1,609 research outputs found
Cohomogeneity one manifolds and selfmaps of nontrivial degree
We construct natural selfmaps of compact cohomgeneity one manifolds with
finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds
with simple cohomology rings this yields in certain cases relations between the
order of the Weyl group and the Euler characteristic of a principal orbit. We
apply our construction to the compact Lie group SU(3) where we extend identity
and transposition to an infinite family of selfmaps of every odd degree. The
compositions of these selfmaps with the power maps realize all possible degrees
of selfmaps of SU(3).Comment: v2, v3: minor improvement
Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach
By employing Hopf's functional method, we find the exact characteristic
functional for a simple nonlinear dynamical system introduced by Orszag.
Steady-state equal-time statistics thus obtained are compared to direct
numerical simulation. The solution is both non-trivial and strongly
non-Gaussian.Comment: 6 pages and 2 figure
Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+\epsilon dimensions
The statistics of 2-dimensional turbulence exhibit a riddle: the scaling
exponents in the regime of inverse energy cascade agree with the K41 theory of
turbulence far from equilibrium, but the probability distribution functions are
close to Gaussian like in equilibrium. The skewness \C S \equiv
S_3(R)/S^{3/2}_2(R) was measured as \C S_{\text{exp}}\approx 0.03. This
contradiction is lifted by understanding that 2-dimensional turbulence is not
far from a situation with equi-partition of enstrophy, which exist as true
thermodynamic equilibrium with K41 exponents in space dimension of . We
evaluate theoretically the skewness \C S(d) in dimensions ,
show that \C S(d)=0 at , and that it remains as small as \C
S_{\text{exp}} in 2-dimensions.Comment: PRL, submitted, REVTeX 4, 4 page
Cutting the same fraction of several measures
We study some measure partition problems: Cut the same positive fraction of
measures in with a hyperplane or find a convex subset of
on which given measures have the same prescribed value. For
both problems positive answers are given under some additional assumptions.Comment: 7 pages 2 figure
Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics
Convergence conditions for quantum annealing are derived for optimization
problems represented by the Ising model of a general form. Quantum fluctuations
are introduced as a transverse field and/or transverse ferromagnetic
interactions, and the time evolution follows the real-time Schrodinger
equation. It is shown that the system stays arbitrarily close to the
instantaneous ground state, finally reaching the target optimal state, if the
strength of quantum fluctuations decreases sufficiently slowly, in particular
inversely proportionally to the power of time in the asymptotic region. This is
the same condition as the other implementations of quantum annealing, quantum
Monte Carlo and Green's function Monte Carlo simulations, in spite of the
essential difference in the type of dynamics. The method of analysis is an
application of the adiabatic theorem in conjunction with an estimate of a lower
bound of the energy gap based on the recently proposed idea of Somma et. al.
for the analysis of classical simulated annealing using a classical-quantum
correspondence.Comment: 6 pages, minor correction
Changes in temperature of heel skin under pressure in hip surgery patients
OBJECTIVE: The aim of the study was to examine the effect of external pressure of the bed surface on heel skin temperature in adults in the first 3 days after hip surgery. DESIGN: A quasi-experimental study in a prospective, within-subjects, repeated-measures design. SETTING: This study was performed at 2 acute-care hospitals. PARTICIPANTS: Eighteen subjects (9 men and 9 women) with a mean age of 58.3 (±16.1) years were recruited after hip surgery at the 2 hospitals. METHODS: Temperature sensors were placed on the plantar surface of each foot, close to the heels. Measures were taken when the heels were (1) suspended above the bed surface for 20 minutes (preload), (2) on the bed surface for 15 minutes (loading), and (3) suspended again above the bed surface for 15 minutes (unloading). MAIN OUTCOME MEASURES: Heel skin temperature and demographic data. RESULTS: Heel temperature increased during loading and unloading in both legs on postoperative days 1 (P = .003) and 3 (P = .04) but not on postoperative day 2. Heel temperature in the nonoperative leg decreased in the first 3 minutes of unloading on postoperative days 2 (P = .02) and 3 (P .01). CONCLUSION: Heel temperature increased with loading and unloading on postoperative days 1 and 3. Upon immediate unloading, hyperemic response was present only in the nonoperative leg. Keeping the heels off the bed surface at all times may avoid heel skin temperature changes and prevent tissue damage. Further research is needed to identify the mechanisms that explain the effect of external pressure on heel temperature
Familiäre Kavernome des Zentralnervensystems: Eine klinische und genetische Studie an 15 deutsche Familien
Zusammenfassung: 1928 beschrieb Hugo Friedrich Kufs erstmalig eine Familie mit zerebralen, retinalen und kutanen Kavernomen. Mittlerweile wurden über 300 weitere Familien beschrieben. Ebenfalls wurden drei Genloci 7q21-q22 (mit dem Gen CCM1), 7p15-p13 (Gen CCM2) und 3q25.2-q27 (Gen CCM3) beschrieben, in denen Mutationen zu Kavernomen führen. Das Genprodukt von CCM1 ist das Protein Krit1 (Krev Interaction Trapped 1), das über verschiedene Mechanismen mit der Angiogenese interagiert. Das neu entdeckte CCM2-Gen enkodiert ein Protein, das möglicherweise eine dem Krit1 ähnliche Funktion in der Regulation der Angiogenese hat. Das CCM3-Gen wurde noch nicht beschrieben. In dieser Arbeit werden sowohl die klinischen und genetischen Befunde bei 15 deutschen Familien beschriebe
On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems
This paper deals with periodic solutions of the Hamilton equation with many
parameters. Theorems on global bifurcation of solutions with periods
from a stationary point are proved. The Hessian matrix of the
Hamiltonian at the stationary point can be singular. However, it is assumed
that the local topological degree of the gradient of the Hamiltonian at the
stationary point is nonzero. It is shown that (global) bifurcation points of
solutions with given periods can be identified with zeros of appropriate
continuous functions on the space of parameters. Explicit formulae for such
functions are given in the case when the Hessian matrix of the Hamiltonian at
the stationary point is block-diagonal. Symmetry breaking results concerning
bifurcation of solutions with different minimal periods are obtained. A
geometric description of the set of bifurcation points is given. Examples of
constructive application of the theorems proved to analytical and numerical
investigation and visualization of the set of all bifurcation points in given
domain are provided.
This paper is based on a part of the author's thesis [W. Radzki, ``Branching
points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD
thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer
Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe
Evolution of the Chern-Simons Vortices
Based on the gauge potential decomposition theory and the -mapping
theory, the topological inner structure of the Chern-Simons-Higgs vortex has
been showed in detail. The evolution of CSH vortices is studied from the
topological properties of the Higgs scalar field. The vortices are found
generating or annihilating at the limit points and encountering, splitting or
merging at the bifurcation points of the scalar field Comment: 10 pages, 10 figure
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