Sensitivity functions

Change Program QWIEN so that the second term on the right of the line below statement 10 is x instead of x/5. Solve for this new equation. Change the line below statement 10 so that the second term on the left is xj2. Repeat with j/3, xj, etc. Tabulate the values of a and the values of the denominator. Is a a sensitive function of the denominator in the second term of Program WIEN ... 

The reaction conditions applied are usually heating the amine with a slight excess of aldehyde and a considerable.excess of 2d-30hydrochloric acid at 100 °C for a few hours, but much milder ( physiological ) conditions can be used with good success. Diols, olefinic double bonds, enol ethers, and glycosidic bonds survive a Pictet-Spengler reaction very well, since phenol and indole systems are much more reactive than any of these acid sensitive functional groups (W.M. Whaley, 1951 J.E.D. Barton, 1965 A.R. Battersby, 1969). 

In general, hydroboration—protonolysis is a stereoselective noncatalytic method of cis-hydrogenation providing access to alkanes, alkenes, dienes, and enynes from olefinic and acetylenic precursors (108,212). Procedures for the protonolysis of alkenylboranes containing acid-sensitive functional groups under neutral or basic conditions have been developed (213,214). 

Transesterification of methyl methacrylate with the appropriate alcohol is often the preferred method of preparing higher alkyl and functional methacrylates. The reaction is driven to completion by the use of excess methyl methacrylate and by removal of the methyl methacrylate—methanol a2eotrope. A variety of catalysts have been used, including acids and bases and transition-metal compounds such as dialkjitin oxides (57), titanium(IV) alkoxides (58), and zirconium acetoacetate (59). The use of the transition-metal catalysts allows reaction under nearly neutral conditions and is therefore more tolerant of sensitive functionality in the ester alcohol moiety. In addition, transition-metal catalysts often exhibit higher selectivities than acidic catalysts, particularly with respect to by-product ether formation. 

Recently photorefractivity in photoconductive polymers has been demonstrated (92—94). The second-order nonlinearity is obtained by poling the polymer doped with a nonlinear chromophore. Such a polymer may or may not be a good photoconductor. Usually sensitizers have to be added to enhance the charge-generation efficiency. The sensitizer function of fuUerene in a photorefractive polymer has been demonstrated (93). 

Miscible blends of high molecular weight polymers often exhibit LOST behavior (3) blends that are miscible only because of relatively low molecular weights may show UCST behavior (11). The cloud-point temperatures associated with Hquid—Hquid phase separation can often be adequately determined by simple visual observations (39) nevertheless, instmmented light transmission or scattering measurements frequendy are used (49). The cloud point observed maybe a sensitive function of the rate of temperature change used, owing to the kinetics of the phase-separation process (39). 

Fig. 7. Photodimerization of light-sensitive functional groups attached to polymer backbone stmctuies (a) polymer containing photosensitive cinnamic...

The 1,3-dioxolane group is probably the most widely used carbonyl protective group. For the protection of carbonyls containing other acid-sensitive functionality, one should use acids of low acidity or pyridinium salts. In general, a molecule containing two similar ketones can be selectively protected at the less hindered carbonyl, assuming that neither or both of the carbonyls are conjugated to an al-kene. ... 

The sulphur pressure of tire sulphides is a sensitive function of die tnetal/sulphur ratio around the stoichiometric composition, rising sharply when the sulphur content exceeds this limit. It follows from die Gibbs-Duhem equation... 

The procedures presented here are simple, Inexpensive, and may be used on a large scale. The use of potassium hydroxide In this reaction may, however, prove Incompatible with certain base-sensitive functional groups. 

All the above results are true and are caused by the increasing void fraction of the bed near the wall, as the previous authors recognized. Pressure drop is a very sensitive function of the void fraction. Because in a... 

In equation (9.131), sup is short for supremum, which means the final result is the least upper bound. Thus the //qo-optimal controller minimizes the maximum magnitude of the weighted sensitivity function over frequency range uj, or in mathematical terms, minimizes the oo-norm of the sensitivity function weighted by fE(jtj). 

Robust performance then means that the closed-loop system will meet the performance specification given in equation (9.145) if and only if the nominal system is closed-loop stable (equation (9.141)) and that the sensitivity function Sm(jar) and complementary sensitivity function for the nominal system satisfy the rela-... 

Fig. 9.26 Bode magnitude plot of weighted sensitivity function for Example 9.4.

As with a SISO system, a sensitivity function may be defined... 

Cationic polymerization in hot melts has been applied to epoxidized polymers [38,39]. No hot melts based on vinyl ether or other cation-sensitive functionalized polymers have been described in the literature. With cationic systems, it is important that the other ingredients in the adhesive be of low basicity to avoid scavenging the initiating acid generated by the photoinitiator. 

Observations of smooth spalls in iron provided an early, dramatic demonstration of the importance of release wave behaviors. In 1956, Dally [61E01] reported the existence of remarkably smooth fracture surfaces in explosively compressed steel. The existence of these smooth spalls was a sensitive function of the sample thickness. Analysis and experiments by Erkman [61E01] confirmed that the smooth spalls were associated with interaction of release-wave shocks and shocks from reduction of pressure at free surfaces. These release shocks are a consequence of differences in compressibility at pressures just below and just above the 13 GPa transformation. 

The linear piezoeleetrie model can be used to demonstrate that the magnitude of the electric field encountered for a given polarization function is a sensitive function of the thickness of the sample. This behavior can be demonstrated by noting that the electric displacement at a given time is inversely proportional to the thickness. Thus, the thickness of the sample is an important variable for investigating effects such as conductivity that depend upon the magnitude of the electric field. Conversely, various input stress wave shapes can be used to cause various field distributions at fixed thicknesses. 

A which is not observed in individual solutions of the two enones at the same concentrations and may thus be indicative of a complex formation. However, the ratio of isomeric cyclobutane products resulting from such photocycloadditions is generally seen to be a quite sensitive function of steric effects and of the properties of the reaction solvent, of the excited state(s) involved (in some cases two different excited triplet states of the same enone have been found to lead to different adducts) and of the substituents of the excited enone and substrate. No fully satisfactory theory has yet been put forth to draw together all the observations reported thus far. 

An excellent alternative route to 5,6-seco-acids of general structure (69) has been used by Knof to prepare B-norsteroids. Although the single-step chromium trioxide oxidation process described in section III-A is convenient when starting materials are readily available and relatively low yields are acceptable, the multistep Knof process may be preferred when high yields are important or when a sensitive functionality is present. 

The rates of most reactions are sensitive functions of temperature, and an understanding of the molecular basis for this dependence is an essential goal in theoretical investigations of kinetics. Experimentally it has been found that the rate constant... 

Thus, A is apparently temperature dependent, but not highly so, because the partition functions are not very sensitive functions of temperature. 

A,A-Diacetyl-2-trifluoromethylaniline, organic solvents, 3-24 h, rt or reflux, 54-99% yield. Acylation selectivity is a very sensitive function of steric effects this reagent selectively acylates pyrrolidine over piperidine (15 1). It is more selective than the diacetylaminoquinazolinones. ... 

Alkylation of orgatiomatigatiese reagaits witli alkyl bromides can also be improved by adrlition of CuCl f3 mol96). Hie reactions proceed at room temperature and are complete witliin a few bouts [123, 130], Hie opening of epoxides is also improved under tliese conditions. Hie reaction also features good clienioselectivity, tolerating tlie presence of sensitive functions sucli as ketones t Sclieme 2.59) [130]. 

For starting materials containing base- and/or acid-sensitive functional groups, modified procedures have been developed—e.g. using oxidizing agents. ... 

Approximate formulae for the point defect concentrations close (but not too close) to the stoichimetric composition in AB alloys have been derived. They show that the prefactors in the Arrhenius formulae are sensitive functions of the stoichiometry, besides representing the usual formation entropy term. 

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