Denominator Values Research Articles

A method for directly finding the denominator values of rational interpolants

In this paper, we give an algorithm for directly finding the denominator values of rational interpolants at the nodes, and present an expression for the corresponding rational interpolant when the latter exists. With these denominator values, our method also provides information concerning the existence of the interpolant and the presence of unattainable points and poles.

Constant denominator perturbative schemes and the partitioning technique

AbstractWith the aid of Löwdin's partitioning theory, an infinite series for the eigenvalue of the Schrödinger equation is derived which does not contain energy differences in denominators. The resulting formulae are compared to those of constant denominator methods, such as perturbation theory within the Unsøld approximation and the connected moment expansion (CMX). The Unsøld formulae are easily obtained from partitioning theory by a suitable choice of the zero order Hamiltonian. Optimizing the value of the energy denominator using the first order wave function in a size‐consistent way, the third order Unsøld correction vanishes, and the corresponding energy correction formula of the CMX is recovered at the second order. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Profiles of hepatic and dysrhythmic cardiovascular events following use of fluoroquinolone antibacterials: experience from large cohorts from the Drug Safety Research Unit Prescription-Event Monitoring database.

To investigate how frequently serious dysrhythmic cardiovascular, and hepatotoxic events are reported during routine clinical use of fluoroquinolones (quinolones) in general practice. Cohorts prescribed quinolones (cohort sizes: ciprofloxacin 11 477; enoxacin 2790; ofloxacin 11 033 and norfloxacin 11 110; mean age in each cohort of 48.6 to 57.0 years) were selected from the Drug Safety Research Unit's Prescription-Event Monitoring (PEM) database. The monitoring periods were November 1988 to January 1989 for ciprofloxacin; April 1989 to January 1991 for enoxacin; May 1991 to December 1991 for ofloxacin and October 1990 to October 1991 for norfloxacin. Data collected over the total PEM surveillance period on selected gastrointestinal events were extracted and reviewed to identify possible hepatic events, together with selected cardiovascular events associated with dysrhythmias. For each quinolone, times to onset of the event and patient-months of observation (denominator values) were calculated. The analysis was based on two observation periods: rate of event during the first 7 days following dispensing of a prescription for each drug (W(1)), and rate of event during the second to sixth week inclusive (W(2)). Scrutiny of original green forms revealed no evidence of drug-induced hepatic dysfunction within 42 days of drug administration for any of the quinolones monitored. No evidence was found of drug-induced dysrhythmic events associated with enoxacin within 42 days of drug administration. Of the other quinolones, 'atrial fibrillation' was reported most often within 42 days following ciprofloxacin administration, with no change in event rate over that time, crude relative risk (CRR)[W(1)/W(2)] 1.0 [95% confidence interval (CI) 0.02 to 8.92]. Other less serious events associated with dysrhythmia were reported with varying incidence within 42 days of quinolone administration. The crude rate of palpitation did not change significantly over that time for ciprofloxacin, ofloxacin and norfloxacin: CRR 0.83 (95% CI 0.02 to 6.86), 2.00 (95% CI 0.19 to 12.20) and 4.99 (95% CI 0.06 to 391.94), respectively. Syncope and tachycardia were also reported for ofloxacin [CRR 9.99 (95% CI 0.52 to 589.49 for both events)] and ciprofloxacin [1.0 (95% CI 0.02, 8.92)] and 2.50 (95% CI 0.04, 47.96) for syncope and tachycardia, respectively]. It cannot be ruled out that some rare hepatic and dysrhythmic events associated with quinolones may be drug related. The primary purpose of PEM is signal generation. Compared with the other quinolones, ciprofloxacin was associated with the highest number of reports of dysrhythmic cardiovascular events occurring within 42 days of administration. This requires further investigation by other types of epidemiological study.

Standard-target calibration of broadband sonars

The object of a standard-target calibration is specification of the overall frequency response function of the system. In terms of the transmit and receive signal spectra ST and SR, standard-target far-field form function F, and two-way acoustic path loss P for an on-axis far-field calibration; the frequency response function is H=SR/(STFP), where each of the displayed functions is frequency-dependent. In practice, a broadband calibration may be hindered by (1) a vanishing denominator value, causing a divergence in H, or (2) a small numerator value or large denominator value, effectively amplifying the influence of noise. The general solution to these problems is to use multiple dissimilar targets to be able to avoid extrema in F, change the transmit signal waveform to avoid nulls in ST, and ensure that the signal-to-noise ratio is high over the frequency band of interest. The near-field case can be addressed by adjusting the target range. Given these measures, the standard-target technique demonstrated by Dragonette et al. [J. Acoust. Soc. Am. 69, 1186–1189 (1981)] for scattering measurements may be rendered into general practice for active broadband sonars.

Undulatory variation of antiferromagnetic strength with magnetic field based on the Hubbard-model Hamiltonian

Using the Hubbard model Hamiltonian in a mean field level, we examine the variation of antiferromagnetic strength with applied magnetic field. It is demonstrated that minima in the antiferromagnetic strength exist at the the even integer denominator values of rational number for magnetic flux per plaquette. The undulatory behavior of antiferromagnetic strength with the external magnetic field is found. It is seen to be related to the undulatory net statistical phase owing to the influence of the applied magnetic field.

Calibration Coefficients Added to ROSESIM Improve Predictions of Growth in Greenhouse Conditions

Growth predictions derived from data collected in controlled-environment chambers would be expected to differ from growth responses observed in variable greenhouse conditions. ROSESIM was developed as a dynamic plant growth model based on `Royalty' rose (Rosa hybrida L.) response to 15 unique treatment combinations of photosynthetic photon flux (PPF), day temperature (DT), and night temperature (NT) under constant growth chamber conditions. Regression coefficients for growth equations are read from an external ASCII file, thus permitting coefficients up to a full quadratic model form. Calibration coefficients (CC) were added to ROSESIM to enable predictions to be altered proportionally to permit improved prediction of specific growth characteristics. Numerator and denominator values for CC are adjustable for the first 10 days (initial) growth equations, subsequent growth until anthesis equations, and for the prediction of anthesis. Validation studies were used to set CC values; this enables the model based on growth in controlled environment chambers to be systematically calibrated on site to fit actual growth measured at a specific greenhouse location.

A Hubbard model study of antiferromagnetic ground states as a function of external magnetic field

The effect of magnetic field on the two-dimensional square lattice of the antiferromagnetically ordered state is examined by using the Hubbard model Hamiltonian in a mean-field level. We examine the variation of antiferromagnetic strength at half-filling with the external magnetic field φ. It is found that local minima in the antiferromagnetic strength exist at even denominator values of φ = p/ q, that is 1 2 , 3 8 , 1 4 , 1 8 .

The adaptation of Pearce element ratio diagrams to complex high silica systems

Pearce element ratios (PERs, of Pearce 1968) express geochemical data in a form where variations in absolute compositions of an igneous suite can be evaluated. Generally the denominator value in the ratio is taken as a major element abundance, but it is argued here that Zr provides a more suitable choice. Zr remains incompatible in magmatic systems up to ≈68 wt.% SiO2 because zircon fractionation can be suppressed by high melt temperatures and increased volatile contents. The use of Zr thus permits PER modelling to be extended to much higher levels of silica than previously investigated. However, such systems are more complex than those just involving simple basaltic magmas. Besides fractionation, the processes of magma mixing, combined assimilation and fractional crystallization, and the initial degree of partial melting in the mantle source must also be considered. To distinguish and evaluate these processes a set of example suites are investigated from a complex synextensional calc-alkaline province in the western USA. Samples within most individual suites can be modelled by fractionation, however a significant trend orthogonal to the main fractionation vector is also apparent, and open system processes are inferred. Successful modelling is achieved on an inter-suite basis using diagrams with axis functions of ([4(Ca+Na)+0.5(Fe+Mg)]/Zr versus (Si+Al)/Zr). Potential open system evolution paths between mafic end members and crustal contaminants are also displayed and evaluated on these same diagrams. The encouraging results suggest that such PER diagrams may be employed as a versatile tool for investigating the systematics of related igneous suites over a wide area.

Operative related infection rates for ventriculoperitoneal shunt procedures in a children's hospital.

We determined the operative related cerebrospinal fluid (CSF) shunt infection rates for our institution over a 3-year period (1982 to 1984) using strictly defined numerator and denominator data. The minimum post-operative follow-up period was 12 months. The average surgical infection risk for a CSF shunt procedure at our institution during the study period was 13.3%. Annual infection rates were relatively constant (13.8%, 13.2% and 12.9%), however both quarterly (5.7% to 23.3%) and surgeon-specific (5.7% to 22.8%) rates varied widely. Infection rates calculated by using "traditional" numerator and denominator data were considerably lower (6.5% to 9.2%). Operative related CSF shunt infection rates should be determined by utilizing strictly defined numerator and denominator values in order to allow valid comparisons of published rates.

Evaluating Rational Functions: Infinite Precision is Finite Cost and Tractable on Average

If one is interested in the computational complexity of problems whose natural domain of discourse is the reals, then one is led to ask: what is the “cost” of obtaining solutions to within a prescribed absolute accuracy$\varepsilon = {1 / {2^s }}$ (or precision$s = - \log _2 \varepsilon $)? The loss of precision intrinsic to solving a problem, independent of method of solution, gives a lower bound on the cost. It also indicates how realistic it is to assume that basic (arithmetic) operations are exact and/or take one step for complexity analyses. For the relative case, the analogous notion is the loss of significance. Let ${{P(X)} / {Q(X)}}$ be a rational function of degree d, dimension n and real coefficients of absolute value bounded by $\rho $. The loss of precision in evaluating ${P / Q}$ will depend on the input x, and, in general, can be arbitrarily large. We show that, w.r.t. normalized Lebesgue measure on $B_r $, the ball of radius r about the origin in $R^n $, the average loss is small: loglinear in d, n, $\rho $, r; and $K_Q $, a simple constant. To get this, we use techniques of integral geometry and geometric measure theory to estimate the volume of the set of points causing the denominator values to be small. Suppose $\varepsilon > 0$ and $d \geqq 1$. Then: Theorem. Normalized volume$\{ x \in B_r | {|Q(x)| < \varepsilon } \} < \varepsilon ^{{1 / d}} K_Q^{{1 / d}} {{nd(d + 1)} / {2r}}$. An immediate application is a loglinear upper bound on the average loss of significance for solving systems of linear equations.

A simple activity quotient for detecting pollution‐induced stress in fishes

Abstract An activity quotient (Aq) is described which can be used to detect the stress response of fishes to sublethal concentrations of pollutants. The quotient considers three variables; ventilation frequency (Y), coughing rate (C), and pectoral fin activity (PA), and is represented importance of a respiratory component.(numerator values) and an activity component (denominator value) are indicated and constancy of one variable does not negate the Aq value. The Aq was found to be adequate to detect stress due to waterborne selenium and should prove to be a useful tool for screening wastewater and estimating chronically safe toxicant concentrations.

Determining Optimum Fluoride Concentrations

T HE FLUID intake study amnong children in Antioch and Brentwood, Calif., in 1953-54 provides a basis for determining the optimum fluoride concentration in water supplies in relation to environmental This study showed that for every degree increase in maximum daily temperature between 50? and 1000 F. water intake increased, on the average, by 0.062 per pound of body weight. For example, the average daily water consumption per pound of body weight was 0.272 when the maximum daily temperature was 50' F. and 0.334 when the maximum daily temperature was 600 F. The relationship between maximum temperature and water intake for the California children was described by the estimation equation ounces of water per pound of body weight= -0.038 + 0.0062 temperature. The validity of this equation should perhaps be checked by studies in other areas of the country, but in the meantime it can be used to illustrate the calculation of optimum fluoride concentrations. As will be pointed out later in the paper, results obtained with the equation in the Chicago area, where optimum fluoride concentration is known from epidemiological studies, indicate that it is reasonably reliable. The basic structure of the formula developed for estimating optimum fluoride concentrations is: parts per million of fluoride= optimum water consumption -. estimated water consumption. Thus, the optimum fluoride concentration for a given community is equal to a constant (the average amount of water containing 1 p.p.m. fluoride that affords optimum protection against dental caries) divided by the estimated water consumption of children in a given community. Both measures are in of water consumed daily per pound of body weight. If daily maximum temperature data for the Chicago area are applied to the water estimation equation, it is possible to calculate a denominator value for the formula, that is, the average amount of water that would be consumed daily per pound of body weight by children in the Chicago area aged 10 years or less. The number derived, although it has no particular meaning in itself, may also serve as the constant for the formula, since it is known from epidemiological data that the optimum fluoride concentration for the Chicago area is 1 p.p.m. The constant, or numerator, in the formula must equal the estimated water consumption, or denominator, for the optimum fluoride concentration to be 1 p.p.m. The estimated water consumption for the Chicago area children is based on weather data for two towns, Maywood and Joliet. Since both of these towns were included in the early studies of Dean (1), the fluoride concentration