Excluded range

Many of the models demand that the temperature at some mass cut above the helium core be in excess of the ignition temperature of hydrogen, Th, and hence, the structure is self-inconsistent. For a helium core mass of 4 M , models with total mass in the range 4.05 to 14 M , are excluded. This conclusion does not depend sensitively on the specific value adopted for Th, since the temperature profiles tend to rise so steeply in the excluded range. Similar conclusions follow for models with larger luminosities and... 

If the simulated system uses periodic boundary conditions, the logical long-range interaction includes a lattice sum over all particles with all their images. Apart from some obvious and resolvable corrections for self-energy and for image interaction between excluded pairs, the question has been raised if one really wishes to enhance the effect of the artificial boundary conditions by including lattice sums. The effect of the periodic conditions should at least be evaluated by simulation with different box sizes or by continuum corrections, if applicable (see below). 

There are two common occasions when rapid measurement is preferable. The first is with ionization sources using laser desorption or radionuclides. A pulse of ions is produced in a very short interval of time, often of the order of a few nanoseconds. If the mass spectrometer takes 1 sec to attempt to scan the range of ions produced, then clearly there will be no ions left by the time the scan has completed more than a few nanoseconds (ion traps excluded). If a point ion detector were to be used for this type of pulsed ionization, then after the beginning of the scan no more ions would reach the collector because there would not be any left The array collector overcomes this difficulty by detecting the ions produced all at the same instant. 

Hydrocarbons, compounds of carbon and hydrogen, are stmcturally classified as aromatic and aliphatic the latter includes alkanes (paraffins), alkenes (olefins), alkynes (acetylenes), and cycloparaffins. An example of a low molecular weight paraffin is methane [74-82-8], of an olefin, ethylene [74-85-1], of a cycloparaffin, cyclopentane [287-92-3], and of an aromatic, benzene [71-43-2]. Cmde petroleum oils [8002-05-9], which span a range of molecular weights of these compounds, excluding the very reactive olefins, have been classified according to their content as paraffinic, cycloparaffinic (naphthenic), or aromatic. The hydrocarbon class of terpenes is not discussed here. Terpenes, such as turpentine [8006-64-2] are found widely distributed in plants, and consist of repeating isoprene [78-79-5] units (see Isoprene Terpenoids). 

The optical appHcation market excluding optical waveguide uses was estimated at 14.6 million ia the United States in 1994 (216). The aimual U.S. consumption of fused quart2 has been estimated at close to 45,000 metric tons. Prices ranged from 50 to 60/kg. 

Most tanks store Hquid rather than gases or soHds. Characteristics and properties such as corrosiveness, internal pressures of multicomponent solutions, tendency to scale or sublime, and formation of deposits and sludges are vital for the tank designer and the operator of the tank and are discussed herein. Excluded from the discussion are the unique properties and hazards of aerosols (qv), unstable Hquids, and emulsions (qv). A good source of information for Hquid properties for a wide range of compounds is available (2). 

The hot-water separation process involves extremely compHcated surface chemistry with interfaces among various combinations of soUds (including both silica sand and alurninosilicate clays), water, bitumen, and air. The control of pH is critical. The preferred range is 8.0—8.5, achievable by use of any of the monovalent bases. Polyvalent cations must be excluded because they tend to flocculate clays and thus raise viscosity of the middlings in the separation cell. 

For most systems, only the first three terms are used. Only the first two terms are used for narrow ranges. If data are available in a wide range extending far above the normal boiling point, all four terms are used, with values of E varying in integers from —10 to 10 (excluding 0 and —I). 

Sa metals, excluding factor E, or bolt design stress Allowable stress range for MPa Idp/im (ksi)... 

A similar problem arises with present cross-validated measures of fit [92], because they also are applied to the final clean list of restraints. Residual dipolar couplings offer an entirely different and, owing to their long-range nature, very powerful way of validating structures against experimental data [93]. Similar to cross-validation, a set of residual dipolar couplings can be excluded from the refinement, and the deviations from this set are evaluated in the refined structures. 

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