4,690 research outputs found
A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds
Warped product CR-submanifolds in Kaehlerian manifolds were intensively
studied only since 2001 after the impulse given by B.Y. Chen. Immediately
after, another line of research, similar to that concerning Sasakian geometry
as the odd dimensional version of Kaehlerian geometry, was developed, namely
warped product contact CR-submanifolds in Sasakian manifolds. In this note we
proved that there exists no proper doubly warped product contact
CR-submanifolds in trans-Sasakian manifolds.Comment: 5 Latex page
A Remarkably Stable and Simple Monocyclic Thiepin. Synthesis and Properties of 2, 7-Di-tert-butyl-4-ethoxycarbonyl-5-methylthiepin
A simple monocyclic 8n electron thiepin, 2,7-di-tert-butyl-4-
-ethoxycarbonyl-5-methylthiepin (13) stabilized by two bulky tert-
-butyl groups at 2- and 7-positions, was synthesized from 2,6-di-
-tert-butyl-4-methylthiopyrylium tetrafluoroborate (11). In spite of
of its monocyclic thiepin structure, the compound 13 showed remarkable
thermal stability and had a half-life of 7.1 h at 130 °C.
Judging from the 1H-NMR spectrum, the thiepin 13 is considered
to be an atropic molecule.
Synthetic details of 11 and 13, and the chemical and physical
properties of 13 are also described
Lax pair tensors and integrable spacetimes
The use of Lax pair tensors as a unifying framework for Killing tensors of
arbitrary rank is discussed. Some properties of the tensorial Lax pair
formulation are stated. A mechanical system with a well-known Lax
representation -- the three-particle open Toda lattice -- is geometrized by a
suitable canonical transformation. In this way the Toda lattice is realized as
the geodesic system of a certain Riemannian geometry. By using different
canonical transformations we obtain two inequivalent geometries which both
represent the original system. Adding a timelike dimension gives
four-dimensional spacetimes which admit two Killing vector fields and are
completely integrable.Comment: 10 pages, LaTe
Evolution of the discrepancy between a universe and its model
We study a fundamental issue in cosmology: Whether we can rely on a
cosmological model to understand the real history of the Universe. This
fundamental, still unresolved issue is often called the ``model-fitting problem
(or averaging problem) in cosmology''. Here we analyze this issue with the help
of the spectral scheme prepared in the preceding studies.
Choosing two specific spatial geometries that are very close to each other,
we investigate explicitly the time evolution of the spectral distance between
them; as two spatial geometries, we choose a flat 3-torus and a perturbed
geometry around it, mimicking the relation of a ``model universe'' and the
``real Universe''. Then we estimate the spectral distance between them and
investigate its time evolution explicitly. This analysis is done efficiently by
making use of the basic results of the standard linear structure-formation
theory.
We observe that, as far as the linear perturbation of geometry is valid, the
spectral distance does not increase with time prominently,rather it shows the
tendency to decrease. This result is compatible with the general belief in the
reliability of describing the Universe by means of a model, and calls for more
detailed studies along the same line including the investigation of wider class
of spacetimes and the analysis beyond the linear regime.Comment: To be published in Classical and Quantum Gravit
Geometry and stability of dynamical systems
We reconsider both the global and local stability of solutions of
continuously evolving dynamical systems from a geometric perspective. We
clarify that an unambiguous definition of stability generally requires the
choice of additional geometric structure that is not intrinsic to the dynamical
system itself. While global Lyapunov stability is based on the choice of
seminorms on the vector bundle of perturbations, we propose a definition of
local stability based on the choice of a linear connection. We show how this
definition reproduces known stability criteria for second order dynamical
systems. In contrast to the general case, the special geometry of Lagrangian
systems provides completely intrinsic notions of global and local stability. We
demonstrate that these do not suffer from the limitations occurring in the
analysis of the Maupertuis-Jacobi geodesics associated to natural Lagrangian
systems.Comment: 22 pages, 2 figure
Navigation in Curved Space-Time
A covariant and invariant theory of navigation in curved space-time with
respect to electromagnetic beacons is written in terms of J. L. Synge's
two-point invariant world function. Explicit equations are given for navigation
in space-time in the vicinity of the Earth in Schwarzschild coordinates and in
rotating coordinates. The restricted problem of determining an observer's
coordinate time when their spatial position is known is also considered
Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
Finsler and Lagrange spaces can be equivalently represented as almost Kahler
manifolds enabled with a metric compatible canonical distinguished connection
structure generalizing the Levi Civita connection. The goal of this paper is to
perform a natural Fedosov-type deformation quantization of such geometries. All
constructions are canonically derived for regular Lagrangians and/or
fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23
page
On the Canonical Formalism for a Higher-Curvature Gravity
Following the method of Buchbinder and Lyahovich, we carry out a canonical
formalism for a higher-curvature gravity in which the Lagrangian density is given in terms of a function of the salar curvature as . The local Hamiltonian is obtained by a
canonical transformation which interchanges a pair of the generalized
coordinate and its canonical momentum coming from the higher derivative of the
metric.Comment: 11 pages, no figures, Latex fil
Scaled penalization of Brownian motion with drift and the Brownian ascent
We study a scaled version of a two-parameter Brownian penalization model
introduced by Roynette-Vallois-Yor in arXiv:math/0511102. The original model
penalizes Brownian motion with drift by the weight process
where and
is the running maximum of the Brownian motion. It was
shown there that the resulting penalized process exhibits three distinct phases
corresponding to different regions of the -plane. In this paper, we
investigate the effect of penalizing the Brownian motion concurrently with
scaling and identify the limit process. This extends a result of Roynette-Yor
for the case to the whole parameter plane and reveals two
additional "critical" phases occurring at the boundaries between the parameter
regions. One of these novel phases is Brownian motion conditioned to end at its
maximum, a process we call the Brownian ascent. We then relate the Brownian
ascent to some well-known Brownian path fragments and to a random scaling
transformation of Brownian motion recently studied by Rosenbaum-Yor.Comment: 32 pages; made additions to Section
- …