Series, termination effect

The maximum entropy method also offers the possibility of super-resolution , i.e., better resolution than might be anticipated than the simple analogy with optical systems (section 2(a)). Series termination effects in conventional Fourier syntheses lead to negative regions around the peaks. The maximum entropy principle ensures that the density is everywhere positive and gives much sharper peaks in which series termination effects have been suppressed [261,263]. 

If the focus of interest is on the carbon clusters themselves, then of course no substitute system can be used. However, for studying the convergence of properties towards bulk values one can minimize the termination effects by saturating the dangling bonds in the simplest possible way, i.e. with hydrogen. By that approach one can both avoid the problem of handling an excessive number of open shells, and obtain a series of molecules that converge towards bulk properties more smoothly than the bare carbon clusters. 

Series-termination errors Errors that result from a limitation in the number of terms in a Fourier series. Ideally an infinite number of data is required to calculate a Fourier series. In practice, the number of data depends on the resolution (reciprocal radius or sin0/A) to which the data have been measured. Because of truncation of the Fourier series at the highest value of sin 0/X of the data, peaks in the resulting Fourier syntheses are surrounded by a series of ripples. These are especially noticeable around a heavy atom because its scattering factor is still appreciable at the highest values of sin 9/X measured. Difference maps (q-v.) can be used to obviate most of the effects of series-termination errors. 

The difference between 1-octyne and 2-octyne is a typical terminal effect for alkynes. Ahyd// of all the linear monoalkynes in this series were measured in -hexane solution. 

The polymerization rate is directly proportional to the monomer concentration for ideal free radical polymerization kinetics. Deviations from this first-order kinetics can be caused by a whole series of effects which must be checked by separate kinetic experiments. These effects include cage effects during initiator free radical formation, solvation of or complex formation by the initiator free radicals, termination of the kinetic chain by primary free radicals, diffusion controlled termination reactions, and transfer reactions with reduction in the degree of polymerization. Deviations from the square root dependence on initiator concentration are to be primarily expected for termination by primary free radicals and for transfer reactions with reduction in the degree of polymerization. 

The upshot of the argument is that even a series that consists of an infinite number of causes possible of existence and includes absolutely all such causes must, as a whole, have a cause that falls outside it. This cause cannot be possible of existence, but must be something necessary of existence in itself. What Avicenna concludes here is effectively that even if an infinite series of possible causes is postulated, it cannot be self-sufficient with respect to its existence for if this infinite series is bracketed and considered as a self-contained whole, it must depend ultimately on a cause necessary of existence, beyond which no further cause exists. Avicenna s proof for the existence of the First Cause concludes with the statement, Therefore, every series terminates (tantahi) in the Necessary of Existence through Itself (Ishardt 11.4.15). Which implies that Avicenna s proof for the existence of God can be read as a reductio ad absurdum, whereby the starting hypothesis (the series is infinite) is shown to be impossible (the series must terminate at some point, and hence must be finite). This conclusion is spelled out explicitly in the Najdt ... 

The effect of forming a more rigid structure in fluorescent dyes of the rhodamine series has been clearly demonstrated (18) with the remarkable dye designated Rhodamine 101 [41175A3-3] (19). This dye has its terminal nitrogen atoms each held in two rings and has a fluorescence quantum yield of virtually 100% independent of the temperature. 

Bismaleimides are best defined as low molecular weight, at least diftinctional monomers or prepolymers, or mixtures thereof, that carry maleimide terminations (Eig. 3). Such maleimide end groups can undergo homopolymerization and a wide range of copolymerizations to form a highly cross-linked network. These cure reactions can be effected by the appHcation of heat and, if required, ia the presence of a suitable catalyst. The first patent for cross-linked resias obtained through the homopolymerization or copolymerization of BMI was granted to Rhc ne Poulenc, Erance, ia 1968 (13). Shordy after, a series of patents was issued on poly(amino bismaleimides) (14), which are synthesized from bismaleimide and aromatic diamines. 

The number of thyristors in series, each selected for an impulse voltage of a little less than the impulse voltage with.stand level of the terminal equipment (Table 11.6) can effectively limit the switching overvoltages within desired safe limits. Then connecting them in anti-parallel will mean that the voltage will be forward for either of... 

Alumiojuffl resists corrosion not because of its position in the electrochemical series but because of the ra Hd formation of a coherent, inert, oxide layer. Contact with grafihite, Fe. Ni. Cu, Ag or Pb is disastrous for corrosion resistance, the effect of contact with steel, Zn and Cd depends on pH and exposure conditions. Protection is enhanced by anodizing the metal this involves immersing it in 15-20% H2SO4 and connecting it to the positive terminal so that it becomes coated with alumina ... 

Replacement of the terminal nitrogen of the piperazine by carbon is said to enhance the antiemetic activity of the phenothiazines at the expense of the other pharmacologic effects. The simplest compound in this series, pipamazine (88), is prepared by alkylation of nipecotamide (87) with the chloropropyl phenothiazine (58). Preparation of the analogous sulfoxide begins with acetylation of the thiomethyl compound, 89 [prepared by a route... 

Table 1 shows the kinetic data available for the (TMSjsSiH, which was chosen because the majority of radical reactions using silanes in organic synthesis deal with this particular silane (see Sections III and IV). Furthermore, the monohydride terminal surface of H-Si(lll) resembles (TMSjsSiH and shows similar reactivity for the organic modification of silicon surfaces (see Section V). Rate constants for the reaction of primary, secondary, and tertiary alkyl radicals with (TMSIsSiH are very similar in the range of temperatures that are useful for chemical transformations in the liquid phase. This is due to compensation of entropic and enthalpic effects through this series of alkyl radicals. Phenyl and fluorinated alkyl radicals show rate constants two to three orders of magnitude... 

A series of theoretical studies of the SCV(C)P have been reported [38,40,70-74], which give valuable information on the kinetics, the molecular weights, the MWD, and the DB of the polymers obtained. Table 2 summarizes the calculated MWD and DB of hyperbranched polymers obtained by SCVP and SCVCP under various conditions. All calculations were conducted, assuming an ideal case, no cyclization (i.e., intramolecular reaction of the vinyl group with an active center), no excluded volume effects (i.e., rate constants are independent of the location of the active center or vinyl group in the macromolecule), and no side reactions (e.g., transfer or termination). 

The effect of core shielding of a porphyrin moiety by peripheral dendrons has been carefully investigated on two series of Zn-phthalocyanine-cored dendrimers with aryl-ether branches [60]. Generation 0,1, and 2 (dendrimer 27) species, terminated with ester groups, are soluble in organic solvents, while the species terminated with carboxylate units (e.g., 28) are soluble in water. 

Johnson, T. W. Kostic, N. M. Steric effect on the rate of hydrolysis by Pd(II) complexes of the C-terminal amide bond in a series of dipeptides Ac-Met-AA, American Chemical Society, Washington, D. C. In Book of Abstracts, 212th ACS National Meeting, Orlando, FL, August 25-29, 1996. 

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