Admix

The quantum phase factor is the exponential of an imaginary quantity (i times the phase), which multiplies into a wave function. Historically, a natural extension of this was proposed in the fonn of a gauge transformation, which both multiplies into and admixes different components of a multicomponent wave function [103]. The resulting gauge theories have become an essential tool of quantum field theories and provide (as already noted in the discussion of the YM field) the modem rationale of basic forces between elementary particles [67-70]. It has already been noted that gauge theories have also made notable impact on molecular properties, especially under conditions that the electronic... 

We now describe the relation between a purely formal calculational device, like a gauge transformation that merely admixes the basis states, and observable effects. 

In Eq. (168), the first, magnetic-field term admixes different components of the spinors both in the continuity equation and in the Hamilton-Jacobi equation. However, with the z axis chosen as the direction of H, the magnetic-field temi does not contain phases and does not mix component amplitudes. Therefore, there is no contribution from this term in the continuity equations and no amplitude mixing in the Hamilton-Jacobi equations. The second, electric-field term is nondiagonal between the large and small spinor components, which fact reduces its magnitude by a further small factor of 0 particle velocityjc). This term is therefore of the same small order 0(l/c ), as those terms in the second line in Eqs. (164) and (166) that refer to the upper components. 

Alkvl Azides from Alkyl Bromides and Sodium Azide General procedure for the synthesis of alkyl azides. In a typical experiment, benzyl bromide (360 mg, 2.1 mmol) in petroleum ether (3 mL) and sodium azide (180 mg, 2.76 mmol) in water (3 mL) are admixed in a round-bottomed flask. To this stirred solution, pillared clay (100 mg) is added and the reaction mixture is refluxed with constant stirring at 90-100 C until all the starting material is consumed, as obsen/ed by thin layer chromatographv using pure hexane as solvent. The reaction is quenched with water and the product extracted into ether. The ether extracts are washed with water and the organic layer dried over sodium sulfate. The removal of solvent under reduced pressure affords the pure alkyl azides as confirmed by the spectral analysis. ... 

The solvents used for liquid chromatography are the commoner ones such as water, acetonitrile, and methanol. For the reasons just stated, it is not possible to put them straight into the ion source without problems arising. On the other hand, the very viscous solvents that qualify as matrix material are of no use in liquid chromatography. Before the low-boiling-point eluant from the LC column is introduced into the ion source, it must be admixed with a high-boiling-point matrix... 

By passing a continuous flow of solvent (admixed with a matrix material) from an LC column to a target area on the end of a probe tip and then bombarding the target with fast atoms or ions, secondary positive or negative ions are ejected from the surface of the liquid. These ions are then extracted into the analyzer of a mass spectrometer for measurement of a mass spectrum. As mixture components emerge from the LC column, their mass spectra are obtained. 

Selectivity. Solvent selectivity is intimately linked to the purity of the recovered extract, and obtaining a purer extract can reduce the number and cost of subsequent separation and purification operations. In aqueous extractions pH gives only limited control over selectivity greater control can be exercised using organic solvents. Use of mixed solvents, for example short-chain alcohols admixed with water to give a wide range of compositions, can be beneficial in this respect (6). 

Triaryl phosphates are produced from the corresponding phenols (usually mixtures) by reaction with phosphoms oxychloride, usually in the presence of a catalyst (94—96). They are subsequently distilled and usually washed with aqueous bases to the desired level of purity. Tricresyl phosphate was originally made from petroleum-derived or coal-tar-derived cresyflc acids, ie, cresols, variously admixed with phenol and xylenols. Discovery of the toxicity of the ortho-cresyl isomers led manufacturers to select cresols having very Httle ortho-isomer. 

Another thermally efficient kiln is the modem mixed-feed vertical kiln ia which coke is admixed with 8.5—20 cm lump limestone and charged into the top of the vertical kiln by a mobile, overhead charging system. However, use of this kiln is waning since the quaUty of mixed-feed kiln lime does not equal that of the other three kilns described above, owing to ash contamination from the coke and poorer reactivity and to the higher cost of coke in most areas. 

A method for physically separating turbostratic carbon and graphite involves shaking a sample into suspension in ethylene bromide of sp gr 2.17 and centrifliging. The method is unreflable except where fine carbon and coarse graphite are admixed it can be an aid in quaUtative examination. 

Reaction Conditions. Typical iadustrial practice of this reaction involves mixing vapor-phase propylene and vapor-phase chlorine in a static mixer, foEowed immediately by passing the admixed reactants into a reactor vessel that operates at 69—240 kPa (10—35 psig) and permits virtual complete chlorine conversion, which requires 1—4 s residence time. The overaE reactions are aE highly exothermic and as the reaction proceeds, usuaEy adiabaticaEy, the temperature rises. OptimaEy, the reaction temperature should not exceed 510°C since, above this temperature, pyrolysis of the chlorinated hydrocarbons results in decreased yield and excessive coke formation (27). 

The ammonia—air dilution system dilutes the vaporized ammonia by a factor of 20 to 25 with air for better admixing through the AIG and to prevent explosive ammonia—air mixtures. Once the catalyst volume is selected, the NO removal is set by the NH /NO mole ratio at the inlet of the SCR system (39). 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

Filter aids as well as flocculants are employed to improve the filtration characteristics of hard-to-filter suspensions. A filter aid is a finely divided solid material, consisting of hard, strong particles that are, en masse, incompressible. The most common filter aids are applied as an admix to the suspension. These include diatomaceous earth, expanded perlite, Solkafloc, fly ash, or carbon. Filter aids build up a porous, permeable, and rigid lattice structure that retains solid particles and allows the liquid to pass through. These materials are applied in small quantities in clarification or in cases where compressible solids have the potential to foul the filter medium. 

The ability of an admix to be retained on the filter medium depends on both the suspension s concentration and the filtration rate during this initial precoat stage. The same relationships for porosity and the specific resistance of the cake as functions of suspension concentration and filtration rate apply equally to filter aid applications. 

BeAnft,/. admixed air secondary air. beim, abbrev. bei dem, beimengen, v.t. admix, add. 

Neben-hoden, m. Anat.) epididymis, -kem, m. Biol.) paranucleus, -kette,/. side chain, subordinate chain, -klasse, f. subsidiary class, -kosten, f.pl. extra costs, extras, -leiter, m. Elec.) branch conductor, -leitung, /. bypass branch line, -linie, /. secondary line branch line, -luft, /. admixed air secondary air, supplementary air. -niere, /. suprarenal capsule. 

Zusatz-. additional, supplementary, auxiliary admixed, added additive, -element, n. (Metal.) alloying element, -feld, n, addi tional field, supplementary field, -gerat, n. Supplementary apparatus, attachment, -glied, n. additional term, supplementary term, -lack, m. blending varnish, zusatzlich, a. additional additive supplementary, auxiliary. 

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