Functors whose domain is a category of morphisms

Summary Connected sequences of functors whose domain, is the category of morphisms of an arbitrary abelian categoryA and whose range categoryB is also abelian are compared with the composition functors of Eckmann and Hilton acting between the same categories Sequences of functors of both types are obtained from any half-exact functorA→B ifA has enough injectives and projectives. This revised version was published online in November 2006 with corrections to the Cover Date.     

Finite dimensional approximation in infinite dimensional mathematical programming

We consider the problem of approximating an optimal solution to a separable, doubly infinite mathematical program (P) with lower staircase structure by solutions to the programs (P(N)) obtained by truncating after the firstN variables andN constraints of (P). Viewing the surplus vector variable associated with theNth constraint as a state, and assuming that all feasible states are eventually reachable from any feasible state, we show that the efficient set of all solutions optimal to all possible feasible surplus states for (P(N)) converges to the set of optimal solutions to (P). A tie-breaking algorithm which selects a nearest-point efficient solution for (P(N)) is shown (for convex programs) to converge to an optimal solution to (P). A stopping rule is provided for discovering a value ofN sufficiently large to guarantee any prespecified level of accuracy. The theory is illustrated by an application to production planning.The work of Robert L. Smith was partially supported by the National Science Foundation under Grant ECS-8700836.     

Capacitive Discharge Graphite Furnace Laser-Excited Atomic Fluorescence of Thallium

For the first time, an anisotropic graphite furnace heated by capacitive discharge was used for laser-excited atomic fluorescence spectrometry. A detection limit of 5 fg for thallium was obtained with a laser repetition rate of 500 Hz and a peak integration time of 80 ms. The use of a capacitive discharge furnace allows for a shorter integration time, which in turn should allow for integration of less background noise, and improved detection limits. Theoretically, the magnitude of the shot noise should be proportional to the square root of the integration time, and inversely proportional to the square root of the laser repetition rate. Experimental data illustrated the effect of laser repetition rate, but were inconclusive with respect to integration time. The linear dynamic range of the calibration curve was six orders of magnitude, which was comparable to that normally obtained for laser-excited atomic fluorescence in modern commercial graphite furnaces. Thallium was accurately determined in NIST biological samples at levels one to two orders of magnitude below the detection limit of electrothermal atomic absorption spectrometry, with an analytical precision between 8 and 20%. The interference effects of calcium, sodium chloride, and potassium chloride on the thallium signal were investigated and shown to be similar to both laser-excited atomic fluorescence in a conventional furnace and capacitive discharge furnace atomic absorption results reported in the literature.     

Chemical shift nonequivalence of sulfinates: Structural,solvent and temperature effects

The structural, solvent and temperature effects on the PMR spectra of several alkyl alkanesulfinates and arenesulfinates are discussed. A low order intrinsic nonequivalence was observed in substituents alpha to the sulfinate sulfur atom, the nonequivalence being significantly less than in sulfoxides, and solvent and temperature dependent. Nonequivalence of diastereotopic substituents on the ester oxygen exceeded nonequivalence in similar sulfoxides and is largely insensitive to temperatures from 25° to 120°C. Benzene complexes with sulfinates greatly enhancing the proton nonequivalence of alpha substituents apparently by causing a further shielding of the already more shielded nonequivalent protons.     

On new kinds of Teichmüller spaces

We introduce a Teichmüller space for a Riemann surface withn distinguished points. Ifn=0 this is the ordinary Teichmüller space. Forn=1, in special cases, it represents the Teichmüller curve and the universal covering space of the Teichmüller curve. The corresponding modular groups and Riemann spaces are investigated. Some purely topological applications on homotopy of self-maps of surfaces are obtained. Research partially supported by NSF Grant GP-19572. The author is currently a Guggenheim Memorial Fellow.     

The effect of deception on optimal decisions

The buyer in a seller-first offer bargaining situation use deception to cause the seller to arrive at an inaccurate subjective probability distribution of the buyer's position. The effects on the optimal behavior of the seller and on the payoffs to the two parties are examined.     

The design of a Tort law to control accidents

In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented.     

Computational modeling of the mechanisms of the free radical-chain reaction of alkanes with oxygen. The oxidation of isobutane,n-butane,and isopentane

A general computational method for obtaining complete solutions of time-dependent kinetic equations has been developed and applied to free radical-initiated reactions of alkanes with oxygen. The method has been applied to the low-temperature, peroxide-initiated oxidations of isobutane and isopentane. Using available independently measured and estimated values for the rate constants and activation parameters for each of the 20 proposed reaction steps for the oxidation of isobutane, the rates and products have been calculated for both the liquid phase and gas phase in the range of 100°–155°C. The calculated rates and products of oxidation agree with published experimental values. The oxidation of isopentane was examined by a 32-reaction model. The rate constants were estimated using values for the appropriate rate steps in the oxidation of n-butane and isobutane. The calculation of the oxidation rate and products agree with our experiments.     

Potential energy surfaces and lifetimes for spontaneous fission of heavy and superheavy elements from a variable density dependent mass formula

The potential energy surface for spontaneous fission is calculated using realistic density distributions for finite nuclei. Particular emphasis is placed on the region of the potential between the saddle and scission point. The method involves computing the energy of the system using an energy density functional consistent with varible density distributions and nuclear masses and obtained from a statistical many body theory. The results show that there exists an external or scission barrier to the fission process. Lifetimes and mass distributions which are computed using these potential energy surfaces are found to be in adequate agreement with observations for ²³⁴U, ²³⁶U, ²⁴⁰Pu, ²⁴⁴Cm, ²⁴⁸Cf, and ²⁵²Cf. Our predicted upper limit for the spontaneous fission half-lives of elements 112 and 114 is one year but the calculation indicates that these could be considerably shorter than a year.