3,989 research outputs found
Classification of linear differential operators with an invariant subspace of monomials
A complete classification of linear differential operators possessing
finite-dimensional invariant subspace with a basis of monomials is presented.Comment: 10 p
Group Identity and Discrimination in Small Markets: Asymmetry of In-Group Favors
We experimentally study the inuence of induced group identity on the determination of prices and beliefs in a small market game. We create group identity through a focal point coordination game. Subjects play a three-person bargaining game where one seller can sell an indivisible good to one of two competing buyers under four different treatments varying the buyer-seller constellation. We find evidence of in group favoritism on the buyer side. However we do not detect a lower ask prices for in-group sellers for in-group buyers, indicating that in-group favoritism is in favor of the more powerful market participant.Group identity, Experiments, Markets, Bargaining
Ceteris Paribus Laws
Laws of nature take center stage in philosophy of science. Laws are usually believed to stand in a tight conceptual relation to many important key concepts such as causation, explanation, confirmation, determinism, counterfactuals etc. Traditionally, philosophers of science have focused on physical laws, which were taken to be at least true, universal statements that support counterfactual claims. But, although this claim about laws might be true with respect to physics, laws in the special sciences (such as biology, psychology, economics etc.) appear to haveâmaybe not surprisinglyâdifferent features than the laws of physics. Special science lawsâfor instance, the economic law âUnder the condition of perfect competition, an increase of demand of a commodity leads to an increase of price, given that the quantity of the supplied commodity remains constantâ and, in biology, Mendel's Lawsâare usually taken to âhave exceptionsâ, to be ânon-universalâ or âto be ceteris paribus lawsâ. How and whether the laws of physics and the laws of the special sciences differ is one of the crucial questions motivating the debate on ceteris paribus laws. Another major, controversial question concerns the determination of the precise meaning of âceteris paribusâ. Philosophers have attempted to explicate the meaning of ceteris paribus clauses in different ways. The question of meaning is connected to the problem of empirical content, i.e., the question whether ceteris paribus laws have non-trivial and empirically testable content. Since many philosophers have argued that ceteris paribus laws lack empirically testable content, this problem constitutes a major challenge to a theory of ceteris paribus laws
The Kernel Polynomial Method
Efficient and stable algorithms for the calculation of spectral quantities
and correlation functions are some of the key tools in computational condensed
matter physics. In this article we review basic properties and recent
developments of Chebyshev expansion based algorithms and the Kernel Polynomial
Method. Characterized by a resource consumption that scales linearly with the
problem dimension these methods enjoyed growing popularity over the last decade
and found broad application not only in physics. Representative examples from
the fields of disordered systems, strongly correlated electrons,
electron-phonon interaction, and quantum spin systems we discuss in detail. In
addition, we illustrate how the Kernel Polynomial Method is successfully
embedded into other numerical techniques, such as Cluster Perturbation Theory
or Monte Carlo simulation.Comment: 32 pages, 17 figs; revised versio
Fast, precise, and widely tunable frequency control of an optical parametric oscillator referenced to a frequency comb
Optical frequency combs (OFC) provide a convenient reference for the
frequency stabilization of continuous-wave lasers. We demonstrate a frequency
control method relying on tracking over a wide range and stabilizing the beat
note between the laser and the OFC. The approach combines fast frequency ramps
on a millisecond timescale in the entire mode-hop free tuning range of the
laser and precise stabilization to single frequencies. We apply it to a
commercially available optical parametric oscillator (OPO) and demonstrate
tuning over more than 60 GHz with a ramping speed up to 3 GHz/ms. Frequency
ramps spanning 15 GHz are performed in less than 10 ms, with the OPO instantly
relocked to the OFC after the ramp at any desired frequency. The developed
control hardware and software is able to stabilize the OPO to sub-MHz precision
and to perform sequences of fast frequency ramps automatically.Comment: 8 pages, 7 figures, accepted for publication in Review of Scientific
Instrument
DelbrĂŒck scattering in a strong external field
We evaluate the DelbrĂŒck scattering amplitude to all orders of the interaction with the external field of a nucleus employing nonperturbative electron Green's functions. The results are given analytically in form of a multipole expansion
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