LONG-TERM FORECASTING OF INTERNATIONAL FOREST PRODUCT MARKETS: THE GFPM MODEL AND IMPLICATIONS FOR EUROPE

The Global Forest Products Model (GFPM) was developed to upgrade the FAO methodology for forest products outlook projections. Its purpose is to analyze and project the consumption, production, trade, and prices of forest products. The system deals with 180 individual countries, three classes of roundwood, sawnwood, three kinds of panels, three of pulp, waste paper, and three types of paper and paperboard. The system is built on market equilibrium theory, with imperfect foresight. The short-term equilibrium is modeled by price-endogenous linear programming determining production, consumption, trade, and market-clearing prices in any given year, subject to short-term capacities of production. Year to year changes are represented by equations predicting shifts in demand due to GDP growth, capacity expansion as a function of profitability, and technical change. The forecasts are conditional on exogenous estimates of timber availability in each country. Inertia constraints limit the short-term adjustment of trade in response to market forces. Results of applications of the model to forecast the situation in European countries until 2010 are described.International Relations/Trade,

An exact solution for arbitrarily rotating gaseous polytropes with index unity

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2015 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.Many gaseous planets and stars are rapidly rotating and can be approximately described by a polytropic equation of state with index unity.We present the first exact analytic solution, under the assumption of the oblate spheroidal shape, for an arbitrarily rotating gaseous polytrope with index unity in hydrostatic equilibrium, giving rise to its internal structure and gravitational field. The new exact solution is derived by constructing the non-spherical Green’s function in terms of the oblate spheroidal wavefunction. We then apply the exact solution to a generic object whose parameter values are guided by the observations of the rapidly rotating star α Eridani with its eccentricity Eα = 0.7454, the most oblate star known. The internal structure and gravitational field of the object are computed from its assumed rotation rate and size. We also compare the exact solution to the three-dimensional numerical solution based on a finite-element method taking full account of rotation-induced shape change and find excellent agreement between the exact solution and the finite-element solution with about 0.001 per cent discrepancy.NSFCScience & Technology Facilities Council (STFC)HKRGCNational Science Foundatio

Confidence Levels for CVaR Risk Measures and Minimax Limits*

Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and it’s impact on optimal decision making when we wish to minimize the respective risk measures. We also investigate the difference between the optimal solutions to the two optimization problems with identical objective function but under constraints on the two risk measures. We discuss the benefits of a sample average approximation scheme for the CVaR constraints and investigate the convergence of the optimal solution obtained from this scheme as the sample size increases. We use some portfolio optimization problems to investigate teh performance of the CVaR approximation approach. Our numerical results demonstrate how reducing the confidence level can lead to a better overall performance

On fluid flows in precessing narrow annular channels: asymptotic analysis and numerical simulation

Copyright © 2010 Cambridge University PressWe consider a viscous, incompressible fluid confined in a narrow annular channel rotating rapidly about its axis of symmetry with angular velocity Ω that itself precesses slowly about an axis fixed in an inertial frame. The precessional problem is characterized by three parameters: the Ekman number E, the Poincaré number ε and the aspect ratio of the channel Γ. Dependent upon the size of Γ, precessionally driven flows can be either resonant or non-resonant with the Poincaré forcing. By assuming that it is the viscous effect, rather than the nonlinear effect, that plays an essential role at exact resonance, two asymptotic expressions for ε ≪ 1 and E ≪ 1 describing the single and double inertial-mode resonance are derived under the non-slip boundary condition. An asymptotic expression describing non-resonant precessing flows is also derived. Further studies based on numerical integrations, including two-dimensional linear analysis and direct three-dimensional nonlinear simulation, show a satisfactory quantitative agreement between the three asymptotic expressions and the fuller numerics for small and moderate Reynolds numbers at an asymptotically small E. The transition from two-dimensional precessing flow to three-dimensional small-scale turbulence for large Reynolds numbers is also investigated

Thermal-gravitational wind equation for the wind-induced gravitational signature of giant gaseous planets: mathematical derivation, numerical method, and illustrative solutions

© 2015. The American Astronomical Society. All rights reserved. Received 26 February 2015, accepted for publication 4 May 2015 Published 23 June 2015Please cite the published version available at DOI: 10.1088/0004-637X/806/2/270The standard thermal wind equation (TWE) relating the vertical shear of a flow to the horizontal density gradient in an atmosphere has been used to calculate the external gravitational signature produced by zonal winds in the interiors of giant gaseous planets. We show, however, that in this application the TWE needs to be generalized to account for an associated gravitational perturbation. We refer to the generalized equation as the thermalgravitational wind equation (TGWE). The generalized equation represents a two-dimensional kernel integral equation with the Green’s function in its integrand and is hence much more difficult to solve than the standard TWE. We develop an extended spectral method for solving the TGWE in spherical geometry. We then apply the method to a generic gaseous Jupiter-like object with idealized zonal winds. We demonstrate that solutions of the TGWE are substantially different from those of the standard TWE. We conclude that the TGWE must be used to estimate the gravitational signature of zonal winds in giant gaseous planets