1,188 research outputs found
Quasi Exactly Solvable 22 Matrix Equations
We investigate the conditions under which systems of two differential
eigenvalue equations are quasi exactly solvable. These systems reveal a rich
set of algebraic structures. Some of them are explicitely described. An exemple
of quasi exactly system is studied which provides a direct counterpart of the
Lam\'e equation.Comment: 14 pages, Plain Te
Canonical and Lie-algebraic twist deformations of -Poincare and contractions to -Galilei algebras
We propose canonical and Lie-algebraic twist deformations of
-deformed Poincare Hopf algebra which leads to the generalized
-Minkowski space-time relations. The corresponding deformed
-Poincare quantum groups are also calculated. Finally, we perform the
nonrelativistic contraction limit to the corresponding twisted Galilean
algebras and dual Galilean quantum groups.Comment: 16 pages, no figures, v3: few changes provided - version for journal,
v2: submitted incidentally, v4: the page numbers for all references in
preprint version are provide
Scalar Differential Equation for Slowly-Varying Thickness-Shear Modes in AT-Cut Quartz Resonators With Surface Impedance for Acoustic Wave Sensor Application
For time-harmonic motions, we generalize a 2-D scalar differential equation derived previously by Tiersten for slowly-varying thickness-shear vibrations of AT-cut quartz resonators. The purpose of the generalization is to include the effects of surface acoustic impedance from, e.g., mass layers or fluids for sensor applications. In addition to the variation of fields along the plate thickness, which is considered in the usual 1-D acoustic wave sensor models, the equation obtained also describes in-plane variations of the fields, and therefore can be used to study the vibrations of finite plate sensors with edge effects. The equation is compared with the theory of piezoelectricity in the special cases of acoustic waves and pure thickness vibrations in unbounded plates. An example of a finite rectangular plate is also given
Scalar Differential Equation for Slowly-Varying Thickness-Shear Modes in AT-Cut Quartz Resonators with Surface Impedance for Acoustic Wave Sensor Application
For time-harmonic motions, we generalize a 2-D scalar differential equation derived previously by Tiersten for slowly-varying thickness-shear vibrations of AT-cut quartz resonators. The purpose of the generalization is to include the effects of surface acoustic impedance from, e.g., mass layers or fluids for sensor applications. In addition to the variation of fields along the plate thickness, which is considered in the usual 1-D acoustic wave sensor models, the equation obtained also describes in-plane variations of the fields, and therefore can be used to study the vibrations of finite plate sensors with edge effects. The equation is compared with the theory of piezoelectricity in the special cases of acoustic waves and pure thickness vibrations in unbounded plates. An example of a finite rectangular plate is also given
Note on clock synchronization and Edwards transformations
Edwards transformations relating inertial frames with arbitrary clock
synchronization are reminded and put in more general setting. Their group
theoretical context is described.Comment: 11 pages, no figures; final version, to appear in Foundations of
Physics Letter
Scalar field propagation in the phi^4 kappa-Minkowski model
In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model
based on the kappa-deformed star product, ({*}_h). The action is modified by
expanding up to linear order in the kappa-deformation parameter a, producing an
effective model on commutative spacetime. For the computation of the tadpole
diagram contributions to the scalar field propagation/self-energy, we
anticipate that statistics on the kappa-Minkowski is specifically
kappa-deformed. Thus our prescription in fact represents hybrid approach
between standard quantum field theory (QFT) and NCQFT on the kappa-deformed
Minkowski spacetime, resulting in a kappa-effective model. The propagation is
analyzed in the framework of the two-point Green's function for low,
intermediate, and for the Planckian propagation energies, respectively.
Semiclassical/hybrid behavior of the first order quantum correction do show up
due to the kappa-deformed momentum conservation law. For low energies, the
dependence of the tadpole contribution on the deformation parameter a drops out
completely, while for Planckian energies, it tends to a fixed finite value. The
mass term of the scalar field is shifted and these shifts are very different at
different propagation energies. At the Planckian energies we obtain the
direction dependent kappa-modified dispersion relations. Thus our
kappa-effective model for the massive scalar field shows a birefringence
effect.Comment: 23 pages, 2 figures; To be published in JHEP. Minor typos corrected.
Shorter version of the paper arXiv:1107.236
Eliashberg's proof of Cerf's theorem
Following a line of reasoning suggested by Eliashberg, we prove Cerf's
theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To
this end we develop a moduli-theoretic version of Eliashberg's
filling-with-holomorphic-discs method.Comment: 32 page
Projective representation of k-Galilei group
The projective representations of k-Galilei group G_k are found by
contracting the relevant representations of k-Poincare group. The projective
multiplier is found. It is shown that it is not possible to replace the
projective representations of G_k by vector representations of some its
extension.Comment: 15 pages Latex fil
Invertible Dirac operators and handle attachments on manifolds with boundary
For spin manifolds with boundary we consider Riemannian metrics which are
product near the boundary and are such that the corresponding Dirac operator is
invertible when half-infinite cylinders are attached at the boundary. The main
result of this paper is that these properties of a metric can be preserved when
the metric is extended over a handle of codimension at least two attached at
the boundary. Applications of this result include the construction of
non-isotopic metrics with invertible Dirac operator, and a concordance
existence and classification theorem.Comment: Accepted for publication in Journal of Topology and Analysi
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