Uniqueness of Equilibrium in the Multi-Country Ricardo Model

We present two arguments, one based on index theory, demonstrating that the multi-country Ricardo model has a unique competitive equilibrium if the aggregate demand functions exhibit gross substitutability. The result is somewhat surprising because the assumption of gross substitutability is sufficient for uniqueness in a model of exchange but not, in general, when production is included in the model.Ricardo model, Gross substitutes, Uniqueness

Dynamic behavior of rectangular plates and cylindrical shells

Numerical integration technique for determining dynamic response of rectangular plates and cylindrical shells subjected to stationary and constant velocity load

The wall of the cave

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang Mills theories must be described by the non-critical strings in the five dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang-Mills theories. The article is written on the occasion of the 40-th anniversary of the IHES.Comment: 18 pages, Late

Onboard sampling of the rockfish and lingcod commerical passenger fishing vessel industry in northern and central California, 1992

In 1992 fishery technicians sampled 230 commercial passenger fishing vessel (CPFV) trips targeting rockfish and lingcod from the port areas of Fort Bragg, Bodega Bay, San Francisco, Monterey, and Morro Bay. The skippers of 44 vessels, and 2,190 anglers, cooperated in the study. Species composition by port area and month, catch-per-unit-effort, mean length, and length frequency of lingcod and the 18 most frequently observed rockfish species are presented, as well as fishing effort relative to time, depth, and distance from port. Total catch estimates based on unadjusted and adjusted logbook records are summarized. Average catch of kept fish per angler day was 12.6 and average catch of kept fish per angler hour was 4.0. A continuing trend of an increasing frequency of trips to deep (> 40 fm) locations was observed in the Bodega Bay, San Francisco, and Monterey areas. Bodega Bay and San Francisco showed the highest frequency of trips to distant locations. Sixty species comprised of 29,731 fish were observed caught during the study. Rockfish comprised 93.5% by number of the total observed catch. The five most frequently observed species were blue, yellowtail, widow and rosy rockfishes, and bocaccio, with lingcod ranking eighth. CPFV angler success, as determined by catch per angler hour, generally increased in all ports in 1992 compared to previous 1988-91 data (Reilly et al. 1993). However, port-specific areas of major concern were identified for chilipepper, lingcod, and black rockfish, and to a lesser extent brown, canary, vermilion, yelloweye, widow and greenspotted rockfishes. These areas of concern included steadily declining catch rate, steadily declining mean length, and/or a high percentage of sexually immature fish in the sampled catch. Recent sampling of the commercial hook-and-line fishery in northern and central California indicates that most rockfishes taken by CPFV anglers are also harvested commercially. (105pp.

Testing isomorphism of graded algebras

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma

Terrain analysis using radar shape-from-shading

This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR data sets containing relatively complex terrain structure