5,543 research outputs found
Essential spectrum of local multi-trace boundary integral operators
Considering pure transmission scattering problems in piecewise constant
media, we derive an exact analytic formula for the spectrum of the
corresponding local multi-trace boundary integral operators in the case where
the geometrical configuration does not involve any junction point and all wave
numbers equal. We deduce from this the essential spectrum in the case where
wave numbers vary. Numerical evidences of these theoretical results are also
presented
Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with
We show that the dragging of the axis directions of local inertial frames by
a weighted average of the energy currents in the universe is exact for all
linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K =
(+1, -1, 0) and of Einstein's static closed universe. This includes FRW
universes which are arbitrarily close to the Milne Universe, which is empty,
and to the de Sitter universe. Hence the postulate formulated by E. Mach about
the physical cause for the time-evolution of the axis directions of inertial
frames is shown to hold in cosmological General Relativity for linear
perturbations. The time-evolution of axis directions of local inertial frames
(relative to given local fiducial axes) is given experimentally by the
precession angular velocity of gyroscopes, which in turn is given by the
operational definition of the gravitomagnetic field. The gravitomagnetic field
is caused by cosmological energy currents via the momentum constraint. This
equation for cosmological gravitomagnetism is analogous to Ampere's law, but it
holds also for time-dependent situtations. In the solution for an open universe
the 1/r^2-force of Ampere is replaced by a Yukawa force which is of identical
form for FRW backgrounds with The scale of the exponential
cutoff is the H-dot radius, where H is the Hubble rate, and dot is the
derivative with respect to cosmic time. Analogous results hold for energy
currents in a closed FRW universe, K = +1, and in Einstein's closed static
universe.Comment: 23 pages, no figures. Final published version. Additional material in
Secs. I.A, I.J, III, V.H. Additional reference
A streamlined proof of the convergence of the Taylor tower for embeddings in
Manifold calculus of functors has in recent years been successfully used in
the study of the topology of various spaces of embeddings of one manifold in
another. Given a space of embeddings, the theory produces a Taylor tower whose
purpose is to approximate this space in a suitable sense. Central to the story
are deep theorems about the convergence of this tower. We provide an exposition
of the convergence results in the special case of embeddings into , which has been the case of primary interest in applications. We try to
use as little machinery as possible and give several improvements and
restatements of existing arguments used in the proofs of the main results.Comment: Minor changes, final versio
An interactive semantics of logic programming
We apply to logic programming some recently emerging ideas from the field of
reduction-based communicating systems, with the aim of giving evidence of the
hidden interactions and the coordination mechanisms that rule the operational
machinery of such a programming paradigm. The semantic framework we have chosen
for presenting our results is tile logic, which has the advantage of allowing a
uniform treatment of goals and observations and of applying abstract
categorical tools for proving the results. As main contributions, we mention
the finitary presentation of abstract unification, and a concurrent and
coordinated abstract semantics consistent with the most common semantics of
logic programming. Moreover, the compositionality of the tile semantics is
guaranteed by standard results, as it reduces to check that the tile systems
associated to logic programs enjoy the tile decomposition property. An
extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory
and Practice of Logic Programmin
Metric on the space of quantum states from relative entropy. Tomographic reconstruction
In the framework of quantum information geometry, we derive, from quantum
relative Tsallis entropy, a family of quantum metrics on the space of full
rank, N level quantum states, by means of a suitably defined coordinate free
differential calculus. The cases N = 2, N = 3 are discussed in detail and
notable limits are analyzed. The radial limit procedure has been used to
recover quantum metrics for lower rank states, such as pure states. By using
the tomographic picture of quantum mechanics we have obtained the Fisher- Rao
metric for the space of quantum tomograms and derived a reconstruction formula
of the quantum metric of density states out of the tomographic one. A new
inequality obtained for probabilities of three spin-1/2 projections in three
perpendicular directions is proposed to be checked in experiments with
superconducting circuits.Comment: 31 pages. No figures. Abstract and Introduction rewritten. Minor
corrections. References adde
On an Intuitionistic Logic for Pragmatics
We reconsider the pragmatic interpretation of intuitionistic logic [21]
regarded as a logic of assertions and their justications and its relations with classical
logic. We recall an extension of this approach to a logic dealing with assertions
and obligations, related by a notion of causal implication [14, 45]. We focus on
the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on
polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the
S4 modal translation, we give a denition of a system AHL of bi-intuitionistic logic
that correctly represents the duality between intuitionistic and co-intuitionistic logic,
correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism
as a distributed calculus of coroutines is then used to give an operational
interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear
calculus of co-intuitionistic coroutines is dened and a probabilistic interpretation
of linear co-intuitionism is given as in [9]. Also we remark that by extending the
language of intuitionistic logic we can express the notion of expectation, an assertion
that in all situations the truth of p is possible and that in a logic of expectations
the law of double negation holds. Similarly, extending co-intuitionistic logic, we can
express the notion of conjecture that p, dened as a hypothesis that in some situation
the truth of p is epistemically necessary
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