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.     

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.     

PHOTOSENSITIZATION BY DRUGS: NALIDIXIC AND OXOLINIC ACIDS

Abstract— The antibacterial drugs, nalidixic acid and oxolinic acid, have been tested as photosensitizers in aqueous solution using 365 nm UV light. Absorption and fluorescence spectra indicate that intramolecular hydrogen bonding stabilizes the unionized form of these compounds in the pH region2–4. The ability of the unionized species to sensitize photooxidation by the type II (singlet oxygen) mechanism was found to be lower than when these drugs were ionized. Comparison withquinoline–3-carboxylic acid and the methyl esters of nalidixic and oxolinic acids emphasised the significance of the hydrogen bonding in relation to the excited state properties. Unionized nalidixic acid undergoes photolysis more readily than the ionized form, apparently by a free radical mechanism, while oxolinic acid is more stable.     

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.     

THE ORIENTATION OF THE REACTION CENTER CAROTENOID TRIPLET STATE MAGNETIC AXES IN CHROMATOPHORES OF Rhodopseudomonas sphaeroides WILD TYPE

Abstract— The orientation of the principal magnetic axes of the reaction center carotenoid from Rps. sphaeroides wild type is presented. The parameters needed to simulate the observed carotenoid triplet state spectra indicate that the carotenoid adopts a planar structure within the reaction center. A high degree of geometrical and structural specificity is shown to exist for this carotenoid molecule.     

Finite Element Approximation of a Rigid Punch Indenting a Membrane

Optimal order H¹ and L error bounds are obtained for a continuouspiecewise linear finite element approximation of an obstacleproblem, where the obstacle's height as well as the contactzone, _c, are a priori unknown. The problem models the indentationof a membrane by a rigid punch. For R², given ,g R⁺ and an obstacle defined over E we consider the minimization of |v|²_1,+gµover (v, µ) H¹₀() x R subject to v+µ on E. In additionwe show under certain nondegeneracy conditions that dist (_c,^h_c)Ch ln 1/h, where ^h_c is the finite element approximation to_c. Finally we show that the resulting algebraic problem canbe solved using a projected SOR algorithm.