Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

Near threshold vibrational excitation of molecules by positron impact: A projection operator approach

We report vibrational excitation (v(i) = 0 -> v(f) = 1) cross-sections for positron scattering by H(2) and model calculations for the (v(i) = 0 -> v(f) = 1) excitation of the C-C symmetric stretch mode of C(2)H(2). The Feshbach projection operator formalism was employed to vibrationally resolve the fixed-nuclei phase shifts obtained with the Schwinger multichannel method. The near threshold behavior of H(2) and C(2)H(2) significantly differ in the sense that no low lying singularity (either virtual or bound state) was found for the former, while a e(+)-acetylene virtual state was found at the equilibrium geometry (this virtual state becomes a bound state upon stretching the molecule). For C(2)H(2), we also performed model calculations comparing excitation cross-sections arising from virtual (-i kappa(0)) and bound (+i kappa(0)) states symmetrically located around the origin of the complex momentum plane (i.e. having the same kappa(0)). The virtual state is seen to significantly couple to vibrations, and similar cross-sections were obtained for shallow bound and virtual states. (c) 2007 Elsevier B.V. All rights reserved.

Estimating losses in an entanglement concentration scheme using the phenomenological operator approach to dissipation in cavity quantum electrodynamics

In a previous paper, we developed a phenomenological-operator technique aiming to simplify the estimate of losses due to dissipation in cavity quantum electrodynamics. In this paper, we apply that technique to estimate losses during an entanglement concentration process in the context of dissipative cavities. In addition, some results, previously used without proof to justify our phenomenological-operator approach, are now formally derived, including an equivalent way to formulate the Wigner-Weisskopf approximation.

An Information Theory framework for two-stage binary image operator design

The design of translation invariant and locally defined binary image operators over large windows is made difficult by decreased statistical precision and increased training time. We present a complete framework for the application of stacked design, a recently proposed technique to create two-stage operators that circumvents that difficulty. We propose a novel algorithm, based on Information Theory, to find groups of pixels that should be used together to predict the Output Value. We employ this algorithm to automate the process of creating a set of first-level operators that are later combined in a global operator. We also propose a principled way to guide this combination, by using feature selection and model comparison. Experimental results Show that the proposed framework leads to better results than single stage design. (C) 2009 Elsevier B.V. All rights reserved.

An eigenvalue problem for the biharmonic operator on Z(2)-symmetric regions

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set Of Z(2)-symmetric regions of R-n, n >= 2, with a suitable topology. To accomplish this, we combine Baire`s lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225-241].

What aspects of rehabilitation provision contribute to self-reported met needs for rehabilitation one year after stroke - amount, place, operator or timing?

BACKGROUND AND OBJECTIVE: To a large extent, people who have suffered a stroke report unmet needs for rehabilitation. The purpose of this study was to explore aspects of rehabilitation provision that potentially contribute to self-reported met needs for rehabilitation 12 months after stroke with consideration also to severity of stroke. METHODS: The participants (n = 173) received care at the stroke units at the Karolinska University Hospital, Sweden. Using a questionnaire, the dependent variable, self-reported met needs for rehabilitation, was collected at 12 months after stroke. The independent variables were four aspects of rehabilitation provision based on data retrieved from registers and structured according to four aspects: amount of rehabilitation, service level (day care rehabilitation, primary care rehabilitation and home-based rehabilitation), operator level (physiotherapist, occupational therapist, speech therapist) and time after stroke onset. Multivariate logistic regression analyses regarding the aspects of rehabilitation were performed for the participants who were divided into three groups based on stroke severity at onset. RESULTS: Participants with moderate/severe stroke who had seen a physiotherapist at least once during each of the 1st, 2nd and 3rd-4th quarters of the first year (OR 8.36, CI 1.40-49.88 P = 0.020) were more likely to report met rehabilitation needs. CONCLUSION: For people with moderate/severe stroke, continuity in rehabilitation (preferably physiotherapy) during the first year after stroke seems to be associated with self-reported met needs for rehabilitation.

Bi-Lipschitz A-triviality of map germs and Newton filtrations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V

In this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours.

On the entropy operator for the general SU(1,1) TFD formulation

In this Letter, an entropy operator for the general unitary SU(1, 1) TFD formulation is proposed and used to lead a bosonic system from zero to finite temperature. Namely, considering the closed bosonic string as the target system, the entropy operator is used to construct the thermal vacuum. The behaviour of such a state under the breve conjugation rules is analyzed and it was shown that the breve conjugation does not affect the thermal effects. From this thermal vacuum the thermal energy, the entropy and the free energy of the closed bosonic string are calculated and the appropriated thermal distribution for the system is found after the free energy minimization. (C) 2004 Elsevier B.V. All rights reserved.

Massive superstring vertex operator in D=10 superspace

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincare covariant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields.

Entanglement and entropy operator for strings in pp-wave time dependent background

In this Letter new aspects of string theory propagating in a pp-wave time dependent background with a null singularity are explored. It is shown the appearance of a 2d entanglement entropy dynamically generated by the background. For asymptotically flat observers, the vacuum close to the singularity is unitarily inequivalent to the vacuum at tau = -infinity and it is shown that the 2d entanglement entropy diverges close to this point. As a consequence. The positive time region is inaccessible for observers in tau = -infinity. For a stationary measure, the vacuum at finite time is seen by those observers as a thermal state and the information loss is encoded as a heat bath of string states. (c) 2006 Elsevier B.V. All rights reserved.