3– (aq), and CrO₃Cl^– (aq). The equilibrium quotients for all three reactions were fitted as a function of temperature and ionic strength, and the molal thermodynamic parameters that were computed from these relationships are tabulated at specific ionic strengths over the experimental temperature range.     

Thermodynamics of molecular interactions in ethyl iodide+toluene mixtures

The excess Gibb's free energy of mixing, G^E, for ethyl iodide+toluene at 25°C have been obtained from the measured vapor pressuure data. The H^E and G^E values for ethyl iodide+toluene are positive throughout the ethyl iodide concentration range and G^E>H^E. The results have been analyzed in terms of Flory and ideal associated model theory of nonelectrolyte solutions. It has been observed that the ideal associated model approach which assumes the presence of AN and A₂B molecular species describes well (within±10 J-mol^–1 in the worst case) the general dependence of H^E on X_A (mole fraction of ethyl iodide) over the whole composition range for ethyl iodide+toluene mixtures. The equilibrium constants for A+A AB and 2A+BA₂B reactions along with the enthalpies of formation of AB and A₂B molecular species have been calculated.     

A two-population game in observable double-ended queuing systems

In this study, the existing game theoretical framework is extended to strategic queuing in search of solutions for a two-population game in observable double-ended queuing systems with zero matching times. We show that multiple Nash equilibria and one unique subgame perfect Nash equilibrium exist in this game.     

两台自私型机器上自私工件排序的PoA紧界

本文研究了两台自私型机器上有自私型工件的关于二元均衡的排序问题。对任意工件序列$L$, 证明了二元均衡排序的PoA的紧界为$\frac{8}{7}$。如果工件尺寸在区间$[1, r](r\ge1)$内, 得到了二元均衡排序的PoA的紧界为关于$r$的分段线性函数。     

Criteria for local equilibrium in a system with transport of heat and mass

Nonequilibrium molecular dynamics is used to compute the coupled heat and mass transport in a binary isotope mixture of particles interacting with a Lennard-Jones/spline potential. Two different stationary states are studied, one with a fixed internal energy flux and zero mass flux, and the other with a fixed diffusive mass flux and zero temperature gradient. Computations are made for one overall temperature,T=2, and three overall number densities,n=0.1, 0.2, and 0.4. (All numerical values are given in reduced, Lennard-Jones units unless otherwise stated.) Temperature gradients are up to T=0.09 and weight-fraction gradients up to w ₁=0.007. The flux-force relationships are found to be linear over the entire range. All four transport coefficients (theL-matrix) are determined and the Onsager reciprocal relationship for the off-diagonal coefficients is verified. Four different criteria are used to analyze the concept of local equilibrium in the nonequilibrium system. The local temperature fluctuation is found to be T0.03T and of the same order as the maximum temperature difference across the control volume, except near the cold boundary. A comparison of the local potential energy, enthalpy, and pressure with the corresponding equilibrium values at the same temperature, density, and composition also verifies that local equilibrium is established, except near the boundaries of the system. The velocity contribution to the BoltzmannH-function agrees with its Maxwellian (equilibrium) value within 1%, except near the boundaries, where the deviation is up to 4%. Our results do not support the Eyring-type transport theory involving jumps across energy barriers; we find that its estimates for the heat and mass fluxes are wrong by at least one order of magnitude.     

Misclassification minimization

The problem of minimizing the number of misclassified points by a plane, attempting to separate two point sets with intersecting convex hulls inn-dimensional real space, is formulated as a linear program with equilibrium constraints (LPEC). This general LPEC can be converted to an exact penalty problem with a quadratic objective and linear constraints. A Frank-Wolfe-type algorithm is proposed for the penalty problem that terminates at a stationary point or a global solution. Novel aspects of the approach include: (i) A linear complementarity formulation of the step function that counts misclassifications, (ii) Exact penalty formulation without boundedness, nondegeneracy or constraint qualification assumptions, (iii) An exact solution extraction from the sequence of minimizers of the penalty function for a finite value of the penalty parameter for the general LPEC and an explicitly exact solution for the LPEC with uncoupled constraints, and (iv) A parametric quadratic programming formulation of the LPEC associated with the misclassification minimization problem.This material is based on research supported by Air Force Office of Scientific Research Grant F49620-94-1-0036 and National Science Foundation Grants CCR-9101801 and CDA-9024618.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions

Recently R. Illner and the author proved that, under a physically realistic truncation on the collision kernel, the Boltzmann equation in the one-dimensional slab [0, 1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. Here it is proved that when the Maxwellians associated with the boundary conditions atx=0 andx=1 are the same MaxwellianM _w , then the solution is uniformly bounded and tends toM _w fort.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.