Remarks on the convergence of pseudospectra

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has constant resolvent norm on an open set. We extend the class of operators for which it is known that the latter cannot happen by showing that if the resolvent norm is constant on an open set, then this constant is the global minimum. We present a number of examples exhibiting various resolvent norm behaviours and illustrating the applicability of this characterisation compared to known results.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Ten-year results of a three-arm prospective cohort study on implants in periodontally compromised patients. Part 1: implant loss and radiographic bone loss

OBJECTIVES: The aim of this study was to compare the long-term outcomes of implants placed in patients treated for periodontitis periodontally compromised patients (PCP) and in periodontally healthy patients (PHP) in relation to adhesion to supportive periodontal therapy (SPT). MATERIAL AND METHODS: One hundred and twelve partially edentulous patients were consecutively enrolled in private specialist practice and divided into three groups according to their initial periodontal condition: PHP, moderate PCP and severe PCP. Perio and implant treatment was carried out as needed. Solid screws (S), hollow screws (HS) and hollow cylinders (HC) were installed to support fixed prostheses, after successful completion of initial periodontal therapy (full-mouth plaque score <25% and full-mouth bleeding score <25%). At the end of treatment, patients were asked to follow an individualized SPT program. At 10 years, clinical measures and radiographic bone changes were recorded by two calibrated operators, blinded to the initial patient classification. RESULTS: Eleven patients were lost to follow-up. During the period of observation, 18 implants were removed because of biological complications. The implant survival rate was 96.6%, 92.8% and 90% for all implants and 98%, 94.2% and 90% for S-implants only, respectively, for PHP, moderate PCP and severe PCP. The mean bone loss was 0.75 (+/- 0.88) mm in PHP, 1.14 (+/- 1.11) mm in moderate PCP and 0.98 (+/- 1.22) mm in severe PCP, without any statistically significant difference. The percentage of sites, with bone loss > or =3 mm, was, respectively, 4.7% for PHP, 11.2% for moderate PCP and 15.1% for severe PCP, with a statistically significant difference between PHP and severe PCP (P<0.05). Lack of adhesion to SPT was correlated with a higher incidence of bone loss and implant loss. CONCLUSION: Patients with a history of periodontitis presented a lower survival rate and a statistically significantly higher number of sites with peri-implant bone loss. Furthermore, PCP, who did not completely adhere to the SPT, were found to present a higher implant failure rate. This underlines the value of the SPT in enhancing the long-term outcomes of implant therapy, particularly in subjects affected by periodontitis, in order to control reinfection and limit biological complications.

Operator variability using different polishing methods and surface geometry of a nanohybrid composite

This study evaluated the operator variability of different finishing and polishing techniques. After placing 120 composite restorations (Tetric EvoCeram) in plexiglassmolds, the surface of the specimens was roughened in a standardized manner. Twelve operators with different experience levels polished the specimens using the following finishing/polishing procedures: method 1 (40 ?m diamond [40D], 15 ?m diamond [15D], 42 ?m silicon carbide polisher [42S], 6 ?m silicon carbide polisher [6S] and Occlubrush [O]); method 2 (40D, 42S, 6S and O); method 3 (40D, 42S, 6S and PoGo); method 4 (40D, 42S and PoGo) and method 5 (40D, 42S and O). The mean surface roughness (Ra) was measured with a profilometer. Differences between the methods were analyzed with non-parametric ANOVA and pairwise Wilcoxon signed rank tests (?=0.05). All the restorations were qualitatively assessed using SEM. Methods 3 and 4 showed the best polishing results and method 5 demonstrated the poorest. Method 5 was also most dependent on the skills of the operator. Except for method 5, all of the tested procedures reached a clinically acceptable surface polish of Ra?0.2 ?m. Polishing procedures can be simplified without increasing variability between operators and without jeopardizing polishing results.

Relevance of In-vitro Tests of Adhesive and Composite Dental Materials. A Review in 3 Parts. Part 2: Non-standardized tests of composite materials

Summary The first part of this review examined ISO approval requirements and in vitro testing. In the second part, non-standardized test methods for composite materials are presented and discussed. Physical tests are primarily described. Analyses of surface gloss and alterations, as well as aging simulations of dental materials are presented. Again, the importance of laboratory tests in determining clinical outcomes is evaluated. Differences in the measurement protocols of the various testing institutes and how these differences can in?uence the results are also discussed. Because there is no standardization of test protocols, the values determined by different institutes cannot be directly compared. However, the ranking of the tested materials should be the same if a valid protocol is applied by different institutes. The modulus of elasticity, the expansion after water sorption, and the polishability of the material are all clinically relevant, whereas factors measured by other test protocols may have no clinical correlation. The handling properties of the materials are highly dependent on operators' preferences. Therefore, no standard values can be given.

Central venous catheter integrity during mechanical power injection of iodinated contrast medium

PURPOSE: To evaluate a widely used nontunneled triple-lumen central venous catheter in order to determine whether the largest of the three lumina (16 gauge) can tolerate high flow rates, such as those required for computed tomographic angiography. MATERIALS AND METHODS: Forty-two catheters were tested in vitro, including 10 new and 32 used catheters (median indwelling time, 5 days). Injection pressures were continuously monitored at the site of the 16-gauge central venous catheter hub. Catheters were injected with 300 and 370 mg of iodine per milliliter of iopamidol by using a mechanical injector at increasing flow rates until the catheter failed. The infusion rate, hub pressure, and location were documented for each failure event. The catheter pressures generated during hand injection by five operators were also analyzed. Mean flow rates and pressures at failure were compared by means of two-tailed Student t test, with differences considered significant at P < .05. RESULTS: Injections of iopamidol with 370 mg of iodine per milliliter generate more pressure than injections of iopamidol with 300 mg of iodine per milliliter at the same injection rate. All catheters failed in the tubing external to the patient. The lowest flow rate at which catheter failure occurred was 9 mL/sec. The lowest hub pressure at failure was 262 pounds per square inch gauge (psig) for new and 213 psig for used catheters. Hand injection of iopamidol with 300 mg of iodine per milliliter generated peak hub pressures ranging from 35 to 72 psig, corresponding to flow rates ranging from 2.5 to 5.0 mL/sec. CONCLUSION: Indwelling use has an effect on catheter material property, but even for used catheters there is a substantial safety margin for power injection with the particular triple-lumen central venous catheter tested in this study, as the manufacturer's recommendation for maximum pressure is 15 psig.