WEAK AND STRONG SUSTAINABILITY,ENVIRONMENTAL CONSERVATION AND ECONOMIC GROWTH

ABSTRACT. To investigate the role of explicit and implicit assumptions in different models of weak and strong sustain‐ability, the Solow/Hartwick model of intergenerational equity with nonrenewable resources is gradually extended to include renewable resources, endogenous technical progress, and stock pollution. This reveals the fundamental role of endogenous technical progress for sustainable development, the inconsistency of implicit sustainability assumptions in various models, as well as the existence of a Hartwick rule for Daly's steady‐state economy. Moreover, it shows that the concepts of Solow sustainability and strong sustainability coincide as a special case of weak sustainability. The latter integrates economic and environmental concerns and aims at maintaining the welfare potential of an economy over time. It does not rule out economic growth by assumption. Rather, the analysis shows that environmental conservation and economic growth can be compatible with each other, without jeopardizing social welfare. Finally, the analysis shows that the discussion of sustain‐ability models cannot be restricted to the explicit differences that are usually pointed out by their authors and commentators. Rather, implicit assumptions must be made explicit.     

Constructive analysis of Takens-Bogdanov points with Z2-symmetry

Assuming a 2-parameter-dependent family of smooth Z₂-equivariantvector fields, a symmetry-breaking Takens-Bogdanov point isconsidered as an isolated organizing centre. Two branches ofsymmetry-breaking and asymmetric Hopf bifurcation points aswell as one branch of Z₂-pitchforks which emanate from the organizingcentre are analyzed via asymptotic expansions. Leading termsof these expansions are calculated explicitly. The input dataare differentials (up to third order) of the mapping evaluatedat the organizing centre along specified directions.     

RED/FAR-RED PHOTOREVERSIBILITY: NOT AN APPROPRIATE PHYTOCHROME ASSAY FOR RED-LIGHT PREIRRADIATED CORN COLEOPTILES

Abstract— Based on measurements with a single beam spectrophotometer, it has been found that subsequent red/far red irradiation cycles, which are usually given to monitor phytochrome content by dual wavelength spectroscopy, induce chlorophyll-related absorption changes in maize coleoptiles. Therefore, the difference signal, usually measured between 730 and 800 nm or 660 and 730 nm after saturating red and far red irradiations, does not represent solely the phytochrome content of preirradiated samples.     

Spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions

An efficient method for the calculation of Breit-Pauli spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions is presented. Instead of taking all two-electron contributions of the wavefunction explicitly into account, the most important two-electron contributions of the spin-orbit operator are incorporated by means of an effective one-electron Fock operator. As a further refinement, explicit two-electron contributions can be reinstated for the dominant all-internal parts of the wavefunctions.     

The ion-molecule reaction O+ (4S) + N2(X1Σ+) → NO+ (X1Σ +, v′) + N(4S) and the predissociation of the A2Σ+ and B2Π states of N2O+

The potential energy surfaces (PESs) for several electronic states involved in the reaction O⁺ (⁴S) + N₂(X¹Σ⁺) → NO⁺ (X¹Σ ⁺, v′) + N(⁴S) and the role of the ionic N₂O⁺ intermediate have been investigated by ab initio calculations. The ⁴A″ PES, which correlates with the ground state educts, has a barrier of about 1 eV, and therefore at low collision energies the reaction cannot take place adiabatically on this surface. However, the spin-orbit coupling in the entrance channel allows the system to pass into the Renner-Teller system of the X² Π electronic ground state of the N₂O⁺ intermediate. The reaction then proceeds on these surfaces up to the region in the exit channel where a similar coupling allows it to reach the product quartet asymptote. At collision energies higher than about 1 eV, the reaction proceeds mainly on the adiabatic PES of the ⁴A″ state. The A²Σ⁺ state of N₂O⁺ predissociates via a vibronic coupling with the B²Π state, and in bent structures via a spin-orbit coupling with the ⁴A″ component of the ⁴II state. The electronic structure of the B²Π state is found to be of crucial importance for the understanding of the reactive processes in low lying electronic states of N₂O⁺.     

On a constraint on the electromagnetic constitutive relations of nonhomogeneous linear media

In addition to certain physical restrictions on the constitutivetensor of linear media, there exists a mathematical constraintin modern electromagnetic theory. This constraint was shownby Post to arise out of general covariance and was stated byhim as a set of two relations. It is shown here that Post'scovariance constraint can be set alternatively in the form ofa single relation.     

Non-simple Turning Points and Cusps

Stimulated by a problem in the theory of thermal ignition, weprove some results on non-simple turning points and correspondingcusps for two parameter-dependent non-linear problems. Theseresults provide a theoretical basis for the numerical computationof non-simple turning points or cusps. The numerical procedureis illustrated for the thermal ignition problem.     

Local heights on abelian varieties with split multiplicative reduction

We express Néron functions and Schneider's local p-adic height pairing on an abelian variety A with split multiplicative reduction with theta functions and their automorphy factors on the rigid analytic torus uniformizing A.Moreover, we show formulas for the -splittingsof the Poincaré biextension corresponding to Néron's and Schneider's local height pairings.     

The adiabatic approximation I. The physical background of the Born-Handy ansatz

There are two current ways to evaluate the adiabatic corrections to a potential energy hypersurface: firstly a rigorous way in which one starts with the separation of the centre-of-mass motion and where one gets rather complicated expressions in terms of relative coordinates in a molecule-fixed frame, and secondly a pragmatic way, recently advocated by Handy et al., where one starts from a one-term Born ansatz in the laboratory system and arrives at a rather simple expression in terms of nuclear coordinates. In this note it is shown that the latter simple expression can also be obtained rigorously, that is by separating the centre-of-mass motion first. Why the pragmatic approach leads to a correct result, and why the specification of a molecule-fixed frame is not necessary for the evaluation of the adiabatic corrections, are analysed.