Resonance ionization mass spectrometry for precise measurements of isotope ratios

Resonance ionization mass spectrometry offers extremely high sensitivity and elemental selectivity in microanalysis, but the isotopic precision attainable by this technique has been limited. Measured isotope ratios are sensitive to small fluctuations in the pointing, pulse timing, and wavelength of the resonance lasers. We show that, by minimizing these fluctuations using feedback controls and by power-broadening the optical transitions, we are able to measure chromium isotope ratios with statistics-limited precision better than 1%. Small additional improvements in reproducibility come from careful shaping of the electric field in the region where atoms are photoionized and from minimizing pulse-to-pulse variations in the time-of-flight mass spectrometer through which the photoions travel. The increased reproducibility of isotopic measurements on standard materials has enabled us to detect anomalous chromium isotopic abundances in presolar SiC grains extracted from primitive meteorites.     

Graded decomposition numbers for cyclotomic Hecke algebras

In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux-Leclerc-Thibon conjecture, describing the decomposition numbers of graded Specht modules over a field of characteristic zero.     

Predicting the event and time horizon of bankruptcy using financial ratios and the maturity schedule of long-term debt

We study the problem of simultaneous and coherent assessment the probability of a firm’s bankruptcy at various time horizons in future. In contrast with usual (one-period) formulations of the problem, such multi-period formulation better matches the nature of bankruptcy process (bankruptcy occurs in time) and allows an easier and more natural incorporation of bankruptcy (default) prognoses in valuation of risky debt and equity, optimization of corporate capital structure etc. The study uses a new mathematical apparatus—multi-alternative decision rules of statistical decision theory. We investigate a new type of predictive variables that can be extracted from the maturity schedule of a firm’s long-term debt. The study develops Bayesian-type forecasting rules that use both maturity schedule factors and traditional financial ratios. These rules noticeably enhance bankruptcy prediction (compared with the familiar one-period Z-score rules of Altman) for bankruptcy within the first 1, 2 or 3 years. Predictive factors derived from schedule information enhance bankruptcy prediction at distant time horizons.     

Comtrans algebras, Thomas sums, and bilinear forms

A comtrans algebra is said to decompose as the Thomas sum of two subalgebras if it is a direct sum at the module level, and if its algebra structure is obtained from the subalgebras and their mutual interactions as a sum of the corresponding split extensions. In this paper, we investigate Thomas sums of comtrans algebras of bilinear forms. General necessary and sufficient conditions are given for the decomposition of the comtrans algebra of a bilinear form as a Thomas sum. Over rings in which 2 is not a zero divisor, comtrans algebras of symmetric bilinear forms are identified as Thomas summands of algebras of infinitesimal isometries of extended spaces, the complementary Thomas summand being the algebra of infinitesimal isometries of the original space. The corresponding Thomas duals are also identified. These results represent generalizations of earlier results concerning the comtrans algebras of finite-dimensional Euclidean spaces, which were obtained using known properties of symmetric spaces. By contrast, the methods of the current paper involve only the theory of comtrans algebras.Received: 30 March 2004     

A lower bound on the rank of mixing extensions

If transformationR is ap-point extension of a mixingT thenp · rank(T) lower bounds the rank ofR. The author was partially supported by NSF grant DMS8501519.     

Equilibrium with strategy-dependent trembles

Trembling-hand arguments, introduced by Selten, where players make errors in implementing a strategy, are a successful and intuitively plausible approach to eliminating some equilibria. Typically, these errors are independent of the strategy the player aims to implement. In many contexts, however, when a player aims at one strategy, some errors are more likely than if a different strategy is the target. We introduce the notion of strategy-dependent trembles where each strategy intended by a player implies a different probability vector of errors over other strategies. This seemingly minor but plausible change makes a major difference. The focus becomes a player's own errors rather than the errors of others. A weakly dominated strategy is not necessarily eliminated if less costly errors arise when aiming at it than at the dominating strategy. Almost every Nash equilibrium in pure strategies is a strategy-dependent trembling-hand perfect equilibrium. We thank the associate editor, two referees, James Friedman, and audiences at the Public Choice Society Meetings and Southeastern Economic Theory Meetings for comments and the Public Utility Research Center and the College of Business Administration at the University of Florida for financial support.     

Associativity of the <Emphasis Type="Italic">∇</Emphasis>-operation on bands in rings

Given a multiplicative band of idempotents S in a ring R, for all e,f∈S the ∇-product e ∇ f=e+f+fe−efe−fef is an idempotent that lies roughly above e and f in R just as ef and fe lie roughly below e and f. In this paper we study ∇-bands in rings, that is, bands in rings that are closed under ∇, giving various criteria for ∇ to be associative, thus making the band a skew lattice. We also consider when a given band S in R generates a ∇-band.