1,354 research outputs found
Thurston's pullback map on the augmented Teichm\"uller space and applications
Let be a postcritically finite branched self-cover of a 2-dimensional
topological sphere. Such a map induces an analytic self-map of a
finite-dimensional Teichm\"uller space. We prove that this map extends
continuously to the augmented Teichm\"uller space and give an explicit
construction for this extension. This allows us to characterize the dynamics of
Thurston's pullback map near invariant strata of the boundary of the augmented
Teichm\"uller space. The resulting classification of invariant boundary strata
is used to prove a conjecture by Pilgrim and to infer further properties of
Thurston's pullback map. Our approach also yields new proofs of Thurston's
theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
Elliptic pseudoanalytic function theory was considered independently by Bers
and Vekua decades ago. In this paper we develop a hyperbolic analogue of
pseudoanalytic function theory using the algebra of hyperbolic numbers. We
consider the Klein-Gordon equation with a potential. With the aid of one
particular solution we factorize the Klein-Gordon operator in terms of two
Vekua-type operators. We show that real parts of the solutions of one of these
Vekua-type operators are solutions of the considered Klein-Gordon equation.
Using hyperbolic pseudoanalytic function theory, we then obtain explicit
construction of infinite systems of solutions of the Klein-Gordon equation with
potential. Finally, we give some examples of application of the proposed
procedure
On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory
Given a particular solution of a one-dimensional stationary Schroedinger
equation (SE) this equation of second order can be reduced to a first order
linear differential equation. This is done with the aid of an auxiliary Riccati
equation. We show that a similar fact is true in a multidimensional situation
also. We consider the case of two or three independent variables. One
particular solution of (SE) allows us to reduce this second order equation to a
linear first order quaternionic differential equation. As in one-dimensional
case this is done with the aid of an auxiliary Riccati equation. The resulting
first order quaternionic equation is equivalent to the static Maxwell system.
In the case of two independent variables it is the Vekua equation from theory
of generalized analytic functions. We show that even in this case it is
necessary to consider not complex valued functions only, solutions of the Vekua
equation but complete quaternionic functions. Then the first order quaternionic
equation represents two separate Vekua equations, one of which gives us
solutions of (SE) and the other can be considered as an auxiliary equation of a
simpler structure. For the auxiliary equation we always have the corresponding
Bers generating pair, the base of the Bers theory of pseudoanalytic functions,
and what is very important, the Bers derivatives of solutions of the auxiliary
equation give us solutions of the main Vekua equation and as a consequence of
(SE). We obtain an analogue of the Cauchy integral theorem for solutions of
(SE). For an ample class of potentials (which includes for instance all radial
potentials), this new approach gives us a simple procedure allowing to obtain
an infinite sequence of solutions of (SE) from one known particular solution
On a factorization of second order elliptic operators and applications
We show that given a nonvanishing particular solution of the equation
(divpgrad+q)u=0 (1) the corresponding differential operator can be factorized
into a product of two first order operators. The factorization allows us to
reduce the equation (1) to a first order equation which in a two-dimensional
case is the Vekua equation of a special form. Under quite general conditions on
the coefficients p and q we obtain an algorithm which allows us to construct in
explicit form the positive formal powers (solutions of the Vekua equation
generalizing the usual powers of the variable z). This result means that under
quite general conditions one can construct an infinite system of exact
solutions of (1) explicitly, and moreover, at least when p and q are real
valued this system will be complete in ker(divpgrad+q) in the sense that any
solution of (1) in a simply connected domain can be represented as an infinite
series of obtained exact solutions which converges uniformly on any compact
subset of . Finally we give a similar factorization of the operator
(divpgrad+q) in a multidimensional case and obtain a natural generalization of
the Vekua equation which is related to second order operators in a similar way
as its two-dimensional prototype does
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RyR1-targeted drug discovery pipeline integrating FRET-based high-throughput screening and human myofiber dynamic Ca2+ assays.
Elevated cytoplasmic [Ca2+] is characteristic in severe skeletal and cardiac myopathies, diabetes, and neurodegeneration, and partly results from increased Ca2+ leak from sarcoplasmic reticulum stores via dysregulated ryanodine receptor (RyR) channels. Consequently, RyR is recognized as a high-value target for drug discovery to treat such pathologies. Using a FRET-based high-throughput screening assay that we previously reported, we identified small-molecule compounds that modulate the skeletal muscle channel isoform (RyR1) interaction with calmodulin and FK506 binding protein 12.6. Two such compounds, chloroxine and myricetin, increase FRET and inhibit [3H]ryanodine binding to RyR1 at nanomolar Ca2+. Both compounds also decrease RyR1 Ca2+ leak in human skinned skeletal muscle fibers. Furthermore, we identified compound concentrations that reduced leak by > 50% but only slightly affected Ca2+ release in excitation-contraction coupling, which is essential for normal muscle contraction. This report demonstrates a pipeline that effectively filters small-molecule RyR1 modulators towards clinical relevance
Comparing metrics at large: harmonic vs quo-harmonic coordinates
To compare two space-times on large domains, and in particular the global
structure of their manifolds, requires using identical frames of reference and
associated coordinate conditions. In this paper we use and compare two classes
of time-like congruences and corresponding adapted coordinates: the harmonic
and quo-harmonic classes. Besides the intrinsic definition and some of their
intrinsic properties and differences we consider with some detail their
differences at the level of the linearized approximation of the field
equations. The hard part of this paper is an explicit and general determination
of the harmonic and quo-harmonic coordinates adapted to the stationary
character of three well-know metrics, Schwarzschild's, Curzon's and Kerr's, to
order five of their asymptotic expansions. It also contains some relevant
remarks on such problems as defining the multipoles of vacuum solutions or
matching interior and exterior solutions.Comment: 27 pages, no figure
The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems
We present a new variational principle for the gyrokinetic system, similar to
the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in
the Eulerian frame and based on constrained variations of the phase space fluid
velocity and particle distribution function. Using a Legendre transform, we
explicitly derive the field theoretic Hamiltonian structure of the system. This
is carried out with a modified Dirac theory of constraints, which is used to
construct meaningful brackets from those obtained directly from
Euler-Poincar\'{e} theory. Possible applications of these formulations include
continuum geometric integration techniques, large-eddy simulation models and
Casimir type stability methods.
[1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur
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