What's the difference between covariant and polynomial?
Covariant
Definition:
(n.) A function involving the coefficients and the variables of a quantic, and such that when the quantic is lineally transformed the same function of the new variables and coefficients shall be equal to the old function multiplied by a factor. An invariant is a like function involving only the coefficients of the quantic.
Example Sentences:
(1) The difference in HDL and HDL2 cholesterol concentrations between the MI+ and MI- groups or between the MI+ and CHD- groups persisted after adjustment by analysis of covariance for the effect of physical activity, alcohol intake, obesity, duration of diabetes, and glycemic control.
(2) We studied the effects of the localisation and size of ischemic brain infarcts and the influence of potential covariates (gender, age, time since infarction, physical handicap, cognitive impairment, aphasia, cortical atrophy and ventricular size) on 'post-stroke depression'.
(3) The multiple logistic model, the most commonly used model for the analysis of coronary heart disease studies, does not consider survival time in assessment of the dependent covariates and does not account for the censoring which usually occurs in such studies.
(4) However, two methodologic factors might account for the covariation of these 'schizophrenia spectrum' personality traits and measures of brain function.
(5) With baseline measures and body mass index controlled for, analyses of covariance showed that adults had greater systolic blood pressure responses than did children; men had greater blood pressure responses to all stressors than did women; and high school boys had greater systolic blood pressure responses than did high school girls.
(6) Analysis of covariance of the Test III means (Test II as covariate) yielded significant (p less than .05)F-ratios for Vo2max and R at Vo2max.
(7) Second, the commonly drawn analogy between blocking in randomized trials and matching in cohort studies is misleading when one considers the impact of matching on covariate distributions.
(8) When rates were covaried for prior violent crime arrests, White House Case subjects with prior arrests had a significantly higher rate of total posthospitalization violent crime arrests than the matched control sample.
(9) Genetic parameters were estimated from sire components of variance and covariance obtained from a multiple-trait restricted maximum likelihood procedure.
(10) The covariates included in the analysis were age, gender, socioeconomic status, and primary language.
(11) Inhibitory ability covaried with victim maturity, and with months spent in a treatment program.
(12) An error and covariances analysis shows that the method is robust and accurate enough for autonomous navigation.
(13) The comparability of therapeutic effect was also evident within the subset of 81 patients who had adenocarcinoma cell type, although MACC showed a small advantage in survival after covariate analysis.
(14) This methodology was used to evaluate possible kinetic isotope effects after the coadministration of an equimolar mixture of ibuprofen and the deuterium-labeled covariant in the beagle.
(15) Using an analysis of covariance to have statistical control on age, occupational level and depression, the results were statistically significant on the 0.05 level.
(16) Analysis of covariance revealed that the onset of the first ME occurred earlier in Day 10 litters than in Day 4 litters, but litter size had no effect.
(17) Furthermore, the approach provides a nice graphical representation of the relationships between the PK-PD parameters and covariates.
(18) The analysis can include covariates and risk factors.
(19) Analysis proceeded by means of the analysis of covariance with the dental dimorphism indices as the dependent variables.
(20) After adjustment for significant covariates (smoking and serum gamma-glutamyl transpeptidase in both sexes, and age and serum ferritin in women), a twofold increase in the Cd concentration in the soil was accompanied by a 6% decrease in blood Cd in men (R2 = 0.03; P = 0.09) and by a 10% decrease in women (R2 = 0.06; P less than 0.01).
Polynomial
Definition:
(n.) An expression composed of two or more terms, connected by the signs plus or minus; as, a2 - 2ab + b2.
(a.) Containing many names or terms; multinominal; as, the polynomial theorem.
(a.) Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.
Example Sentences:
(1) The dual-line and polynomial regression techniques fit the data better (mean residual square deviation 0.024 and 0.031, respectively) than the single-regression line approach (0.110).
(2) The N2O dose-response data for each animal were fit by a second-order polynomial equation to estimate the value of a second-order coefficient.
(3) The calculation is made from a newly derived third-degree polynomial reflecting the ratio of the optic densities of whole nonstabilized blood hemoglobin aqueous solution in the 560-580 and 535-560 nm bands.
(4) Relative dose functions for 125I for these phantom media are fitted to second-degree polynomials.
(5) For this purpose we employed a third-degree polynomial regression analysis which showed a better fit of the data.
(6) Changes in pressures (IAP, CVP) and shunt flow were tabulated and analyzed with linear and polynomial regression.
(7) Trend analysis of the fatigue patterns revealed that a cubic orthogonal polynomial equation was sufficient to describe the profile of MVC decrement for all conditions.
(8) The superiority of the R3SSE over two related equations--a simple second-degree polynomial equation and a simplified form of the R3SSE which neglects contributions to solubility from the solvent mixture--is also demonstrated for a number of solutes.
(9) The polynomial logit-log procedure gave the best fit, but this was probably due to the inherent flexibility of this curve-fitting process since the analytical precision achieved with it was not better than what was obtained with most of the other procedures.
(10) A theorem about correspondence of the graph constructed and coefficients of the characteristic polynomial of linearized kinetic equations is proved.
(11) A tabulation is given of the polynomials for all possible stereoisomers of many of the knotted and catenated forms that are found in DNA.
(12) We present a polynomial algorithm (O(n X L4), where n is the number of sequences) for generating strings related to the LCS and constructed with the sequence alphabet and an indetermination symbol.
(13) The LV volume curve was smoothed by fitting a fourth order polynomial curve of Fourier's analysis.
(14) This case reduces to Wyman's binding polynomial analysis.
(15) Hence, the dose response relationship for the trophic effect of gastrin on the enterochromaffin like cells seems to follow a polynomial rather than a linear function.
(16) Polynomial curves were fitted to each race and sex group and, from these, estimates were made of the 3rd, 50th, and 97th percentiles for height and weight.
(17) The H-H rate constants, alpha and beta, are approximated by polynomial functions rather than exponential functions, since the former are handled more efficiently by SPICE.
(18) A third-order polynomial function would theoretically explain better than a linear relation or a parabolic fit the curved shape of experimentally obtained P-Q relationships.
(19) A polynomial regression fits the best the results: the speed of acquisition of this kind of learning decreases between the ages of 3 and 35 days, a plateau being observed in flies older than 35 days.
(20) It involves a conceptual dissection of the polypeptide chain into interacting blocks; the behavior of any block with side-chain interactions is treated then with conventional binding polynomial techniques.