Nonequilibrium lattice models: Series analysis of steady states

A perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state. The expansion is expressed directly in terms of the kinetic parameter (creation rate), rather than in powers of the interaction. An algorithm for generating series expansions for local properties is described. Order parameter series (16 terms) and precise estimates of critical properties are presented for the one-dimensional contact process and several related models.     

Approach to equilibrium in a one-dimensional,two-component gas of Maxwellian molecules

The coupled Boltzmann equations describing the evolution of the velocity distributions of a one-dimensional, two-component gas of Maxwellian molecules are analyzed. When the two species have different masses, the system approaches equilibrium. The complete eigenvalue spectrum of the linearized collision operator is obtained, and is found to exhibit an interesting dependence on the mass ratio. The response of one species to an external field, when the other species is regarded as a host fluid, is also examined.     

Optimization in Multiple-objective Linear Programming Problems with Pre-emptive Priorities

A decision-maker, using mathematical programming optimization models, is often faced with a choice of many alternative solutions optimizing the objective function. The decision may be based on secondary, tertiary or higher-order objectives. Such problems are usually handled using goal programming (GP) with pre-emptive priorities. Pre-emptive prioritization is discussed in the literature in the context of GP. This paper suggests that the two are separable, and presents algorithms to accomplish this. It argues that in a truly pre-emptive situation, direct lexicographical optimization of the objectives, without introduction of goals, has a number of advantages. In addition, when applied to special structure models such as transportation or assignment, this approach enables one to maintain the structure and hence the efficiency of those algorithms.     

The monolanthanide-containing silicotungstates [Ln(beta2-SiW11O39)2]13- (Ln = La, Ce, Sm, Eu, Gd, Tb, Yb, Lu): a synthetic and structural investigation

We have synthesized and structurally characterized the monolanthanide-containing polyanions [Ln(beta2-SiW11O39)2]13- (Ln = La (1), Ce (2), Sm (3), Eu (4), Gd (5), Tb (6), Yb (7), Lu (8)). Synthesis was accomplished by reaction of the respective lanthanide ion with the monolacunary Keggin-type precursor [beta2-SiW11O39]8- in a 1:2 molar ratio in 1 M KCl medium at pH 5. Polyanions 1-8 were isolated as potassium salts and then characterized by IR, single-crystal X-ray diffraction, and elemental as well as thermogravimetric analysis. The structures of 1-8 are composed of an eight-coordinated Ln3+ center sandwiched by two chiral (beta2-SiW11O39) units. Large Ln3+ ions appear to favor an (R,R) (or (S,S)) configuration (point group C2) of the Keggin units, with an increasing amount of (R,S) (or (S,R)) configuration (point group C1) found in the solid state as the Ln3+ ion decreases in size. This trend is also supported by solution 183W NMR results for the diamagnetic La3+ and Lu3+ derivatives.     

13-tungstoborate stabilized by an organostannoxane hexamer

The novel dimethyltin-containing polyanion [{(CH3)2Sn}6(OH)2O2(H2BW13O46)2]12- (1) is composed of two [H2BW13O46]9- clusters linked by an unprecedented planar, hexameric [{(CH3)2Sn}6(OH)2O2]8+ organostannoxane moiety, representing the first X-ray structural characterization of a molecular hybrid organic-inorganic tungstoborate and of the elusive [HnBW13O46](11-n)- species.     

Dimerization of mono-ruthenium substituted alpha-Keggin-type tungstosilicate [alpha-SiW11O39RuIII(H2O)]5- to micro-oxo-bridged dimer in aqueous solution: synthesis, structure, and redox studies

We report the dimerization of a mono-ruthenium(III) substituted alpha-Keggin-type tungstosilicate [alpha-SiW(11)O(39)Ru(III)(H2O)](5-) to a micro-oxo-bridged dimer [{alpha-SiW(11)O(39)Ru(m)}2O](n-) (m = III, n = 12; m = IV/III, n = 11; m = IV, n = 10). Single crystal X-ray structure analysis of Rb(10)[{alpha-SiW(11)O(39)Ru(IV)}2O].9.5H2O (triclinic, P1, with a = 12.7650(6) A, b = 18.9399(10) A, c = 20.2290(10) A, alpha = 72.876(3) degrees, beta = 88.447(3) degrees, gamma = 80.926(3) degrees, V = 4614.5(4) A(3), Z = 2) reveals that two mono-ruthenium substituted tungstosilicate alpha-Keggin units are connected through micro-oxo-bridging Ru-O-Ru bonds. Solution (183)W-NMR of [{SiW(11)O(39)Ru(IV)}2O](10-) resulted in six peaks (-63, -92, -110, -128, -132, and -143 ppm, intensities 2 : 2 : 1 : 2 : 2 : 2) confirming that the micro-oxo bridged dimer structure is maintained in aqueous solution. The dimerization mechanism is presumably initiated by deprotonation of the aqua-ruthenium complex [alpha-SiW(11)O(39)Ru(III)(H2O)](5-) leading to a hydroxy-ruthenium complex [alpha-SiW(11)O(39)Ru(III)(OH)](6-). Dimerization of two hydroxy-ruthenium complexes produces the micro-oxo bridged dimer [{alpha-SiW(11)O(39)Ru(III)}2O](12-) and a water molecule. The Ru(III) containing dimer is oxidized by molecular oxygen to produce a mixed valence species [{alpha-SiW(11)O(39)Ru(IV-III)}2O](11-), and further oxidation results in the Ru(IV) containing [{alpha-SiW(11)O(39)Ru(IV)}2O](10-).