Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

Projection of primary and revision hip arthroplasty surgery in Denmark from 2020 to 2050

BACKGROUND AND PURPOSE: The incidence of primary and revision total hip arthroplasty (THA) has increased over the last decades. Previous forecasts from different healthcare systems have predicted a continuous increase. We present a forecast of both primary and revision surgery from 2020 to 2050 based on 25 years data from the healthcare system in Denmark. PATIENTS AND METHODS: We retrieved data from the Danish Hip Arthroplasty Register on 198,835 primary and 29,456 revision surgeries. Historical censuses and population forecasts were retrieved from Statistics Denmark. Logistic and Gompertz regression analysis was used to forecast incidence rates (IR) and total numbers in the next 30 years. RESULTS: Our forecast predicts an increase in IR of 3–9% and an increase in total numbers of primary THA of between 12% and 19% in 2050. For revision THA the IRs have reached a plateau but total numbers are predicted to increase by 19% in 2050. CONCLUSION: Our forecast shows that both primary and revision THA will increase in total numbers in the next decades, but the IR for primary THA is near its plateau and for revision THA the plateau has already been reached. The forecast may aid in healthcare resource planning for the decades to come

Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports

We demonstrate a new class of hollow-core Bragg fibers that are composed of concentric cylindrical silica rings separated by nanoscale support bridges. We theoretically predict and experimentally observe hollow-core confinement over an octave frequency range. The bandwidth of bandgap guiding in this new class of Bragg fibers exceeds that of other hollow-core fibers reported in the literature. With only three rings of silica cladding layers, these Bragg fibers achieve propagation loss of the order of 1 dB/m.Comment: 9 pages including 5 figure

Supercooled Liquid Dynamics Studied via Shear-Mechanical Spectroscopy

We report dynamical shear-modulus measurements for five glass-forming liquids (pentaphenyl trimethyl trisiloxane, diethyl phthalate, dibutyl phthalate, 1,2-propanediol, and m-touluidine). The shear-mechanical spectra are obtained by the piezoelectric shear-modulus gauge (PSG) method. This technique allows one to measure the shear modulus ($10^{5} -10^{10}$ Pa) of the liquid within a frequency range from 1 mHz to 10 kHz. We analyze the frequency-dependent response functions to investigate whether time-temperature superposition (TTS) is obeyed. We also study the shear-modulus loss-peak position and its high-frequency part. It has been suggested that when TTS applies, the high-frequency side of the imaginary part of the dielectric response decreases like a power law of the frequency with an exponent -1/2. This conjecture is analyzed on the basis of the shear mechanical data. We find that TTS is obeyed for pentaphenyl trimethyl trisiloxane and in 1,2-propanediol while in the remaining liquids evidence of a mechanical $\beta$ process is found. Although the the high-frequency power law behavior $\omega^{-\alpha}$ of the shear-loss may approach a limiting value of $\alpha=0.5$ when lowering the temperature, we find that the exponent lies systematically above this value (around 0.4). For the two liquids without beta relaxation (pentaphenyl trimethyl trisiloxane and 1,2-propanediol) we also test the shoving model prediction, according to which the the relaxation-time activation energy is proportional to the instantaneous shear modulus. We find that the data are well described by this model.Comment: 7 pages, 6 figure

Diagnostic stability among chronic patients with functional psychoses: an epidemiological and clinical study

<p>Abstract</p> <p>Background</p> <p>Diagnostic stability and illness course of chronic non-organic psychoses are complex phenomena and only few risk factors or predictors are known that can be used reliably. This study investigates the diagnostic stability during the entire course of illness in patients with non-organic psychoses and attempts to identify non-psychopathological risk factors or predictors.</p> <p>Method</p> <p>100 patients with functional psychosis were initially characterised using the Operational Criteria Checklist for Psychotic Illness and Affective Illness (OPCRIT), medical records and health registers. To study the stability of diagnoses (i.e. shifts per time), we used registry data to define four measures of diagnostic variation that were subsequently examined in relation to four possible measures of time (i.e. observation periods or hospitalisation events). Afterwards, we identified putative co-variables and predictors of the best measures of diagnostic stability.</p> <p>Results</p> <p>All four measures of diagnostic variation are very strongly associated with numbers-of-hospitalisations and less so with duration-of-illness, duration-of-hospitalisation and with year-of-first-admission. The four measures of diagnostic variation corrected for numbers-of-hospitalisations were therefore used to study the diagnostic stability. Conventional predictors of illness course – e.g. age-of-onset and premorbid-functioning – are not significantly associated with stability. Only somatic-comorbidity is significantly associated with two measures of stability, while family-history-of-psychiatric-illness and global-assessment-of-functioning (GAF) scale score show a trend. However, the traditional variables age-of-first-admission, civil-status, first-diagnosis-being-schizophrenia and somatic-comorbidity are able to explain two-fifth of the variation in numbers-of-hospitalisations.</p> <p>Conclusion</p> <p>Diagnostic stability is closely linked with the contact between patient and the healthcare system. This could very likely be due to fluctuation of disease manifestation over time or presence of co-morbid psychiatric illness in combination with rigid diagnostic criteria that are unable to capture the multiple psychopathologies of the functional psychoses that results in differential diagnoses and therefore diagnostic instability. Not surprisingly, somatic-comorbidity was found to be a predictor of diagnostic variation thereby being a non-psychiatric confounder.</p