Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

ON GENERIC ROTATIONLESS DIFFEOMORPHISMS OF THE ANNULUS

Let f be a C(r)-diffeomorphism of the closed annulus A that preserves the orientation, the boundary components and the Lebesgue measure. Suppose that f has a lift (f) over tilde to the infinite strip (A) over tilde which has zero Lebesgue measure rotation number. If the rotation number of f restricted to both boundary components of (f) over tilde is positive, then for such a generic f (r >= 16), zero is an interior point of its rotation set. This is a partial solution to a conjecture of P. Boyland.

Retention-favorable timing of propagule release in barnacles and periwinkles

Recent studies on the ecology of marine larvae suggest that retention near coastal areas and self-recruitment are probably much more common than previously thought. In light of this, the advective potential of pelagic stages can be partially determined by the timing of propagule release. We sampled the upper-shore levels of a subtropical coastline in southeastern Brazil to examine the temporal patterns of propagule release for the common barnacle Chthamalus bisinuatus and the periwinkle Nodilittorina lineolata. The release timing in both species was very consistent between sites a few kilometers apart. Barnacles released nauplii in a rhythmic pattern, mostly coinciding with neap tides, when the speed of tidal currents was lowest. There was no variation in propagule release in relation to diel or flood-ebb tidal cycles. Periwinkles released propagules in a very irregular pattern, which remarkably matched a time series of wave heights. Egg capsules were released during periods of rough seas, when onshore surface currents were expected to prevail. Eggs were released mostly during ebb tides, and there was no diel variation. Propagule release rhythms are usually viewed as a means to ensure fast offshore advection, thus avoiding presumed hazardous conditions for larvae. However, propagule release strategies in these upper-shore species would more likely contribute to the retention of offspring close to parental stocks.

Justified Fault-Ride-Through Requirements for Wind Turbines in Power Systems

In this paper, a novel adaptive strategy to obtain technically justified fault-ride-through requirements for wind turbines (WTs) is proposed. The main objective is to promote an effective integration of wind turbines into power systems with still low penetration levels of wind power based on technical and economical considerations. The level of requirement imposed by the strategy is increased stepwise over time, depending on system characteristics and on wind power penetration level. The idea behind is to introduce stringent requirements only when they are technically needed for a reliable and secure power system operation. Voltage stability support and fault-ride-through requirements are considered in the strategy. Simulations are based on the Chilean transmission network, a midsize isolated power system with still low penetration levels of wind power. Simulations include fixed speed induction generators and doubly fed induction generators. The effects on power system stability of the wind power injections, integrated into the network by adopting the adaptive strategy, are compared with the effects that have the same installed capacity of wind power but only considering WTs able to fulfill stringent requirements (fault-ride-through capability and support voltage stability). Based on simulations and international experience, technically justified requirements for the Chilean case are proposed.

Er(3+)-doped silica-hafnia films for optical waveguides and spherical resonators

In this paper we present some result on sol-gel derived silica-hafnia systems. In particular we focus on fabrication, morphological and spectroscopic assessment of Er(3+)-activated thin films. Two examples of silica-hafnia-derived waveguiding glass ceramics, prepared by top-down and bottom-up techniques are reported, and the main optical properties are discussed. Finally, some properties of activated microspherical resonators, having a silica core, obtained by melting the end of a telecom fiber, coated with an Er(3+)-doped 70SiO(2)-30HfO(2) film, are presented. (C) 2009 Elsevier B.V. All rights reserved.

Incidence of ipsilateral postoperative deep venous thrombosis in the amputated lower extremity of patients with peripheral obstructive arterial disease

Objective: Patients undergoing amputation of the lower limb due to peripheral arterial disease (PAD) are at risk of developing deep venous thrombosis (DVT). Few studies in the research literature report the incidence of DVT during the early postoperative period or the risk factors for the development of DVT in the amputation stump. This prospective study evaluated the incidence of DVT during the first 35 postoperative days in patients who had undergone amputation of the lower extremity due to PAD and its relation to comorbidities and death. Methods: Between September 2004 and March 2006, 56 patients (29 men), with a mean age of 67.25 years, underwent 62 amputations, comprising 36 below knee amputations (BKA) and 26 above knee amputations (AKA). Echo-Doppler scanning was performed preoperatively and on postoperative days 7 and 31 (approximately). All patients received acetylsalicylic acid (100 mg daily) preoperatively and postoperatively, but none received prophylactic anticoagulation. Results: DVT occurred in 25.8% of extremities with amputations (10 ARA and 6 BKA). The cumulative incidence in the 35-day postoperative period was 28% (Kaplan-Meier). There was a significant difference (P = .04) in the incidence of DVT between AKA (37.5%) and BKA (21.2%). Age >= 70 years (48.9% vs 16.8%, P = .021) was also a risk factor for DVT in the univariate analysis. Of the 16 cases, 14 (87.5%) were diagnosed during outpatient care. The time to discharge after amputation was averaged 6.11 days in-hospital stay (range, 1-56 days). One symptomatic nonfatal pulmonary embolism occurred in a patient already diagnosed with DVT. There was no relation between other comorbidities and DVT. The multivariate analysis showed no association between risk factors and the occurrence of DVT in the amputated extremity. DVT ipsilateral to the amputation did not influence the mortality rate (9.7%). Conclusion: The incidence of DVT in the early postoperative period (<= 35 days) was elevated principally in patients aged >= 70 years and for AKA. Patients with PAD who have recently undergone major amputations should be considered at high risk for DVT, even after hospital discharge. Given the high rate of postoperative DVT observed in this study, we now recommend prophylactic anticoagulation for these patients, but further study is needed to determine the optimal duration and efficacy of this treatment. (J Vasc Surg 2008;48:1514-9.)

Local and remote tissue injury upon intestinal ischemia and reperfusion depends on the TLR/MyD88 signaling pathway

Innate immune responses against microorganisms may be mediated by Toll-like receptors (TLRs). Intestinal ischemia-reperfusion (i-I/R) leads to the translocation of bacteria and/or bacterial products such as endotoxin, which activate TLRs leading to acute intestinal and lung injury and inflammation observed upon gut trauma. Here, we investigated the role of TLR activation by using mice deficient for the common TLR adaptor protein myeloid differentiation factor 88 (MyD88) on local and remote inflammation following intestinal ischemia. Balb/c and MyD88(-/-) mice were subjected to occlusion of the superior mesenteric artery (45 min) followed by intestinal reperfusion (4 h). Acute neutrophil recruitment into the intestinal wall and the lung was significantly diminished in MyD88(-/-) after i-I/R, which was confirmed microscopically. Diminished neutrophil recruitment was accompanied with reduced concentration of TNF-alpha and IL-1 beta level. Furthermore, diminished microvascular leak and bacteremia were associated with enhanced survival of MyD88(-/-) mice. However, neither TNF-alpha nor IL-1 beta neutralization prevented neutrophil recruitment into the lung but attenuated intestinal inflammation upon i-I/R. In conclusion, our data demonstrate that disruption of the TLR/MyD88 pathway in mice attenuates acute intestinal and lung injury, inflammation, and endothelial damage allowing enhanced survival.

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x) = g(1)x(-1) + g(2)x(-2), x is an element of R(+) = [0, infinity). For g(2) > 0 and g(1) < 0, the potential is known as the Kratzer potential V(K)(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein`s method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.