Similarity types

Once the grid (or two grids) are prepared, there are two similar types of approaches to propagate the initial wavefiinction forward with time. One approach is split-operator methods, [59] where the short-time propagator is divided into a kinetic and potential parts so that... 

Expert systems have been applied in various fields such as medicine, chemistiy, engineering, or business. Within all these fields, expert systems are used for similar types of tasks. They can, for example, be used for classification, i.c, to select one... 

Other similar types of manometer, usually reading over a range of about 10-60 mm., are available in many laboratories. 

Examples of this degradation of bands are shown in Figures 7.44 and 7.45. Figure 7.44(a) shows the rotational fine structure of the Oj] band of the —X Ag system of 1,4-diffuorobenzene, belonging to the >2 point group. The fine structure is in the form of a contour of tens of thousands of unresolved rotational transitions which, nevertheless, shows well-defined features (B is an overlapping weaker band of a similar type). Since Biu = r(T ), as given by Table A.32 in Appendix A, the electronic transition is allowed and... 

Boron also reacts with hydroxyl-containing polymers such as cellulose. When exposed to a flame the boron and hydroxyl groups form a glassy ester that coats the substrate and reduces polymer degradation. A similar type of action has been observed in the boron—alumina tfihydrate system. 

The conversion of coal to gas on an industrial scale dates to the early nineteenth century (14). The gas, often referred to as manufactured gas, was produced in coke ovens or similar types of retorts by simply heating coal to vaporize the volatile constituents. Estimates based on modem data indicate that the gas mixture probably contained hydrogen (qv) (ca 50%), methane (ca 30%), carbon monoxide (qv) and carbon dioxide (qv) (ca 15%), and some inert material, such as nitrogen (qv), from which a heating value of approximately 20.5 MJ/m (550 Btu/fT) can be estimated (6). 

Other analytical techniques ate also available for the determination of maleic anhydride sample purity. For example, maleic anhydride content can be determined by reacting it with a known excess of aniline [62-53-3] in an alcohol mixture (170). The solution is then titrated with an acid to determine the amount of unconsumed aniline. This number is then used to calculate the amount of maleic anhydride reacted and thus its concentration. Another method of a similar type has also been reported (171). 

Similar types of cross-linking reactions are observed for polymers to which photosensitive molecules ate chemically attached to the backbone of the polymer stmcture (Fig. 7). Radiation curing of polymers using uv and visible light energies is used widely in photoimaging and photoresist technology (Table 8) (58,59). 

The term babbitt iacludes high tin ahoys (substantiahy lead-free) containing >80 wt % tin, and high lead ahoys containing >70 wt % lead and <12 wt % tin. Both have the characteristic stmcture of hard compounds ia a soft matrix, and although they contain the same or similar types of compounds, they differ ia composition and properties of the matrix. 

Hydrated Stannic Oxide. Hydrated stannic oxide of variable water content is obtained by the hydrolysis of stannates. Acidification of a sodium stannate solution precipitates the hydrate as a flocculent white mass. The colloidal solution, which is obtained by washing the mass free of water-soluble ions and peptization with potassium hydroxide, is stable below 50°C and forms the basis for the patented Tin Sol process for replenishing tin in staimate tin-plating baths. A similar type of solution (Staimasol A and B) is prepared by the direct electrolysis of concentrated potassium staimate solutions (26). 

Other countries have similar types, some classifications, as in Germany, are based on age-strength levels by standard tests (70). A product made in Italy and Prance known as Perrari cement is similar to Type V and is sulfate-resistant. Such cements have high iron oxide and low alumina contents, and harden more slowly. 

Raoult s Law for component j (7 1 and 7 < 1). Compounds of similar type and size, eg, pentane—hexane or methanol—ethanol, tend to behave ideally... 

In a series of organic acids of similar type, not much tendency exists for one acid to be more reactive than another. For example, in the replacement of stearic acid in methyl stearate by acetic acid, the equilibrium constant is 1.0. However, acidolysis in formic acid is usually much faster than in acetic acid, due to higher acidity and better ionizing properties of the former (115). Branched-chain acids, and some aromatic acids, especially stericaHy hindered acids such as ortho-substituted benzoic acids, would be expected to be less active in replacing other acids. Mixtures of esters are obtained when acidolysis is carried out without forcing the replacement to completion by removing one of the products. The acidolysis equilibrium and mechanism are discussed in detail in Reference 115. 

Reactions involving quinoline hydrazide derivatives have been noted in the pyridazino-[4,3-c]- (64MI21500), -[4,5-f ]- (31M(58)238) and -[4,5-c]-quinoline (71CB3341) series, whilst the double cyclization of (358) to the pyridazino[4,5-f ]quinoline (359) (80CPB3457) and related cyclizations in the same series (80H(14)267) are of a basically similar type. A lone cyclization of this type from cinnoline intermediates involves the o-acetonylcarboxamide type formation of the pyridine ring to give the pyrido[3,4-c]cinnoline (360) (76JCS(Pl)592). 

A somewhat similar type of ring interconversion involving attack on sulfur has been postulated in the 1,2,4-thiadiazole series, e.g. (337) (338). Such reactions are common in the 1,2,4-dithiazolium series, e.g. (339) —> (340). 

Again the specific remarks for y" + ay + hy =f x) apply to differential equations of similar type but higher order. We shall discuss two general methods. 

Order-of-magnitude estimate (ratio estimate). Rule-of-thumb method based on cost data for previous similar types of plant probable error within 10 to 50 percent. 

Powder Sy.stems) serves as grinder or prebreaker and is of similar type. The Rietz prebreaker differs somewhat from these. 

A similar type of open-loop control response is combined with closed-loop control in a patented method of surge protection. In this control method an open-loop control response is added before surge occurs. 

With 50 articles, organization of the book was difficult certain techniques could equally well have appeared in more than one place. The organizational intent of the Editors was to group techniques that have a similar physical basis, or that provide similar types of information. This is not the traditional organization of an encyclopedia, where articles are ordered alphabetically. Such ordering seemed less useful here, in part because many of the techniques have multiple possible acronyms (an Acronyms Glossary is provided to help the reader). 

The vulcanisation of natural rubber, a long chain polyisoprene, with sulphur involves a similar type of cross-linking. 

Using the data incorporated in Fig. 3.3 and assuming the additivity of gauche and eclipsing interactions of similar type, sketch the rotational energy profile you would expect for 2,3-dimethylbutane. 

While not exactly labels, repositionable paper notes, such as Post-iF Notes, and tape flags (u.sed to call a reader s attention to certain pages in a document) have to meet similar types of release requirements. Like linerless labels, reliable... 

The slow rate of hydration for buried surfaces is desirable from a service point of view, but makes the study and evaluation of the durability of surface treatments difficult unless wedge tests (ASTM D3762) or similar tests are used to accelerate the degradation. As for the wedge test, the stress at the crack tip, together with the presence of moisture at the tip, make this a more severe test than soaked lap shear specimens or similar types and therefore a better measure of relative durability. 

In order to develop measures for removal of debris from the waste matrix, the general types of debris anticipated need to be identified. A composite list, based on debris found at 29 Superfund sites, was developed. The list includes cloth, glass, ferrous materials, nonferrous materials, metal objects, construction debris, electrical devices, wood existing in a number of different forms, rubber, plastic, paper, etc., as presented in Table 11. Similar types of debris would be expected at RCRA sites. 

In order to illustrate the use of cost indices and scaling factors, let us consider the following example. In 1992, the cost of a 50 m shell-and-tube beat exchanger was 24,000. Estimate the cost of a 100 m shell-and-tube heat exchanger of a similar type and materials of construction in 1996. 

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