Linear extrapolation concerning Hilbert valued planar functions

1990 ◽  
pp. 244-268
Author(s):  
Francesco Russo
Keyword(s):  
Linear Extrapolation ◽  
Planar Functions

Totally and Partially Ambiguous Points of Planar Functions

1977 ◽  
Vol 2 (2) ◽  
pp. 109
Author(s):  
Mikkelson
Keyword(s):  
Planar Functions

scholarly journals The volume coefficients of expansion of several gases at pressures below one metre

1934 ◽  
Vol 143 (850) ◽  
pp. 487-505 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Linear Function ◽  
Rate Of Change ◽  
Linear Extrapolation ◽  
Satisfactory Explanation ◽  
Volume Coefficient ◽  
Temperature Ranges ◽  
The Mean ◽  
Permanent Gases ◽  
Limiting Value

There have not appeared recently any new determinations of the rate of change of the volume coefficient of expansion of condensable gases at pressures in the neighbourhood of a half to one metre. The work of Henning and Heuse and Heuse and Otto has been confined to a study of the permanent gases, their results leading to the conclusion that up to a pressure of 1 metre the rate of change of either the pressure or volume coefficient is a linear function of the pressure. Our knowledge of the behaviour of the condensable gases in this connection rests almost entirely on the very careful work of Chappuis, who in 1907 made a series of accurate determinations of the volume coefficient of expansion of carbon dioxide at a series of pressures from 1500 mm. to 500 mm. and over several temperature ranges. The investigation led to one unexpected conclusion which Chappuis left largely unexplained. On linear extrapolation to zero pressure of the graph of pressure against the mean coefficient of expansion over temperature intervals 0-20º, 0-40º, 0-100ºC., the limiting value of the coefficient rose from the normal value of 0.003661 for the 0-20º determinations to 0.003671 for those made over the range 0-100ºC. Chappuis concludes "that condensation on the reservoir surface plays a part in the irregularities but it is difficult to obtain a satisfactory explanation." As far back as 1853 Magnus demonstrated that the adsorption of sukphur dioxide on glass was sufficient to affect measurements of the expansion coefficient of gasses, and the importance of this error was recognized by Chappuis who in 1879 applied a correction to Regnault's measurements. Richards and Mark and Baly and Ramsay have pointed out the necessity for a knowledge of the amount of adsorption on the walls of the containing vessels when undertaking such determinations.

The design and conduct of experiments to measure animal and herbage production responses to fertilizer nitrogen under cutting and grazing managements

1985 ◽  
Vol 104 (1) ◽  
pp. 85-94 ◽  
Author(s):  
R. V. Large ◽  
J. M. Cobby ◽  
R. D. Baker
Keyword(s):  
Weight Gain ◽  
Live Weight ◽  
Continuous Systems ◽  
Linear Extrapolation ◽  
Rotational Grazing ◽  
Response Curves ◽  
Live Weight Gain ◽  
Continuous Grazing ◽  
Consistent Manner ◽  
Fourth Experiment

SummaryTwo experiments were conducted to provide information on the precision of herbage sampling, the degree of replication and the logistics of managing rotational and continuous grazing experiments. In a third experiment the possibility of estimating herbage growth, during the rotational grazing of paddocks for 4 days, by linear extrapolation of measured growth estimates made during the interval between grazings was investigated. A fourth experiment was then conducted to investigate animal and herbage production responses to nitrogen applied at five levels over the range 80–900 kg N/ha with three replicates per treatment.Results from Expts 1 and 2 showed that similar precision could be obtained under both rotational and continuous systems of grazing with the same number of replicates and samples of herbage. There was little advantage in having more than three replicates and four samples per paddock or two replicates and eight samples per paddock. Under continuous grazing a 3-weekly sampling and movement of exclosure cages was indicated. It was also found, from Expt 3 that, under rotational grazing, linear extrapolation of growth from 0–24 days did not reflect growth to 28 days in a consistent manner. Six animals per treatment, permanently in the paddocks, proved adequate for the estimation of live-weight gain.Experiment 4 confirmed that response curves could be fitted with an acceptable degree of precision if there was one low, one very high, and two intermediate levels of nitrogen. Adjustment of the number of animals to maintain sward height at between 5 and 7 cm ensured similar sward conditions and rates of live-weight gain across all treatments.The problems associated with the measurement of herbage production under grazing are discussed.

A comparison of the compressibilities of some gases with that of nitrogen at pressures below one atmosphere

1950 ◽  
Vol 200 (1061) ◽  
pp. 201-218 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Differential Method ◽  
Linear Extrapolation ◽  
Volume Changes ◽  
Pure Nitrogen ◽  
Molecular Weights ◽  
Nitrous Oxide Oxygen ◽  
The Individual ◽  
Straight Lines ◽  
High Degree

A differential method for comparing the compressibilities of gases at pressures below 1 atm. has been developed in which many of the errors inherent in methods employed previously have been to a large extent eliminated, especially those due to meniscus volume changes and capillary depression. Using pure nitrogen as a standard the low-pressure isothermals of carbon monoxide, carbon dioxide, nitrous oxide, oxygen, ethylene and propane have been determined at a temperature of 22-05° C. The deviations of the individual points from straight lines do not in most cases exceed 2 parts in 100,000. In no case, even with propane, was any curvature in the isotherms detectable. The contention of Moles and other recent workers that the molecular weights of liquefiable gases can be determined to a high degree of accuracy by linear extrapolation is rendered highly probable by this fresh evidence.

Methods of Predicting the Drift of the Parameters of Dynamic Objects on the Basis of a Linear Extrapolation Model

2018 ◽  
Vol 60 (10) ◽  
pp. 979-984 ◽  
Author(s):  
Yu. S. Sysoev ◽  
V. G. Beketov
Keyword(s):  
Linear Extrapolation ◽  
Extrapolation Model ◽  
Dynamic Objects

Uncertainty of Estimates of Cancer Risks Derived by Extrapolation from High to Low Doses and from Animals to Humans

1997 ◽  
Vol 16 (4-5) ◽  
pp. 449-460 ◽  
Author(s):  
Ralph L. Kodell ◽  
David W. Gaylor
Keyword(s):  
Human Cancer ◽  
Model Fitting ◽  
Real Data ◽  
Data Uncertainty ◽  
Low Doses ◽  
Linear Extrapolation ◽  
Cancer Risks ◽  
Uncertainty Model ◽  
Animal Data ◽  
Model Selection Uncertainty

The uncertainties associated with extrapolating model-based cancer risks from high to low doses and animal-based cancer risks to humans are examined. It is argued that low-dose linear extrapolation based on statistical confidence limits calculated from animal data is designed to account for data uncertainty, model-selection uncertainty, and model-fitting instability. The intent is to err on the side of safety, that is, overstating rather than understating the true risk. The tendency toward conservatism in predicting human cancer risks from animal data based on linear extrapolation is confirmed by a real-data analysis of the various sources of uncertainty involved in extrapolating from animals to humans. Along with the tendency toward conservatism, a high degree of overall uncertainty in the interspecies extrapolation process is demonstrated. It is concluded that human cancer risk estimates based on animal data may underestimate the true risk by a factor of 10 or may overestimate that risk by a factor of 1,000.

scholarly journals The non-existence of right cyclic planar functions of degree pn for n ⩾ 2

1993 ◽  
Vol 63 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Nobuo Nakagawa
Keyword(s):  
Planar Functions

scholarly journals How to deal with non-linear pathways towards energy futures

2019 ◽  
Vol 28 (3) ◽  
pp. 20-26
Author(s):  
Stefan Vögele ◽  
Witold-Roger Poganietz ◽  
Philip Mayer
Keyword(s):  
Policy Advice ◽  
Linear Extrapolation ◽  
Energy Futures ◽  
The Past ◽  
Non Linear ◽  
Simplifying Assumptions ◽  
Novel Approaches ◽  
The Creation ◽  
Linear Trends

Energy scenarios currently in use for policy advice are based on a number of simplifying assumptions. This includes, in particular, the linear extrapolation of trends. However, this approach ignores the fact that central variables were highly dynamic in the past. For an assessment of energy futures and the specification of measures, novel approaches are necessary which can implement non-linear trends. In this paper, we show how cross-impact balance (CIB) analysis can be applied to map dynamic trends. Using a small CIB model, we highlight the need for novel approaches in the creation and evaluation of energy futures and the possible contribution of CIB analysis.

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