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 K=(±1,0)K = (\pm 1, 0)

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 $K = (-1, 0).$ 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 Rn\mathbb R^n

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 $\mathbb R^n$, 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