Bispectral quantum Knizhnik-Zamolodchikov equations for arbitrary root systems

The bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equation corresponding to the affine Hecke algebra $H$ of type $A_{N-1}$ is a consistent system of $q$-difference equations which in some sense contains two families of Cherednik's quantum affine Knizhnik-Zamolodchikov equations for meromorphic functions with values in principal series representations of $H$. In this paper we extend this construction of BqKZ to the case where $H$ is the affine Hecke algebra associated to an arbitrary irreducible reduced root system. We construct explicit solutions of BqKZ and describe its correspondence to a bispectral problem involving Macdonald's $q$-difference operators.Comment: 31 page

Biofuel scenarios in a water perspective: the global blue and green water footprint of road transport in 2030

The trend towards substitution of conventional transport fuels by biofuels requires additional water. The EU aims In the last two centuries, fossil fuels have been our major source of energy. However, issues concerning energy security and the quality of the environment have given an impulse to the development of alternative, renewable fuels. Particularly the transport sector is expected to steadily switch from fossil fuels to a larger fraction of biofuels - liquid transport fuels derived from biomass. Many governments believe that biofuels can replace substantial volumes of crude oil and that they will play a key role in diversifying the sources of energy supply in the coming decades. The growth of biomass requires water, a scarce resource. The link between water resources and (future) biofuel consumption, however, has not been analyzed in great detail yet. Existing scenarios on the use of water resources usually only consider the changes in food and livestock production, industry and domestic activity. The aim of this research is to assess the change in water use related to the expected increase in the use of biofuels for road transport in 2030, and subsequently evaluate the contribution to potential water scarcity. The study builds on earlier research on the relation between energy and water and uses the water footprint (WF) methodology to investigate the change in water demand related to a transition to biofuels in road transport. Information about this transition in each country is based on a compilation of different energy scenarios. The study distinguishes between two different bio-energy carriers, bio-ethanol and biodiesel, and assesses the ratio of fuel produced from selected first-generation energy crops per country. For ethanol these crops are sugar cane, sugar beet, sweet sorghum, wheat and maize. For biodiesel they are soybean, rapeseed, jatropha, and oil palm

Theoretical study on the protonation of AZA-aromatics

The protonation of azanaphthalenes and azabenzenes has been studied theoretically using CNDO/2 wavefunctions and perturbation theory in order to examine the correlation between pKa values and quantum-mechanical quantities

The photoelectron spectra of the diazanaphthalenes

The high-resolution He 584 Å photoelectron spectra of ten diazanaphthalenes are presented. The ordering of the π orbitals and the nitrogen “lone-pair” orbitals is discussed. Several semi-empirical quantum-chemical calculation methods have been screened against the experimental evidence

Double affine Hecke algebras and bispectral quantum Knizhnik-Zamolodchikov equations

We use the double affine Hecke algebra of type GL_N to construct an explicit consistent system of q-difference equations, which we call the bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik's quantum affine KZ equations associated to principal series representations of the underlying affine Hecke algebra, a compatible system of q-difference equations acting on the central character of the principal series representations. We construct a meromorphic self-dual solution \Phi of BqKZ which, upon suitable specializations of the central character, reduces to symmetric self-dual Laurent polynomial solutions of quantum KZ equations. We give an explicit correspondence between solutions of BqKZ and solutions of a particular bispectral problem for the Ruijsenaars' commuting trigonometric q-difference operators. Under this correspondence \Phi becomes a self-dual Harish-Chandra series solution \Phi^+ of the bispectral problem. Specializing the central character as above, we recover from \Phi^+ the symmetric self-dual Macdonald polynomials.Comment: 52 page

Problems in the context evaluation of individualized courses

From 1970 to 1974 an Individualized Study System (ISS) for mathematics courses for first year engineering students was developed. Because of changes in the curriculum, new courses had to be developed from August 1974. The context evaluation of these new courses (ISS-calculus) consisted mainly of the evaluation of the mathematics courses developed during the preceding years. After a year the Department decided to suspend ISS as a teaching system for calculus partly because of dissatisfaction of the teachers with ISS-calculus.\ud This paper consists of two parts. Part one (sections 1,2) is a case study and summarizes the development of the system from 1970 to 1975. It examines in detail the problems encountered in this development with special attention to the role of the executive teacher. The organization of an ISS-course and the planning decisions to be taken become more complex according to the number of executive teachers. In part two (sections 3,4) we provide a classification of ISS courses to illustrate the complexity of the system and we offer some general advice on the management of individualized study systems

Perfluoro effect in the photoelectron spectra of quinoline and isoquinoline

The high-resolution He 584Aophotoelectron spectra of heptafluoroquinoline and heptafluoroisoquinoline are compared with those of the parent compounds. Shifts in π ionisation potentials, due to the fluorine substitution, can be described with an inductive and a combined inductive-conjugative Hu¨ckel model

Overschooling and unemployment

Although overschooling is regarded as the result of imperfect allocation in the labour market, hardly any attention has been given to the influence of another imperfection, unemployment. Several researchers report about an increasing incidence of overschooling in the Netherlands. Although a lot of research has been done in the Netherlands on overschooling, this is not a phenomenon restricted to the Netherlands. Overschooling was found and measured in the United States, Germany, Spain, Portugal the United Kingdom and may be around in other Western European countries as well. Remarkably, however, is that in this line of research no attention has been paid to the effect of unemployment on overschooling. Because it can be argued that almost all unemployed are overschooled, the incidence and amount of overschooling and its rate of return should be directly affected by the unemployment rate in a country. However for the Netherlands we cannot find a relation between the unemployment rate and the amount of overschooling. The amount of overschooling is in 1998, a year with low unemployment, as high as in 1985, a year with high unemployment. After correcting the selectivity bias, caused by the unemployed, we also do not find changes in the rate of return on education, suggesting that wages in the Netherlands are rather sticky. Therefore efficiency wage theory seems to be a better candidate in explaining overschooling than a matching model as propesed by Hartog.