Heavy water reactions with atomic transition-metal and main-group cations: gas phase room-temperature kinetics and periodicities in reactivity

Reactions of heavy water, D(2)O, have been measured with 46 atomic metal cations at room temperature in a helium bath gas at 0.35 Torr using an inductively coupled plasma/selected ion flow tube tandem mass spectrometer. The atomic cations were produced at ca. 5500 K in an ICP source and were allowed to decay radiatively and thermalize by collisions with Ar and He atoms prior to reaction. Rate coefficients and product distributions are reported for the reactions of fourth-row atomic cations from K+ to Se+, of fifth-row atomic cations from Rb+ to Te+ (excluding Tc+), and of sixth-row atomic cations from Cs+ to Bi+. Primary reaction channels were observed leading to O-atom transfer, OD transfer, and D2O addition. O-Atom transfer occurs almost exclusively (>or=90%) in the reactions with most early transition-metal cations (Sc+, Ti+, V+, Y+, Zr+, Nb+, Mo+, Hf+, Ta+, and W+) and to a minor extent (10%) with one main-group cation (As+). OD transfer is observed to occur only with three cations (Sr+, Ba+, and La+). Other cations, including most late transition and main-group cations, were observed to react with D2O exclusively and slowly by D2O addition or not at all. O-Atom transfer proceeds with rate coefficients in the range of 8.1 x 10(-13) (As+) to 9.5 x 10(-10) (Y+) cm3 molecule(-1)(s-1) and with efficiencies below 0.1 and even below 0.01 for the fourth-row atomic cations V+ (0.0032) and As+ (0.0036). These low efficiencies can be understood in terms of the change in spin required to proceed from the reactant to the product potential energy surfaces. Higher order reactions are also measured. The primary products, NbO+, TaO+, MoO+, and WO+, are observed to react further with D(2)O by O-atom transfer, and ZrO+ and HfO+ react further through OD group abstraction. Up to five D(2)O molecules were observed to add sequentially to selected M+ and MO+ as well as MO2+ cations and four to MO(2)D+. Equilibrium measurements for sequential D(2)O addition to M+ are also reported. The periodic variation in the efficiency (k/k(c)) of the first addition of D(2)O appears to be similar to the periodic variation in the standard free energy (DeltaG degrees) of hydration.     

A superadditive solution for cephoidal bargaining problems

We present a bargaining solution defined on a class of polytopes in called “cephoids”. The solution generalizes the superadditive solution exhibited by Maschler and Perles for two dimensions. It is superadditive on a subclass of cephoids.      

On regularity and stability in semi-infinite optimization

For stationary solutions and Langrange multipliers of a semi-infinite program withC ¹ data, we study some stability behaviour which is closely related to (metric) regularity of the constraint system. The multiplier set mapping considered here has its images in a finite-dimensional space. In this framework, regularity is a necessary and sufficient condition to have bounded sets of multipliers.     

Metric regularity of the feasible set mapping in semi-infinite optimization

For parametric systems of (finitely many) equations and (infinitely many) inequalities the well-known concept of metric regularity is shown to be equivalent to the so-called extended Mangasarian-Fromovitz constraint qualification. By this, a corresponding result obtained by Robinson for finite optimization problems my be transferred to semi-infinite optimization. For the proof a local epigraph representation of the constraint set is mainly used.     

On Khachian's algorithm and minimal ellipsoids

Summary Khachian's algorithm for solving a system of linear inequalities is accelerated by choosing smaller ellipsoids than in the original version. Furthermore, certain inequalities can be successively eliminated, from the constraints, yielding a different stopping rule.     

Optimization methods and stability of inclusions in Banach spaces

Our paper deals with the interrelation of optimization methods and Lipschitz stability of multifunctions in arbitrary Banach spaces. Roughly speaking, we show that linear convergence of several first order methods and Lipschitz stability mean the same. Particularly, we characterize calmness and the Aubin property by uniformly (with respect to certain starting points) linear convergence of descent methods and approximate projection methods. So we obtain, e.g., solution methods (for solving equations or variational problems) which require calmness only. The relations of these methods to several known basic algorithms are discussed, and errors in the subroutines as well as deformations of the given mappings are permitted. We also recall how such deformations are related to standard algorithms like barrier, penalty or regularization methods in optimization.     

A Frank–Wolfe Type Theorem for Convex Polynomial Programs

In 1956, Frank and Wolfe extended the fundamental existence theorem of linear programming by proving that an arbitrary quadratic function f attains its minimum over a nonempty convex polyhedral set X provided f is bounded from below over X. We show that a similar statement holds if f is a convex polynomial and X is the solution set of a system of convex polynomial inequalities. In fact, this result was published by the first author already in a 1977 book, but seems to have been unnoticed until now. Further, we discuss the behavior of convex polynomial sets under linear transformations and derive some consequences of the Frank–Wolfe type theorem for perturbed problems.