Construction of exactly solvable quantum models of Calogero and Sutherland type with translation invariant four-particle interactions

We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.Comment: 14 pages, no figures, 1 table, replaced and enlarged version, a note adde

An exactly solvable model of the Calogero type for the icosahedral group

We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.Comment: 13 pages, no figures, latex 2epsilo

Exactly solvable dynamical systems in the neighborhood of the Calogero model

The Hamiltonian of the $N$-particle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For N=3 and N=4 such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all $N$.Comment: 23 pages, 2 figures, replaced and enlarged versio

The construction of trigonometric invariants for Weyl groups and the derivation of corresponding exactly solvable Sutherland models

Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the coroot lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The invariants of the basis can be used as coordinates in any cell of the coroot space and lead to an exactly solvable model of Sutherland type. We apply this construction to the $F_4$ caseComment: 13 pages, no figures, latex 2epsilon, corrected versio

Is it possible to construct exactly solvable models?

We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schr\"odinger operator. We prove the feasibility of our method by constructing a new "$AG_3$ model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the $B_3$ model. In order to better understand features of our construction we exhibit the $F_4$ rational model with our method.Comment: 22 pages, 2 eps figures, latex 2epsilon, usepackage epsfi

Will You Accept Without Knowing What? A Thuringian Newspaper Experiment of the Yes-No Game

Many economic experiments are run in the laboratory with students as participants. In this paper we use a newspaper experiment to learn more about external validity of lab research. Our workhorse is the Yes-No game. Unlike in ultimatum games responders of the Yes-No games do not know the proposal when deciding between whether to accept it or not. We use two different amounts that can be shared (100 Euro and 1000 Euro). In line with findings for the ultimatum game, offers were fairer and rejections less likely when participants are older and submit their decisisons via mail rather than the Internet. By comparing our results with other studies (using executives or students), we demonstrate, at least for this type of game, the external validity of lab research.

Demography and Innovative Entrepreneurship

Demographic change will be one of the major challenges for economic policy in the developed world in the next decades. In this article, we analyze the relationship between age structure and the number of startups. We argue that an individual’s decision to start a business is determined by his or her age and, therefore, that a change in a region’s age distribution affects the expected number of startups in the region. Using German regional data, we estimate a count-data model and find that the expected number of startups is positively influenced by the fraction of individuals of working age—20–64 years old. A more detailed analysis of the working-age distribution suggests that startups in knowledge-based (high-tech) manufacturing industries are affected by changes in this distribution whereas firms in other industries are not. In particular, increases in the fraction of individuals in the 20–30 age range and individuals in the 40–50 age range have a positive effect on the number of high-tech startups.demography, age distribution, entrepreneurship, innovation, region

Face Cognition: A Set of Distinct Mental Abilities

Perceiving, learning, and recognizing faces swiftly and accurately is of paramount importance to humans as a social species. Though established functional models of face cognition<sup>1,2</sup> suggest the existence of multiple abilities in face cognition, the number of such abilities and the relationships among them and to other cognitive abilities can only be determined by studying individual differences. Here we investigated individual differences in a broad variety of indicators of face cognition and identified for the first time three component abilities: face perception, face memory, and the speed of face cognition. These component abilities were replicated in an independent study and were found to be robustly separable from established cognitive abilities, specifically immediate and delayed memory, mental speed, general cognitive ability, and object cognition. The analysis of individual differences goes beyond functional and neurological models of face cognition by demonstrating the difference between face perception and face learning, and by making evident the distinction between speed and accuracy of face cognition. Our indicators also provide a means to develop tests and training programs for face cognition that are broader and more precise than those currently available).<sup>3,4</sup&#x3e

Testing Forbearance Experimentally - Duopolistic Competition of Conglomerate Firms

Like Feinberg and Sherman (1985) and Phillips and Mason (1992) we test experimentally whether conglomerate firms, i.e., firms competing on multiple structurally unrelated markets, can effectively limit competition. Our more general analysis assumes differentiated rather than homogeneous products and distinguishes strategic substitutes as well as complements to test this forbearance hypothesis. Rather than only a partners design we also explore a random strangers design to disentangle effects of forbearance and repeated interaction. Surprisingly, conglomerate firms do not limit competition, they rather foster it. More in line with our expectations we find more cooperation in complement markets than in substitute markets and also more cooperation in a partners than in a strangers matching.Experiment, Forbearance, Competition