358 research outputs found
Atoms with bosonic "electrons" in strong magnetic fields
We study the ground state properties of an atom with nuclear charge and
bosonic ``electrons'' in the presence of a homogeneous magnetic field .
We investigate the mean field limit with fixed, and identify
three different asymptotic regions, according to , , and
. In Region 1 standard Hartree theory is applicable. Region 3 is
described by a one-dimensional functional, which is identical to the so-called
Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with
fermionic electrons in the region ; i.e., for very strong magnetic
fields the ground state properties of atoms are independent of statistics. For
Region 2 we introduce a general {\it magnetic Hartree functional}, which is
studied in detail. It is shown that in the special case of an atom it can be
restricted to the subspace of zero angular momentum parallel to the magnetic
field, which simplifies the theory considerably. The functional reproduces the
energy and the one-particle reduced density matrix for the full -particle
ground state to leading order in , and it implies the description of the
other regions as limiting cases.Comment: LaTeX2e, 37 page
Translation Invariant States on Twisted Algebras on a Lattice
We construct an algebra with twisted commutation relations and equip it with
the shift. For appropriate irregularity of the non-local commutation relations
we prove that the tracial state is the only translation-invariant state
Semiparametric Multinomial Logit Models for Analysing Consumer Choice Behaviour
The multinomial logit model (MNL) is one of the most frequently used statistical models in marketing applications. It allows to relate an unordered categorical response variable, for example representing the choice of a brand, to a vector of covariates such as the price of the brand or variables characterising the consumer. In its classical form, all covariates enter in strictly parametric, linear form into the utility function of the MNL model. In this paper, we introduce semiparametric extensions, where smooth effects of continuous covariates are modelled by penalised splines. A mixed model representation of these penalised splines is employed to obtain estimates of the corresponding smoothing parameters, leading to a fully automated estimation procedure. To validate semiparametric models against parametric models, we utilise proper scoring rules and compare parametric and semiparametric approaches for a number of brand choice data sets
Atoms in strong magnetic fields: The high field limit at fixed nuclear charge
Let E(B,Z,N) denote the ground state energy of an atom with N electrons and
nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of
E(B,Z,N) as with N and Z fixed but arbitrary. It is shown that
the leading term has the form , where e(Z,N) is the ground
state energy of a system of N {\em bosons} with delta interactions in {\em one}
dimension. This extends and refines previously known results for N=1 on the one
hand, and with on the other hand
The state space for two qutrits has a phase space structure in its core
We investigate the state space of bipartite qutrits. For states which are
locally maximally mixed we obtain an analog of the ``magic'' tetrahedron for
bipartite qubits--a magic simplex W. This is obtained via the Weyl group which
is a kind of ``quantization'' of classical phase space. We analyze how this
simplex W is embedded in the whole state space of two qutrits and discuss
symmetries and equivalences inside the simplex W. Because we are explicitly
able to construct optimal entanglement witnesses we obtain the border between
separable and entangled states. With our method we find also the total area of
bound entangled states of the parameter subspace under intervestigation. Our
considerations can also be applied to higher dimensions.Comment: 3 figure
Conjoint-Analyse und Marktsegmentierung
Die Marktsegmentierung zählt neben der Neuproduktplanung und Preisgestaltung zu den wesentlichen Einsatzgebieten der Conjoint-Analyse. Neben traditionell eingesetzten zweistufigen Vorgehensweisen, bei denen Conjoint-Analyse und Segmentierung in zwei getrennten Schritten erfolgen, stehen heute mit Methoden wie der Clusterwise Regression oder Mixture-Modellen neuere Entwicklungen, die eine simultane Segmentierung und Präferenzschätzung ermöglichen, zur Verfügung. Der Beitrag gibt einen Überblick über die vorliegenden methodischen Ansätze zur Verknüpfung von Conjoint-Analyse und Marktsegmentierung und zeigt die Vorzüge simultaner Conjointsegmentierungsmethoden gegenüber den in der Unternehmenspraxis noch immer weit verbreiteten zweistufigen Verfahren auf. Along with new product/concept identification and pricing, market segmentation ranks among the primary purposes in commercial conjoint applications. Traditionally, this conjoint segmentation has been accomplished by a two-step procedure, (1) either by first segmenting markets and subsequently estimating conjoint models at the segment level or (2) by first conducting conjoint analysis at the individual level and then clustering individual level part-worths. However, in recent years, some powerful techniques for simultaneously performing market segmentation and calibrating segment-level part-worths such as clusterwise regression procedures and mixture models have been proposed. This article provides an overview of existing conjoint segmentation methods and particularly focuses on the newer simultaneous approaches which offer substantial advantages compared to the traditional two-step procedures.Marktsegmentierung; Conjoint-Analyse ; Simultanverfahren;
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