A Topological Separation Condition for Fractal Attractors

We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundant on every level. In general this separation condition is weaker than the strong open set condition and is not equivalent to the weak separation property. We prove that this separation condition is equivalent to the strong Markov property (see definition below). We also show that the set of $N$-tuples of contractive homeomorphisms, which are non-redundant on every level, is a $G_\delta$ set in the topology of pointwise convergence of every component mapping with an additional requirement that the supremum of contraction coefficients of mappings be strictly less than one. We give several sufficient conditions for this separation property. For every fixed $N$-tuple of $d\times d$ invertible contraction matrices from a certain class, we obtain density results for $N$-tuples of fixed points which define $N$-tuples of mappings non-redundant on every level.Comment: 19 page

On a two variable class of Bernstein-Szego measures

The one variable Bernstein-Szego theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.Comment: minor change

The PreAmplifier ShAper for the ALICE TPC-Detector

In this paper the PreAmplifier ShAper (PASA) for the Time Projection Chamber (TPC) of the ALICE experiment at LHC is presented. The ALICE TPC PASA is an ASIC that integrates 16 identical channels, each consisting of Charge Sensitive Amplifiers (CSA) followed by a Pole-Zero network, self-adaptive bias network, two second-order bridged-T filters, two non-inverting level shifters and a start-up circuit. The circuit is optimized for a detector capacitance of 18-25 pF. For an input capacitance of 25 pF, the PASA features a conversion gain of 12.74 mV/fC, a peaking time of 160 ns, a FWHM of 190 ns, a power consumption of 11.65 mW/ch and an equivalent noise charge of 244e + 17e/pF. The circuit recovers smoothly to the baseline in about 600 ns. An integral non-linearity of 0.19% with an output swing of about 2.1 V is also achieved. The total area of the chip is 18 mm$^2$ and is implemented in AMS's C35B3C1 0.35 micron CMOS technology. Detailed characterization test were performed on about 48000 PASA circuits before mounting them on the ALICE TPC front-end cards. After more than two years of operation of the ALICE TPC with p-p and Pb-Pb collisions, the PASA has demonstrated to fulfill all requirements

Clinical Mortality in a Large COVID-19 Cohort: Observational Study.

BACKGROUND: Northwell Health, an integrated health system in New York, has treated more than 15,000 inpatients with COVID-19 at the US epicenter of the SARS-CoV-2 pandemic. OBJECTIVE: We describe the demographic characteristics of patients who died of COVID-19, observation of frequent rapid response team/cardiac arrest (RRT/CA) calls for non-intensive care unit (ICU) patients, and factors that contributed to RRT/CA calls. METHODS: A team of registered nurses reviewed the medical records of inpatients who tested positive for SARS-CoV-2 via polymerase chain reaction before or on admission and who died between March 13 (first Northwell Health inpatient expiration) and April 30, 2020, at 15 Northwell Health hospitals. The findings for these patients were abstracted into a database and statistically analyzed. RESULTS: Of 2634 patients who died of COVID-19, 1478 (56.1%) had oxygen saturation levels ≥90% on presentation and required no respiratory support. At least one RRT/CA was called on 1112/2634 patients (42.2%) at a non-ICU level of care. Before the RRT/CA call, the most recent oxygen saturation levels for 852/1112 (76.6%) of these non-ICU patients were at least 90%. At the time the RRT/CA was called, 479/1112 patients (43.1%) had an oxygen saturation of \u3c80%. CONCLUSIONS: This study represents one of the largest reviewed cohorts of mortality that also captures data in nonstructured fields. Approximately 50% of deaths occurred at a non-ICU level of care despite admission to the appropriate care setting with normal staffing. The data imply a sudden, unexpected deterioration in respiratory status requiring RRT/CA in a large number of non-ICU patients. Patients admitted at a non-ICU level of care suffered rapid clinical deterioration, often with a sudden decrease in oxygen saturation. These patients could benefit from additional monitoring (eg, continuous central oxygenation saturation), although this approach warrants further study

Two variable orthogonal polynomials on the bicircle and structured matrices

Review of Scientific Instruments, 78(11): pp. 796–825.We consider bivariate polynomials orthogonal on the bicircle with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between the polynomials of different degrees. These formulas link the orthogonal polynomials constructed using the lexicographical ordering with those constructed using the reverse lexicographical ordering. Relations between the coefficients in the recurrence formulas are derived and used to give necessary and sufficient conditions for the existence of a positive linear functional. These results are then used to construct a class of two variable measures supported on the bicircle that are given by one over the magnitude squared of a stable polynomial. Applications to Fej´er–Riesz factorization are also given

A Search for Variation in the H_2O Ortho-Para Ratio and Rotational Temperature in the Inner Coma of Comet C/2004 Q2 (Machholz)

We present spatially resolved measurements of the rotational temperature and ortho-para ratio for H_2O in the inner coma of the Oort Cloud comet C/2004 Q2 (Machholz). Our results are based on direct simultaneous detections of ortho-H_2O and para-H_2O via "hot-band" fluorescence near 2.9 μm. We find a well-defined decline in rotational temperature with increasing nucleocentric distance (up to ~1000 km). The ortho-para ratio remains constant (within stochastic uncertainty) with increasing nucleocentric distance and is close to the statistical equilibrium value of 3.0 (2.86 ± 0.06 [0.17], including, respectively, stochastic [systematic] uncertainty), resulting in spin temperature T_(spin) ≥ 34 K. We compare the present results with those reported for other comets and discuss the difficulties in interpreting spin temperatures deduced from measured ortho-para ratios. Improved understanding of the special conditions that enable nuclear spin conversion would test the extent to which derived spin temperatures reflect the formative history or the processing record of cometary ices

Moment determinants as isomonodromic tau functions

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann-Hilbert problem associated to certain classes of (multiple) orthogonal polynomials. The determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants appear also as partition functions of random matrix models, including an instance of a two-matrix model.Comment: 24 page