2,826 research outputs found
L1-determined ideals in group algebras of exponential Lie groups
A locally compact group is said to be -regular if the natural map
\Psi:\Prim C^\ast(G)\to\Prim_{\ast} L^1(G) is a homeomorphism with respect to
the Jacobson topologies on the primitive ideal spaces \Prim C^\ast(G) and
\Prim_{\ast} L^1(G). In 1980 J. Boidol characterized the -regular ones
among all exponential Lie groups by a purely algebraic condition. In this
article we introduce the notion of -determined ideals in order to discuss
the weaker property of primitive -regularity. We give two sufficient
criteria for closed ideals of to be -determined. Herefrom
we deduce a strategy to prove that a given exponential Lie group is primitive
-regular. The author proved in his thesis that all exponential Lie groups
of dimension have this property. So far no counter-example is known.
Here we discuss the example , the only critical one in dimension
Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory
We isolate a large class of self-adjoint operators H whose essential spectrum
is determined by their behavior at large x and we give a canonical
representation of their essential spectrum in terms of spectra of limits at
infinity of translations of H. The configuration space is an arbitrary abelian
locally compact not compact group.Comment: 63 pages. This is the published version with several correction
Locally Trivial W*-Bundles
We prove that a tracially continuous W-bundle over a
compact Hausdorff space with all fibres isomorphic to the hyperfinite
II-factor that is locally trivial already has to be globally
trivial. The proof uses the contractibility of the automorphism group
shown by Popa and Takesaki. There is no
restriction on the covering dimension of .Comment: 20 pages, this version will be published in the International Journal
of Mathematic
Robustness and Enhancement of Neural Synchronization by Activity-Dependent Coupling
We study the synchronization of two model neurons coupled through a synapse
having an activity-dependent strength. Our synapse follows the rules of
Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the
coupling between neurons produces enlarged frequency locking zones and results
in synchronization that is more rapid and much more robust against noise than
classical synchronization arising from connections with constant strength. We
also present a simple discrete map model that demonstrates the generality of
the phenomenon.Comment: 4 pages, accepted for publication in PR
Aspects of noncommutative Lorentzian geometry for globally hyperbolic spacetimes
Connes' functional formula of the Riemannian distance is generalized to the
Lorentzian case using the so-called Lorentzian distance, the d'Alembert
operator and the causal functions of a globally hyperbolic spacetime. As a step
of the presented machinery, a proof of the almost-everywhere smoothness of the
Lorentzian distance considered as a function of one of the two arguments is
given. Afterwards, using a -algebra approach, the spacetime causal
structure and the Lorentzian distance are generalized into noncommutative
structures giving rise to a Lorentzian version of part of Connes'
noncommutative geometry. The generalized noncommutative spacetime consists of a
direct set of Hilbert spaces and a related class of -algebras of
operators. In each algebra a convex cone made of self-adjoint elements is
selected which generalizes the class of causal functions. The generalized
events, called {\em loci}, are realized as the elements of the inductive limit
of the spaces of the algebraic states on the -algebras. A partial-ordering
relation between pairs of loci generalizes the causal order relation in
spacetime. A generalized Lorentz distance of loci is defined by means of a
class of densely-defined operators which play the r\^ole of a Lorentzian
metric. Specializing back the formalism to the usual globally hyperbolic
spacetime, it is found that compactly-supported probability measures give rise
to a non-pointwise extension of the concept of events.Comment: 43 pages, structure of the paper changed and presentation strongly
improved, references added, minor typos corrected, title changed, accepted
for publication in Reviews in Mathematical Physic
Boosting Biomass Quantity and Quality by Improved Mixotrophic Culture of the Diatom Phaeodactylum tricornutum
Diatoms are photoautotrophic unicellular algae and are among the most abundant, adaptable, and diverse marine phytoplankton. They are extremely interesting not only for their ecological role but also as potential feedstocks for sustainable biofuels and high-value commodities such as omega fatty acids, because of their capacity to accumulate lipids. However, the cultivation of microalgae on an industrial scale requires higher cell densities and lipid accumulation than those found in nature to make the process economically viable. One of the known ways to induce lipid accumulation in Phaeodactylum tricornutum is nitrogen deprivation, which comes at the expense of growth inhibition and lower cell density. Thus, alternative ways need to be explored to enhance the lipid production as well as biomass density to make them sustainable at industrial scale. In this study, we have used experimental and metabolic modeling approaches to optimize the media composition, in terms of elemental composition, organic and inorganic carbon sources, and light intensity, that boost both biomass quality and quantity of P. tricornutum. Eventually, the optimized conditions were scaled-up to 2 L photobioreactors, where a better system control (temperature, pH, light, aeration/mixing) allowed a further improvement of the biomass capacity of P. tricornutum to 12 g/L
Polymer and Fock representations for a Scalar field
In loop quantum gravity, matter fields can have support only on the
`polymer-like' excitations of quantum geometry, and their algebras of
observables and Hilbert spaces of states can not refer to a classical,
background geometry. Therefore, to adequately handle the matter sector, one has
to address two issues already at the kinematic level. First, one has to
construct the appropriate background independent operator algebras and Hilbert
spaces. Second, to make contact with low energy physics, one has to relate this
`polymer description' of matter fields to the standard Fock description in
Minkowski space. While this task has been completed for gauge fields, important
gaps remained in the treatment of scalar fields. The purpose of this letter is
to fill these gaps.Comment: 13 pages, no figure
Fermion mixing in quasi-free states
Quantum field theoretic treatments of fermion oscillations are typically
restricted to calculations in Fock space. In this letter we extend the
oscillation formulae to include more general quasi-free states, and also
consider the case when the mixing is not unitary.Comment: 10 pages, Plain Te
Positronium S state spectrum: analytic results at O(m alpha^6)
We present an analytic calculation of the O(m alpha^6) recoil and radiative
recoil corrections to energy levels of positronium nS states and their
hyperfine splitting. A complete analytic formula valid to O(m alpha^6) is given
for the spectrum of S states. Technical aspects of the calculation are
discussed in detail. Theoretical predictions are given for various energy
intervals and compared with experimental results.Comment: 29 pages, revte
Random graphs with arbitrary degree distributions and their applications
Recent work on the structure of social networks and the internet has focussed
attention on graphs with distributions of vertex degree that are significantly
different from the Poisson degree distributions that have been widely studied
in the past. In this paper we develop in detail the theory of random graphs
with arbitrary degree distributions. In addition to simple undirected,
unipartite graphs, we examine the properties of directed and bipartite graphs.
Among other results, we derive exact expressions for the position of the phase
transition at which a giant component first forms, the mean component size, the
size of the giant component if there is one, the mean number of vertices a
certain distance away from a randomly chosen vertex, and the average
vertex-vertex distance within a graph. We apply our theory to some real-world
graphs, including the world-wide web and collaboration graphs of scientists and
Fortune 1000 company directors. We demonstrate that in some cases random graphs
with appropriate distributions of vertex degree predict with surprising
accuracy the behavior of the real world, while in others there is a measurable
discrepancy between theory and reality, perhaps indicating the presence of
additional social structure in the network that is not captured by the random
graph.Comment: 19 pages, 11 figures, some new material added in this version along
with minor updates and correction
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