1,428 research outputs found
Hierarchy of Chaotic Maps with an Invariant Measure
We give hierarchy of one-parameter family F(a,x) of maps of the interval
[0,1] with an invariant measure. Using the measure, we calculate
Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of
these maps analytically, where the results thus obtained have been approved
with numerical simulation. In contrary to the usual one-parameter family of
maps such as logistic and tent maps, these maps do not possess period doubling
or period-n-tupling cascade bifurcation to chaos, but they have single fixed
point attractor at certain parameter values, where they bifurcate directly to
chaos without having period-n-tupling scenario exactly at these values of
parameter whose Lyapunov characteristic exponent begins to be positive.Comment: 18 pages (Latex), 7 figure
Experimental determination of the 6s^2 ^1S_0 -> 5d6s ^3 D_1 magnetic-dipole transition amplitude in atomic ytterbium
We report on a measurement of the highly forbidden 6s^2 ^1S_0 \to 5d6s ^3
D_1 magnetic-dipole transition in atomic ytterbium using the
Stark-interference technique. This amplitude is important in interpreting a
future parity nonconservation experiment that exploits the same transition. We
find , where the larger uncertainty comes from the previously
measured vector transition polarizability . The amplitude is small
and should not limit the precision of the parity nonconservation experiment.Comment: 4 pages, 5 figures Paper resubmitted with minor corrections and
additions based on comments from referee
The factor structure of the Forms of Self-Criticising/Attacking & Self-Reassuring Scale in thirteen distinct populations
There is considerable evidence that self-criticism plays a major role in the vulnerability to and recovery from psychopathology. Methods to measure this process, and its change over time, are therefore important for research in psychopathology and well-being. This study examined the factor structure of a widely used measure, the Forms of Self-Criticising/Attacking & Self-Reassuring Scale in thirteen nonclinical samples (N = 7510) from twelve different countries: Australia (N = 319), Canada (N = 383), Switzerland (N = 230), Israel (N = 476), Italy (N = 389), Japan (N = 264), the Netherlands (N = 360), Portugal (N = 764), Slovakia (N = 1326), Taiwan (N = 417), the United Kingdom 1 (N = 1570), the United Kingdom 2 (N = 883), and USA (N = 331). This study used more advanced analyses than prior reports: a bifactor item-response theory model, a two-tier item-response theory model, and a non-parametric item-response theory (Mokken) scale analysis. Although the original three-factor solution for the FSCRS (distinguishing between Inadequate-Self, Hated-Self, and Reassured-Self) had an acceptable fit, two-tier models, with two general factors (Self-criticism and Self-reassurance) demonstrated the best fit across all samples. This study provides preliminary evidence suggesting that this two-factor structure can be used in a range of nonclinical contexts across countries and cultures. Inadequate-Self and Hated-Self might not by distinct factors in nonclinical samples. Future work may benefit from distinguishing between self-correction versus shame-based self-criticism.Peer reviewe
Clones with finitely many relative R-classes
For each clone C on a set A there is an associated equivalence relation
analogous to Green's R-relation, which relates two operations on A iff each one
is a substitution instance of the other using operations from C. We study the
clones for which there are only finitely many relative R-classes.Comment: 41 pages; proofs improved, examples adde
Interaction energy functional for lattice density functional theory: Applications to one-, two- and three-dimensional Hubbard models
The Hubbard model is investigated in the framework of lattice density
functional theory (LDFT). The single-particle density matrix with
respect the lattice sites is considered as the basic variable of the many-body
problem. A new approximation to the interaction-energy functional
is proposed which is based on its scaling properties and which recovers exactly
the limit of strong electron correlations at half-band filling. In this way, a
more accurate description of is obtained throughout the domain of
representability of , including the crossover from weak to strong
correlations. As examples of applications results are given for the
ground-state energy, charge-excitation gap, and charge susceptibility of the
Hubbard model in one-, two-, and three-dimensional lattices. The performance of
the method is demonstrated by comparison with available exact solutions, with
numerical calculations, and with LDFT using a simpler dimer ansatz for .
Goals and limitations of the different approximations are discussed.Comment: 25 pages and 8 figures, submitted to Phys. Rev.
Magnetic properties of the three-dimensional Hubbard model at half filling
We study the magnetic properties of the 3d Hubbard model at half-filling in
the TPSC formalism, previously developed for the 2d model. We focus on the
N\'eel transition approached from the disordered side and on the paramagnetic
phase. We find a very good quantitative agreement with Dynamical Mean-Field
results for the isotropic 3d model. Calculations on finite size lattices also
provide satisfactory comparisons with Monte Carlo results up to the
intermediate coupling regime. We point out a qualitative difference between the
isotropic 3d case, and the 2d or anisotropic 3d cases for the double occupation
factor. Even for this local correlation function, 2d or anisotropic 3d cases
are out of reach of DMF: this comes from the inability of DMF to account for
antiferromagnetic fluctuations, which are crucial.Comment: RevTex, 9 pages +10 figure
The anapole moment and nucleon weak interactions
From the recent measurement of parity nonconservation (PNC) in the Cs atom we
have extracted the constant of the nuclear spin dependent electron-nucleon PNC
interaction, ; the anapole moment constant, ; the strength of the PNC proton-nucleus potential, ; the -meson-nucleon interaction constant,
; and the strength of the neutron-nucleus potential, .Comment: Uses RevTex, 12 pages. We have added an explanation of the effect of
finite nuclear siz
Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces
This paper is the third in a sequel to develop a super-analogue of the
classical Selberg trace formula, the Selberg supertrace formula. It deals with
bordered super Riemann surfaces. The theory of bordered super Riemann surfaces
is outlined, and the corresponding Selberg supertrace formula is developed. The
analytic properties of the Selberg super zeta-functions on bordered super
Riemann surfaces are discussed, and super-determinants of Dirac-Laplace
operators on bordered super Riemann surfaces are calculated in terms of Selberg
super zeta-functions.Comment: 43 pages, amste
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