Formula-based

Gaussian Quadrature Gaussian quadrature provides a highly accurate formula based on irregularly spaced points, but the integral needs to be transformed onto the intei val 0 to I. 

Some formulas based upon the adiabatic equation and useful in compressor work are as follows ... 

To these alkaloids Asahina and Mayeda assigned formulae, based on the reactions described, and on the first assumption, referred to above, that 2- -aminoethylindole was the scission product of evodiamine. Kermack, Perkin and Robinson pointed out that the evidence did not exclude the possibility that the base produced was in reality 3-)3-amino-ethylindole, in which case evodiamine and rutascarpine could be represented by the following formulas, which would bring them into line with harmine. 

The formation abrasiveness, drillability and bit-bearing parameters are calculated from the following formulas based on data available from previous drilling experience. 

The capacity of the accumulator is important, and one formula based on experience for sudden valve closure is... 

The calculation of every heat transfer coefficient for a refrigeration or air-conditioning system would be a very time-consuming process, even with modern methods of calculation. Formulas based on these factors will be found in standard reference works, expressed in terms of heat transfer coefficients under different conditions of fluid flow [1, 4-8]. 

Polya 3, 4, 5. The last paper contains a direct proof for the equivalence of the recursion formulas based on combinatorial considerations and on the functional equation (4). 

Gravitational settlement is allowed to proceed for 4 to 10 minutes, according to the particle-size range of the sample. The sedimentation tube is then centrifuged to reduce the time required for the smaller particles to reach the bottom. By measuring the volume of particles accumulated as a function of time, the equivalent spherical size distribution of the sample may be computed from formulae based upon Stokes law. In addition to the specially designed sedi-... 

TABLE P a 10.3 Conjugate Acid-Base Pairs Arranged by Strength Acid name Acid formula Base formula Base name PKb... 

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

Likewise, one can check the second formula based on another relation V iji Vi) = A. ... 

Specific heat of each species is assumed to be the function of temperature by using JANAF [7]. Transport coefficients for the mixture gas such as viscosity, thermal conductivity, and diffusion coefficient are calculated by using the approximation formula based on the kinetic theory of gas [8]. As for the initial condition, a mixture is quiescent and its temperature and pressure are 300 K and 0.1 MPa, respectively. 

Following previous works on physico-chemical characterisation of sunflower low-methoxyl pectins (Alarc o-Silva, 1990, Leitao at al., 1995) and technological utilisation in the manufacture of low calorie gels (Alarc o-Silva et al., 1992), this investigation was carried out to test the suitability of that pectin to the confection of grape juice reduced calorie jellies in comparison with two types of commercial pectin. Aiming at the optimisation of low-calorie jelly formula, based on consumers preferences, the jellies were submitted to a sensory panel test judgement and instrumental texture-analysis. 

Calvert AH, Newell DR, Gumbrell LA, et al. Carboplatin dosage Prospective evaluation of a simple formula based on renal function. J Clin Oncol 1989 7( 11) 1748-1756. 

Choose an appropriate feeding formula based on patient-specific factors. This necessitates assessing the patient s nutritional requirements. Standard polymeric formulas are appropriate for the majority of patients. 

Specific information on instability of individual chemical compounds, and on hazardous interactions of elements and/or compounds, is contained in the main formula-based Volume 1 of the Handbook. For an example of an unstable compound, see Ethyl perchlorate... 

MM3(2000) has also included a new approach to obtain bond polarizabilities and induced dipole moments.69 A general formula based on the original MM3 force constants and bond polarizabilities was derived and is used to compute bond polarizabilities, and then molecular polarizabilities by an additive model. 

Greg Fu supervised the proofreading and provided the structural formula based on the x-ray data for the new Sharpless catalytic reagent for osmylation of alkenes. Martita F. Barsotti is the photographer for the picture of some present and former co-workers for Reagents. 

The mathematical methods used for interpolation and extrapolation of the data obtained from accelerated tests, as described in Chapters 8 and 9, include both the mechanistic and the empirical. Arrhenius formula, based on chemical rate kinetics and relating the rate of degradation to temperature, is used very widely. Where there are sufficient data, statistical methods can be applied and probabilities and confidence limits calculated. For many applications a high level of precision is unnecessary. The practitioners of accelerated weathering are only too keen to tell you of its quirks and inaccuracies, but this obscures... 

Spence, S., Soper, K., Hoe, C.M. and Coleman, J. (1998) The heart rate-corrected QT interval of conscious beagle dogs a formula based on analysis of covariance. Toxicological Sciences, 45, 247-258. 

In addition, Perrin tended to interest himself in individual atomic events rather than in the molecule as a complex entity. The radiation theory of chemical activation attempted a mathematical representation in simple and general formulas, based on axiomatic principles. Perrin s work in radiation bears more resemblance to his reformulation of thermodynamics in the early 1900s than to his experimental work on x-rays and cathode rays in the 1890s or on colloids and Brownian motion in the early 1900s. What binds all his work together is interest in single events or the individual corpuscle. 106... 

Semi-empirical formulae, based only on molecular structure, have been derived which allow flammability limits to be calculated for hydrocarbons and alcohols. Flash points, autoignition temperatures and boiling points may also be calculated from molecular structure for these classes. Quoted examples indicate the methods... 

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