Effective Free Energy for Individual Dynamics

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc

Coherent state triplets and their inner products

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being correcte

Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras

Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding Lie algebras.Comment: LaTeX, 14pages, no figur

A Luminous and Fast-Expanding Type Ib Supernova SN 2012au

We present a set of photometric and spectroscopic observations of a bright Type Ib supernova SN 2012au from -6d until ~+150d after maximum. The shape of its early R-band light curve is similar to that of an average Type Ib/c supernova. The peak absolute magnitude is M_R=-18.7+-0.2 mag, which suggests that this supernova belongs to a very luminous group among Type Ib supernovae. The line velocity of He I {\lambda}5876 is about 15,000 km/s around maximum, which is much faster than that in a typical Type Ib supernova. From the quasi-bolometric peak luminosity of (6.7+-1.3)x10^(42) erg/s, we estimate the \Ni mass produced during the explosion as ~0.30 Msun. We also give a rough constraint to the ejecta mass 5-7 Msun and the kinetic energy (7-18)x10^(51) erg. We find a weak correlation between the peak absolute magnitude and He I velocity among Type Ib SNe. The similarities to SN 1998bw in the density structure inferred from the light curve model as well as the large peak bolometric luminosity suggest that SN 2012au had properties similar to energetic Type Ic supernovae.Comment: 15 pages, 5 figures; accepted to ApJ

The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model

The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar to what is observed in the model of quantum optics. The collapses and revivals of the spin which result extend to a relativistic theory our previous findings on nonrelativistic oscillator where they were known under the name of `spin-orbit pendulum'. There are important relativistic effects (lack of periodicity, zitterbewegung, negative energy states). Many of them disappear after a Foldy-Wouthuysen transformation.Comment: LaTeX2e, uses IOP style files (included), 14 pages, 9 separate postscript figure

Cloning and sequence analysis of cDNAs encoding the cytosolic precursors of subunits GapA and GapB of chloroplast glyceraldehyde-3-phosphate dehydrogenase from pea and spinach

Chloroplast glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is composed of two different subunits, GapA and GapB. cDNA clones containing the entire coding sequences of the cytosolic precursors for GapA from pea and for GapB from pea and spinach have been identified, sequenced and the derived amino acid sequences have been compared to the corresponding sequences from tobacco, maize and mustard. These comparisons show that GapB differs from GapA in about 20% of its amino acid residues and by the presence of a flexible and negatively charged C-terminal extension, possibly responsible for the observed association of the enzyme with chloroplast envelopes in vitro. This C-terminal extension (29 or 30 residues) may be susceptible to proteolytic cleavage thereby leading to a conversion of chloroplast GAPDH isoenzyme I into isoenzyme II. Evolutionary rate comparisons at the amino acid sequence level show that chloroplast GapA and GapB evolve roughly two-fold slower than their cytosolic counterpart GapC. GapA and GapB transit peptides evolve about 10 times faster than the corresponding mature subunits. They are relatively long (68 and 83 residues for pea GapA and spinach GapB respectively) and share a similar amino acid framework with other chloroplast transit peptides

Nonlinear collective nuclear motion

For each real number $\Lambda$ a Lie algebra of nonlinear vector fields on three dimensional Euclidean space is reported. Although each algebra is mathematically isomorphic to $gl(3,{\bf R})$, only the $\Lambda=0$ vector fields correspond to the usual generators of the general linear group. The $\Lambda < 0$ vector fields integrate to a nonstandard action of the general linear group; the $\Lambda >0$ case integrates to a local Lie semigroup. For each $\Lambda$, a family of surfaces is identified that is invariant with respect to the group or semigroup action. For positive $\Lambda$ the surfaces describe fissioning nuclei with a neck, while negative $\Lambda$ surfaces correspond to exotic bubble nuclei. Collective models for neck and bubble nuclei are given by irreducible unitary representations of a fifteen dimensional semidirect sum spectrum generating algebra $gcm(3)$ spanned by its nonlinear $gl(3,{\bf R})$ subalgebra plus an abelian nonlinear inertia tensor subalgebra.Comment: 13 pages plus two figures(available by fax from authors by request

On some nonlinear extensions of the angular momentum algebra

Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are associative for any choice of the deformation parameters. Their Casimir operators are obtained and some of their unitary irreducible representations are constructed. For vanishing deformation, the latter go over into those of the corresponding Lie algebras that contain each of the so(3) unitary irreducible representations at most once. It is also proved that similar deformations of the Lie algebras su(3), sl(3,R), and of the semidirect sum of an abelian algebra t(5) and so(3) do not lead to associative algebras.Comment: 22 pages, plain TeX + preprint.sty, no figures, to appear in J.Phys.

Beyond Prejudice as Simple Antipathy: Hostile and Benevolent Sexism Across Cultures

The authors argue that complementary hostile and benevolent componen:s of sexism exist ac ro.ss cultures. Male dominance creates hostile sexism (HS). but men's dependence on women fosters benevolent sexism (BS)-subjectively positive attitudes that put women on a pedestal but reinforce their subordination. Research with 15,000 men and women in 19 nations showed that (a) HS and BS are coherenl constructs th at correlate positively across nations, but (b) HS predicts the ascription of negative and BS the ascription of positive traits to women, (c) relative to men, women are more likely to reject HS than BS. especially when overall levels of sexism in a culture are high, and (d) national averages on BS and HS predict gender inequal ity across nations. These results challenge prevailing notions of prejudice as an antipathy in that BS (an affectionate, patronizing ideology) reflects inequality and is a cross-culturally pervasive complement to HS

Optical and Near-Infrared Polarimetry of Highly Reddened Type Ia Supernova 2014J: Peculiar Properties of Dust in M82

We presented optical and near-infrared multi-band linear polarimetry of the highly reddened Type Ia SN~2014J appeared in M82. SN~2014J exhibits large polarization at shorter wavelengths, e.g., $4.8$\% in $B$ band, and the polarization decreases rapidly at longer wavelengths, with the position angle of the polarization remaining at approximately $40^{\circ}$ over the observed wavelength range. These polarimetric properties suggest that the observed polarization is likely to be caused predominantly by the interstellar dust within M82. Further analysis shows that the polarization peaks at a wavelengths much shorter than those obtained for the Galactic dust. The wavelength dependence of the polarization can be better described by an inverse power law rather than by Serkowski law for Galactic interstellar polarization. These suggests that the nature of the dust in M82 may be different from that in our Galaxy, with polarizing dust grains having a mean radius of $<0.1\ \mu$m.Comment: 8 pages, 4 figures, accepted for publication in ApJ Letter