ON HYPERBOLIC TIME DISCOUNTING IN EXHAUSTIBLE RESOURCE MODELS: AN APPLICATION TO WORLD OIL RESOURCES

ABSTRACT. Recent research on discounting in long term economic models involves hyperbolic discounting, in which the marginal discount rate shrinks as time passes. To investigate hyperbolic discounting and exhaustible resource allocation, this work develops a discrete‐time world oil model and model solution procedure, then uses the model to examine the consequences of adopting conventional (constant annual) discounting when hyperbolic discounting is appropriate, of adopting one hyperbolic discount rate path when a different hyperbolic path is appropriate, and of adopting hyperbolic discounting when conventional discounting is appropriate. Five conventional and two hyperbolic discount rate paths are considered. One hyperbolic path is that used by Nordhaus and Boyer [2000]; the other is that recommended by Weitzman [2001]. The generality of the findings is also assessed.     

Online Cooperative Learning in Physical Chemistry

The use of cooperative learning in an online setting is examined using the online segment of a recently offered physical chemistry course as an example. The nature and function of classical, face-to-face cooperative learning are outlined. The online course segment is outlined and is analyzed with regard to the criteria for classical cooperative learning. Though this specific course segment functioned poorly when taught as online cooperative learning, it is possible to structure online courses to take advantage of the strengths of cooperative learning. The possible structure and function of an online cooperative learning community are explored, concluding with a specific model for online cooperative learning.     

GOLDEN AGES OR MAGIC MOMENTS?

ABSTRACT. The paper is an attempt to refute Quinn's ‘the Golden Age of fisheries population models has ended “hypothesis. The approach is to show it is possible to provide simple matrix based theory for use with delay difference equations applied to products of the 0th to 4th powers of length and numbers at length (Alias” proto‐moments“). It compares these to models just based upon numbers and biomass. It also shows examples (of comparatively little moment) indicating how using multiple proto‐moments could improve the ability of delay difference equations to handle the size dependent processes of maturity, selection, natural mortality rates and predation rates and thus improving the biological reality of these models.     

Finite-Element Approximation of a Plasma Equilibrium Problem

The plasma problem studied is: given R⁺ find (, d, u) R ?R ? H¹() such that Let ₁ < ₂ be the first two eigenvalues of the associatedlinear eigenvalue problem: find $$\left(\lambda ,\phi \right)\in\mathrm{R;}\times {\hbox{ H }}_{0}^{1}\left(\Omega \right)$$such that For ₀(0,₂) it is well known that there exists a unique solution(₀, d₀, u₀) to the above problem. We show that the standard continuous piecewise linear Galerkinfinite-element approximatinon $$\left({\lambda }_{0},{\hbox{d }}_{0}^{k},{u}_{0}^{h}\right)$$, for ₀(0,₂), converges atthe optimal rate in the H¹, L², and L norms as h, the mesh length,tends to 0. In addition, we show that dist (, ^h)Ch² ln 1/h,where $${\Gamma }^{\left(h\right)}=\left\{x\in \Omega :{u}_{0}^{\left(h\right)}\left(x\right)=0\right\}$$.Finally we consider a more practical approximation involvingnumerical integration.     

Total Flux Estimates for a Finite-Element Approximation of Elliptic Equations

An elliptic boundary-value problem on a domain with prescribedDirichlet data on _I is approximated using a finite-elementspace of approximation power h^K in the L² norm. It is shownthat the total flux across _I can be approximated with an errorof O(h^K) when is a curved domain in Rⁿ (n = 2 or 3) and isoparametricelements are used. When is a polyhedron, an O(h^2K–2)approximation is given. We use these results to study the finite-elementapproximation of elliptic equations when the prescribed boundarydata on _I is the total flux. Present address: School of Mathematical and Physical Sciences,University of Sussex, Brighton, Sussex BN1 9QH.     

Victor Moritz Goldschmidt (1888–1947): A Tribute to the Founder of Modern Geochemistry on the Fiftieth Anniversary of His Death

Goldschmidt combined a number of widely separated sciences to synthesize a new structural crystal chemistry. Although his work on the relative abundances of the elements, atomic and ionic radii, interionic distances, the effect of radius ratio on coordination number in crystals, replacement of ions in minerals, and the lanthanide contraction is found in almost every textbook of general and inorganic chemistry and has provided the basis for modern crystal chemistry and the use of size relationships for interpreting properties of inorganic substances, Goldschmidts name, life, and career remain relatively unknown to most chemical educators and practicing chemists.Goldschmidt used the basic properties of matter to provide simple and elegant explanations for the composition of our environment. Throughout his relatively brief career, filled with sorrow and tragedy, he continued to maintain his intense interest in the elements and their genesis, affinities, and associations despite his changes from one method to another in his attempts to obtain new and more complete data. Thus, although he used petrology, crystallography, and chemistry and enriched all these fields greatly, to him they were only tools for exploring the earth and its history.     

Evard Immanuel Hjelt (1855–1921): Finnish Chemist and Historian of Chemistry

Although today unjustly neglected abroad and often even in his native land, Edvard Immanuel Hjelt (1855–1921), was an exceptionally gifted, dedicated, and multifaceted individual who made important contributions to chemistry, the history of chemistry, politics, and the management of national and international affairs. Little information about him is available in English. The present article supplements the only two English sources available [1, pp 66–83; 2] and makes this chemist-statesman better known to those chemists and historians who do not read Swedish or Finnish.In this section we present articles by leading scientific historians that chronicle the important events, persons, and publications that make up the rich history of chemical science. The history, and the articles in this ection often make that very clear. Chemists and their research are always influenced by current events. These articles are intended to describe the setting in which important discoveries occurred and to humazine their discoveres.     

NANOSECOND KINETIC ABSORPTION AND CALORIMETRIC STUDIES OF CYCLOPENTENONE: THE TRIPLET, SELF-QUENCHING, AND THE PREDIMERIZATION BIRADICALS

The photolysis of 2-cyclopentenone has been studied by a combination of kinetic absorption spectrophotometry and time-resolved photoacoustic calorimetry. The lifetime of the cyclopentenone triplet is strongly concentration dependent and corresponds to a value of 380 +/- 75 ns at infinite dilution in acetonitrile. The biradical intermediate (or pair of isomeric biradicals) immediately preceding formation of photodimer forms with very high efficiency upon quenching of triplet cyclopentenone by a second ground state cyclopentenone molecule and has an energy of 47 kcal/mol relative to two molecules of reactant. Quenching of the cyclopentenone triplet by conjugated dienes is much slower than expected, which is the reason that early estimates of the triplet lifetime were much too short.     

SPECTRAL CHARACTERISTICS OF THE EXCITED STATES OF THE PRODUCT OF THE CHEMILUMINESCENCE OF LUMINOL*

Abstract— In dimethylsulfoxide the emission spectrum of luminol chemiluminescence is red-shifted by 300 cm^-1 from the photoexcited fluorescence of the product 3-aminophthalate dianion, while in aqueous solvent the two spectra are identical. The spectral properties of the product dianion have been measured in aqueous solvent and in a number of aprotic solvents, both at room temperature and at 77°K. The ground states and the excited states from which emissions are observed are characterized. Two alternatives are presented to explain the aprotic emission spectra.     

EFFECTS OF ULTRAVIOLET RADIATION ON THE MITOTIC CYCLE AND DNA, RNA AND PROTEIN SYNTHESIS IN MAMMALIAN EPIDERMIS IN VIVO

Abstract— Acute effects of ultraviolet radiation on the mitotic cycle and macromolecular synthesis were investigated on hairless mouse epidermis in vivo. Colcemid was used to arrest mitoses in metaphase and thus allow more accurate mitotic counts. The radioactive tracers, TdR-³H, cytidine-³H, and the amino acids, histidine-³H and methionine-³H were used to examine DNA, RNA and protein synthesis, respectively. Using these techniques, we found that wavelengths shorter than 320 nm markedly inhibited mitosis, increased the basal cell turnover time and depressed DNA, RNA and protein synthesis within the first few hours post-irradiation. By 24hr, recovery and acceleration of these functions were in progress, reaching a peak by 48–72 hr and persisting though to a lesser degree for 7 days. This stage of acceleration was associated with epidermal hyperplasia and most likely represented post-injury cell renewal.