3,702 research outputs found
Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
We examine the completeness of bi-orthogonal sets of eigenfunctions for
non-Hermitian Hamiltonians possessing a spectral singularity. The correct
resolutions of identity are constructed for delta like and smooth potentials.
Their form and the contribution of a spectral singularity depend on the class
of functions employed for physical states. With this specification there is no
obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde
Hot Electron Capture Dissociation Distinguishes Leucine from Isoleucine in a Novel Hemoglobin Variant, Hb Askew, β54(D5)ValâIle
Population migration has led to the global dispersion of human hemoglobinopathies and has precipitated a need for their identification. An effective mass spectrometry-based procedure involves analysis of the intact Îą- and β-globin chains to determine their mass, followed by location of the variant amino acid residue by direct analysis of the enzymatically digested chains and low-energy collision induced dissociation of the variant peptide. Using this procedure, a variant was identified as either β54ValâLeu or β54ValâIle, since the amino acids leucine and isoleucine cannot be distinguished using low-energy collisions. Here, we describe how hot electron capture dissociation on a Fourier transform-ion cyclotron resonance mass spectrometer was used to distinguish isoleucine from leucine and identify the mutation as β54(D5)ValâIle. This is a novel variant, and we have named it Hb Askew
Bogoliubov compensation approach in QCD and in the electroweak theory
We describe application of Bogoliubov compensation principle to calculation
of non-perturbative contribution in the electroweak theory and QCD. We obtain
unique solutions of compensation equations, which impose strong restrictions on
parameters of theories and on functional dependence of corresponding
form-factors. We calculate value of running gauge electroweak coupling
, that differs from the experimental value less than by
10%. We derive effective Nambu-Jona-Lasinio interaction from fundamental QCD
and express its parameters in terms of initial QCD parameters: at
low-momenta and current mass of light quarks. This leads to satisfactory
description of low-mass hadron physics.Comment: 6 pages, no figures, talk presented at the International Bogolyubov
Conference, August 21-27, 2009, Moscow-Dubna, Russi
Arbitrary Rotation Invariant Random Matrix Ensembles and Supersymmetry
We generalize the supersymmetry method in Random Matrix Theory to arbitrary
rotation invariant ensembles. Our exact approach further extends a previous
contribution in which we constructed a supersymmetric representation for the
class of norm-dependent Random Matrix Ensembles. Here, we derive a
supersymmetric formulation under very general circumstances. A projector is
identified that provides the mapping of the probability density from ordinary
to superspace. Furthermore, it is demonstrated that setting up the theory in
Fourier superspace has considerable advantages. General and exact expressions
for the correlation functions are given. We also show how the use of hyperbolic
symmetry can be circumvented in the present context in which the non-linear
sigma model is not used. We construct exact supersymmetric integral
representations of the correlation functions for arbitrary positions of the
imaginary increments in the Green functions.Comment: 36 page
Conservation laws for vacuum tetrad gravity
Ten conservation laws in useful polynomial form are derived from a Cartan
form and Exterior Differential System (EDS) for the tetrad equations of vacuum
relativity. The Noether construction of conservation laws for well posed EDS is
introduced first, and an illustration given, deriving 15 conservation laws of
the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS
and tetrad gravity EDS have parallel structures, with their numbers of
dependent variables, numbers of generating 2-forms and generating 3-forms, and
Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding
symmetries with the same Lorentz algebra, and 10 corresponding conservation
laws.Comment: Final version with additional reference
Finite Euler Hierarchies And Integrable Universal Equations
Recent work on Euler hierarchies of field theory Lagrangians iteratively
constructed {}from their successive equations of motion is briefly reviewed. On
the one hand, a certain triality structure is described, relating arbitrary
field theories, {\it classical\ts} topological field theories -- whose
classical solutions span topological classes of manifolds -- and
reparametrisation invariant theories -- generalising ordinary string and
membrane theories. On the other hand, {\it finite} Euler hierarchies are
constructed for all three classes of theories. These hierarchies terminate with
{\it universal\ts} equations of motion, probably defining new integrable
systems as they admit an infinity of Lagrangians. Speculations as to the
possible relevance of these theories to quantum gravity are also suggested.Comment: (replaces previous unprintable version corrupted mailer) 13 p.,
(Plain TeX), DTP-92/3
Biopython: freely available Python tools for computational molecular biology and bioinformatics
Summary: The Biopython project is a mature open source international collaboration of volunteer developers, providing Python libraries for a wide range of bioinformatics problems. Biopython includes modules for reading and writing different sequence file formats and multiple sequence alignments, dealing with 3D macro molecular structures, interacting with common tools such as BLAST, ClustalW and EMBOSS, accessing key online databases, as well as providing numerical methods for statistical learning.
Availability: Biopython is freely available, with documentation and source code at www.biopython.org under the Biopython license.
Contact: All queries should be directed to the Biopython mailing lists, see www.biopython.org/wiki/[email protected]
Quantum Fluctuations of a Coulomb potential
Long-range properties of the two-point correlation function of the
electromagnetic field produced by an elementary particle are investigated.
Using the Schwinger-Keldysh formalism it is shown that this function is finite
in the coincidence limit outside the region of particle localization. In this
limit, the leading term in the long-range expansion of the correlation function
is calculated explicitly, and its gauge independence is proved. The leading
contribution turns out to be of zero order in the Planck constant, and the
relative value of the root mean square fluctuation of the Coulomb potential is
found to be 1/\sqrt{2}, confirming the result obtained previously within the
S-matrix approach. It is shown also that in the case of a macroscopic body, the
\hbar^0 part of the correlation function is suppressed by a factor 1/N, where N
is the number of particles in the body. Relation of the obtained results to the
problem of measurability of the electromagnetic field is mentioned.Comment: 15 pages, 2 figure
On the Plants Leaves Boundary, "Jupe \`a Godets" and Conformal Embeddings
The stable profile of the boundary of a plant's leaf fluctuating in the
direction transversal to the leaf's surface is described in the framework of a
model called a "surface \`a godets". It is shown that the information on the
profile is encoded in the Jacobian of a conformal mapping (the coefficient of
deformation) corresponding to an isometric embedding of a uniform Cayley tree
into the 3D Euclidean space. The geometric characteristics of the leaf's
boundary (like the perimeter and the height) are calculated. In addition a
symbolic language allowing to investigate statistical properties of a "surface
\`a godets" with annealed random defects of curvature of density is
developed. It is found that at the surface exhibits a phase transition
with critical exponent from the exponentially growing to the flat
structure.Comment: 17 pages (revtex), 8 eps-figures, to appear in Journal of Physics
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