Operators that are points of spectral continuity,II

This paper continues an earlier study of those bounded operators on a Hilbert space at which the spectrum is continuous, where the spectrum is considered as a function whose domain is the set of all bounded operators furnished with the norm topology and whose range is the collection of compact subsets of the complex plane furnished with the Hausdorff metric. In this paper the points of continuity of the essential spectrum, the approximate point spectrum, and certain related subsets of the spectrum are characterized.The first author was supported by National Science Foundation Grant MCS 77-28396.     

The median procedure in cluster analysis and social choice theory

Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed.     

Two-step melting in two dimensions: first-order liquid-hexatic transition

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte?Carlo algorithm allows us to thermalize systems large enough to access the thermodynamic regime. We show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research.     

Optimal branching asymmetry of hydrodynamic pulsatile trees

Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow, as it is the case for mammalian respiration. We report here that introducing a systematic branching asymmetry allows the tree to reduce the average delivery time of the products. It simultaneously increases its robustness against the inevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to match the asymmetry measured in the human lung. This could indicate that the structure is tuned at the maximum asymmetry level that allows the lung to feed all terminal units with fresh air.     

Laryngostroboscopic Evaluation After Supracricoid Partial Laryngectomy

BACKGROUND: Supracricoid partial laryngectomy (SCPL) results in laryngeal preservation in more than 95% of patients with T2 glottic carcinoma. Postsurgical glottic function is characterized by an absence of vocal cords, and phonation quality is a key post-SCPL quality-of-life factor. OBJECTIVE: This investigation was designed to enhance post-SCPL vocal function, study anatomic function of the post-SCPL larynx, and correlate anatomic findings with perceptual and instrumented measurements of voice. METHOD: Twenty-five patients were included. All had undergone SCPL with cricoepiglottopexy for T2 glottic carcinoma. All patients were evaluated by laryngostroboscopic examination, voice sample recording, and instrumented voice analysis with the aim of gaining further insight into postoperative larynx function. Laryngostroboscopic parameters such as laryngeal occlusion, epiglottic length, arytenoid movement, and vibratory area were assessed. The perceptual evaluation was based on the GRBAS scale. Acoustic and aerodynamic parameters were recorded, including fundamental frequency (F0), intensity, jitter, shimmer, signal-to-noise ratio (SNR), oral airflow (OAF), maximum phonation time (MPT), and estimated subglottic pressure (ESGP). Nonparametric tests were used to compare laryngostroboscopic parameters with instrumented measurements and perceptual evaluations of voice quality. RESULTS: Correlations were established among occlusion, epiglottic length, and general grade of dysphonia. Oral air flow (P = 0.006) was found to be correlated with occlusion. Voice roughness was correlated with the presence of a clearly identifiable vibratory area (P = 0.003), whereas these vibratory areas were correlated with shimmer (P = 0.041), OAF (P = 0.001), and SNR (P = 0.001). The number of preserved arytenoids was not identified as a voice quality factor (P = 0.423). CONCLUSION: This study highlighted correlations between the laryngostroboscopic examination results and the perceptive and instrumented measurements of voice. Glottis occlusion and epiglottis length were found to be key factors for postoperative voice quality. These results should help to advance technical development on surgical techniques to enhance voice results.     

The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Ultrafast laser excitation of CO/Pt(111) probed by sum frequency generation: coverage dependent desorption efficiency

CO photodesorption from Pt(111) induced by femtosecond laser pulses is probed by IR+visible sum frequency generation (SFG). Steady state analysis of SFG spectra at varying CO pressure and laser fluence allows one to measure a approximately 5 orders of magnitude decrease of the photodesorption rate constant when CO coverage decreases from 0.37 to 0.07 monolayer. We ascribe this effect in the framework of the Menzel-Gomer-Redhead mechanism to electron delocalization in the CO layer. The lifetime of electronic excitation decreases when coverage decreases.     

Photothermal microanalysis of thermal discontinuities in metallic samples

Modeling the behavior of a protective coating during a thermal shock not only requires the knowledge of its own thermophysical characteristics, but also those of the coating–substrate discontinuity. According to its nature, this discontinuity can be modeled as a zero-thickness interface (thermal contact resistance) or a finite thickness layer (thermal third body). This paper presents an experimental device and two associated thermal transfer models developed in view of the microscale characterization of such discontinuities.