3,550 research outputs found
Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
We study the Hamiltonian formulation of f(R) theories of gravity both in
metric and in Palatini formalism using their classical equivalence with
Brans-Dicke theories with a non-trivial potential. The Palatini case, which
corresponds to the w=-3/2 Brans-Dicke theory, requires special attention
because of new constraints associated with the scalar field, which is
non-dynamical. We derive, compare, and discuss the constraints and evolution
equations for the ww=-3/2 and w\neq -3/2 cases. Based on the properties of the
constraint and evolution equations, we find that, contrary to certain claims in
the literature, the Cauchy problem for the w=-3/2 case is well-formulated and
there is no reason to believe that it is not well-posed in general.Comment: 17 pages, no figure
A Jacobian module for disentanglements and applications to Mond's conjecture
Given a germ of holomorphic map from to ,
we define a module whose dimension over is an upper bound
for the -codimension of , with equality if is weighted
homogeneous. We also define a relative version of the module, for
unfoldings of . The main result is that if are nice
dimensions, then the dimension of over is an upper bound of
the image Milnor number of , with equality if and only if the relative
module is Cohen-Macaulay for some stable unfolding . In particular,
if is Cohen-Macaulay, then we have Mond's conjecture for .
Furthermore, if is quasi-homogeneous, then Mond's conjecture for is
equivalent to the fact that is Cohen-Macaulay. Finally, we observe
that to prove Mond's conjecture, it suffices to prove it in a suitable family
of examples.Comment: 19 page
Geonic black holes and remnants in Eddington-inspired Born-Infeld gravity
We show that electrically charged solutions within the Eddington-inspired
Born-Infeld theory of gravity replace the central singularity by a wormhole
supported by the electric field. As a result, the total energy associated with
the electric field is finite and similar to that found in the Born-Infeld
electromagnetic theory. When a certain charge-to-mass ratio is satisfied, in
the lowest part of the mass and charge spectrum the event horizon disappears
yielding stable remnants. We argue that quantum effects in the matter sector
can lower the mass of these remnants from the Planck scale down to the TeV
scale.Comment: 7 double column pages, 1 figur
A version of the Stone-Weierstrass theorem in fuzzy analysis
Let
C
(
K
,
E
1
)
be the space of continuous functions defined between a compact Hausdorff space
K
and the space of fuzzy
numbers
E
1
endowed with the supremum metric. We provide a set of sufficient conditions on a subspace of
C
(
K
,
E
1
)
in order
that it be dense. We also obtain a similar result for interpolating families of
C
(
K
,
E
1
)
. As a corollary of the above results we prove
that certain fuzzy-number-valued neural networks can approximate any continuous fuzzy-number-valued function defined on
a compact subspace of
R
Completeness, metrizability and compactness in spaces of fuzzy-number-valued functions
Fuzzy-number-valued functions, that is, functions defined on a topological space taking values in the space of fuzzy numbers, play a central role in the development of Fuzzy Analysis. In this paper we study completeness, metrizability and compactness of spaces of continuous fuzzy-number-valued functions
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