What's the difference between polynomial and rational?
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.
Rational
Definition:
(n.) A rational being.
(a.) Relating to the reason; not physical; mental.
(a.) Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning.
(a.) Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.
(a.) Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.
Example Sentences:
(1) Our data suggest that a rational use of surveillance cultures and serological tests may aid in an earlier diagnosis of FI in BMT patients.
(2) Consensual but rationally weak criteria devised to extract inferences of causality from such results confirm the generic inadequacy of epidemiology in this area, and are unable to provide definitive scientific support to the perceived mandate for public health action.
(3) We are the generation who saw the war,, who ate bread received with ration cards.
(4) The yeasts amounts used did not protect the test animals from the kidney infiltration with lipids and cholesterol; 12 g of yeasts per 100 g of the ration promoted elevation of sialic acid content in the blood plasma.
(5) Spontaneous reports of suspected adverse reactions may be the only way of revealing very rare events but they present great difficulties of rational interpretation.
(6) The rational surgical methods of treatment in 85 patients with suppurative hepatic echinococcosis penetrating into the abdomen cavity are presented.
(7) Knowledge of these lesions could form the basis for establishing a useful and rational therapy for such cases.
(8) It seams rational to proceed to an earlier total correction in these cases when well defined criteria are fullfilled, as the mortality figures of the palliative and corrective procedures have a tendency to reach each other: (3,2 versus 5,7%).
(9) --The influence of the digestibility of the energy in the ration on the energetic retention effect of BFC is small.
(10) The length of delay is determined by unconscious, non-rational processes, and other factors beyond her control.
(11) But it can be a more rational and better developed approach to long-term care based on the experience and knowledge we have gained in the past 50 years.
(12) The authors further show how test results can be used rationally by clinicians by so-called threshold analysis.
(13) The aetiology remains at present uncertain and therefore rational therapeutic strategies are difficult to plan.
(14) The origin of these substances is unknown, but these findings provide a rational basis for trials of benzodiazepine-receptor antagonists in the management of this disorder.
(15) We reviewed our experience with 245 thyroidectomies to define the spectrum of hypocalcemia, elucidate the mechanisms of hypocalcemia, and formulate a rational basis for its management.
(16) The data obtained can be useful when choosing a rational method for the therapy of gastric scretory disorders.
(17) Willie Spies, its legal representative, said: "Rationality has to return to the debate.
(18) A 35-kg Duroc pig died 3 days after eating a ration containing aflatoxin B1, B2, G1, and G2.
(19) In a Europe (including Britain) where austerity has become the economic dogma of the elite in spite of massive evidence that it is choking growth and worsening the very sickness it claims to heal, there are plenty of rational, sensible arguments for taking to the streets.
(20) The resolution of the cellular events which underlie the development of pancreatitis in combination with the introduction of new therapeutic agents may enable a rational and safe protocol to be developed for the support of patients with pancreatitis.