On effectively computable realizations of choice functions: Dedicated to Professors Kenneth J. Arrow and Anil Nerode

Let X be a compact, convex subset of R_n, and let $\text{〈R(X),}\text{F}{}_{\mathrm{R}}\text{〉}$ be a recursive space of alternatives, where R(X) is the image of X in a recursive metric space, and $\text{F}{}_{\mathrm{R}}$ is the family of all recursive subsets of R(X). If $\text{C:}\text{F}{}_{\mathrm{R}}\text{→}\text{F}{}_{\mathrm{R}}$ is a non-trivial recursively representable choice function that is rational in the sense of Richter, we prove that C has no recursive realization within Church's Thesis. Our proof is not a diagonalization argument and uses no paradoxical statements from formal systems. Instead, the proof is a Kleene-Post reduction style argument and uses the Turing equivalence between mechanical devices of computation and the recursive functions of Gödel and Kleene.     

CLAUS工艺复杂化学反应平衡计算的新方法——原子自由能贡献法

本文根据最小自由能法原理推导了复杂气相反应平衡的原子自由能贡献法的计算模型,提出了用此法计算Claus工艺复杂化学反应平衡,获得了满意的效果,为精确及优化设计提供了理论依据和手段。本文还给出了再热炉设计时天然气和空气配比对出口燃烧产物组成更正确的平衡关系。文中的方法不必涉及具体的反应,通用性强且计算速度快。     

Landslides, forest fires, and earthquakes: examples of self-organized critical behavior

Per Bak conceived self-organized criticality as an explanation for the behavior of the sandpile model. Subsequently, many cellular automata models were found to exhibit similar behavior. Two examples are the forest-fire and slider-block models. Each of these models can be associated with a serious natural hazard: the sandpile model with landslides, the forest-fire model with actual forest fires, and the slider-block model with earthquakes. We examine the noncumulative frequency–area statistics for each natural hazard, and show that each has a robust power-law (fractal) distribution. We propose an inverse-cascade model as a general explanation for the power-law frequency–area statistics of the three cellular-automata models and their ‘associated’ natural hazards.     

Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors

We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is to bias jumps in the field direction and thus produce a current carrying steady state. Simulations on a periodic 30 × 30 square lattice with attractive nearest-neighbor interactions suggest a nonequilibrium phase transition from a disordered phase to an ordered one, similar to the para-to-ferromagnetic transition in equilibriumE=0. At low temperatures and largeE the system segregates into two phases with an interface oriented parallel to the field. The critical temperature is larger than the equilibrium Onsager value atE=0 and increases with the field. For repulsive interactions the usual equilibrium phase transition (ordering on sublattices) is suppressed. We report on conductivity, bulk diffusivity, structure function, etc. in the steady state over a wide range of temperature and electric field. We also present rigorous proofs of the Kubo formula for bulk diffusivity and electrical conductivity and show the positivity of the entropy production for a general class of stochastic lattice gases in a uniform electric field.Supported in part by National Science Foundation Grant DMR81-14726 and NATO Grant 040.82.Work supported in part by a Lafayette College Junior Faculty Leave Grant.Work supported in part by a Heisenberg fellowship of the Deutsche Forschungsgemeinschaft.     

Minimum information estimation of allocation models of different sizes

For allocation models consisting of n = 10, 6 and 4 equations, constrained generalized least squares coefficient estimates are compared with those obtained from the minimum information (MI) criterion in the sense of statistical information theory. The MI estimates are more efficient for n = 10. The bootstrap procedure is illustrated for the assessment of the variability of these estimates.     

HARVESTING IN POPULATION MODELS WITH DELAYED RECRUITMENT AND AGE-DEPENDENT MORTALITY

We formulate a Volterra equation model to describe the effect of harvesting on populations with delayed recruitment and age-dependent mortality. This model is more complicated mathematically than the unharvested model, and we describe some numerical simulations which indicate the possible qualitative behaviours.     

Rigid interfaces for lattice models at low temperatures

Lattice models (on a hypercubic lattice of dimension larger than or equal to three) with spins attaining a finite number of values and finite-range interactions at low temperatures are considered. The existence of rigid interfaces as well as of surface tension under appropriate conditions is proven and the properties of corresponding Gibbs states are investigated.     

Some investigations in a new algorithm for nonlinear optimization based on conic models of the objective function

An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been recently introduced by Davidon. It leads to a broad class of algorithms which, in some sense, can be considered to generalize the existing quasi-Newton algorithms. One particular member of this class has been deeply examined by Sorensen, who has proved some interesting theoretical properties. A new interpretation of this algorithm is suggested in this paper from a more straightforward and somewhat familiar point of view. In addition, numerical experiments have been carried out to compare the Sorensen algorithm with a straightforward BFGS implementation of the classical quasi-Newton method with the final aim to assess the real merits and benefits of the new algorithm. Although some challenging test functions are used in computational experiments, the results are not particularly favorable to the new algorithm. As a matter of fact they do not exhibit any jump of quality, as it might be expected. Lastly, it is pointed out that a difficulty may affect the new method in situations in which it is necessary to exploit the special structure of large-scale problems.This work was supported by the National Research Council of Italy under Grant No. 80-01144.     

Boson Fields on the Circle as Generalized Wightman Fields

We define an operator-valued distribution on the circle with the expected properties (correlation functions, Hermiticity, etc.) of the logarithmic boson field in the cylinder compact picture. This is done starting from the known Krein space realization of the right and left movers on the light cone and considering its relation with the U(1)-current algebra. The relevance of this construction fortwo-dimensional conformal quantum field theory is discussed.