698 research outputs found
Elementary Kaluza-Klein Towers revisited
Considering that the momentum squared in the extra dimensions is the
physically relevant quantity for the generation of the Kaluza-Klein mass
states, we have reanalyzed mathematically the procedure for five dimensional
scalar fields within the Arkhani-Ahmed, Dimopoulos and Dvali scenario. We find
new sets of physically allowed boundary conditions. Beside the usual results,
they lead to new towers with non regular mass spacing, to lonely mass states
and to tachyons. We remark that, since the SO(1,4) symmetry is to be broken due
to the compactification of the extra dimensions, the speed of light could be
different in the fifth dimension. This would lead to the possible appearance of
a new universal constant besides and .Comment: 20 pages, 1 figur
Non-linearity and related features of Makyoh (magic-mirror) imaging
Non-linearity in Makyoh (magic-mirror) imaging is analyzed using a geometrical optical approach. The sources of non-linearity are identified as (1) a topological mapping of the imaged surface due to surface gradients, (2) the hyperbolic-like dependence of the image intensity on the local curvatures, and (3) the quadratic dependence of the intensity due to local Gaussian surface curvatures. Criteria for an approximate linear imaging are given and the relevance to Makyoh-topography image evaluation is discussed
Infinite matrices may violate the associative law
The momentum operator for a particle in a box is represented by an infinite
order Hermitian matrix . Its square is well defined (and diagonal),
but its cube is ill defined, because . Truncating these
matrices to a finite order restores the associative law, but leads to other
curious results.Comment: final version in J. Phys. A28 (1995) 1765-177
Critical strength of attractive central potentials
We obtain several sequences of necessary and sufficient conditions for the
existence of bound states applicable to attractive (purely negative) central
potentials. These conditions yields several sequences of upper and lower limits
on the critical value, , of the coupling constant
(strength), , of the potential, , for which a first
-wave bound state appears, which converges to the exact critical value.Comment: 18 page
A Simple Proof of the Fundamental Theorem about Arveson Systems
With every Eo-semigroup (acting on the algebra of of bounded operators on a
separable infinite-dimensional Hilbert space) there is an associated Arveson
system. One of the most important results about Arveson systems is that every
Arveson system is the one associated with an Eo-semigroup. In these notes we
give a new proof of this result that is considerably simpler than the existing
ones and allows for a generalization to product systems of Hilbert module (to
be published elsewhere).Comment: Publication data added, acknowledgements and a note after acceptance
added, corrects a number of inconveniences that have been produced in the
published version during the publication proces
Quantum Degenerate Systems
Degenerate dynamical systems are characterized by symplectic structures whose
rank is not constant throughout phase space. Their phase spaces are divided
into causally disconnected, nonoverlapping regions such that there are no
classical orbits connecting two different regions. Here the question of whether
this classical disconnectedness survives quantization is addressed. Our
conclusion is that in irreducible degenerate systems --in which the degeneracy
cannot be eliminated by redefining variables in the action--, the
disconnectedness is maintained in the quantum theory: there is no quantum
tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces
are boundaries separating distinct physical systems, not only classically, but
in the quantum realm as well. The relevance of this feature for gravitation and
Chern-Simons theories in higher dimensions cannot be overstated.Comment: 18 pages, no figure
Tests for conditional heteroscedasticity of functional data
Functional data objects derived from high-frequency financial data often exhibit volatility clustering. Versions of functional generalized autoregressive conditionally heteroscedastic (FGARCH) models have recently been proposed to describe such data, however so far basic diagnostic tests for these models are not available. We propose two portmanteau type tests to measure conditional heteroscedasticity in the squares of asset return curves. A complete asymptotic theory is provided for each test. We also show how such tests can be adapted and applied to model residuals to evaluate adequacy, and inform order selection, of FGARCH models. Simulation results show that both tests have good size and power to detect conditional heteroscedasticity and model mis-specification in finite samples. In an application, the tests show that intra-day asset return curves exhibit conditional heteroscedasticity. This conditional heteroscedasticity cannot be explained by the magnitude of inter-daily returns alone, but it can be adequately modeled by an FGARCH(1,1) model
An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution
Producción CientíficaWe solve the Cauchy problem defined by the fractional partial differential
equation [∂tt − κD]u = 0, with D the pseudo-differential Riesz operator of first
order, and certain initial conditions. The
solution of the Cauchy problem resulting from the substitution of the Gaussian pulse
u(x, 0) by the Dirac delta distribution ϕ(x) = μδ(x) is obtained as corollary.MINECO grant MTM2014-57129-C2-1-P
Solving the difference initial-boundary value problems by the operator exponential method
We suggest a modification of the operator exponential method for the
numerical solving the difference linear initial boundary value problems. The
scheme is based on the representation of the difference operator for given
boundary conditions as the perturbation of the same operator for periodic ones.
We analyze the error, stability and efficiency of the scheme for a model
example of the one-dimensional operator of second difference
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