Character transformation

Just as the expansion in the zeroth-order states can describe the exact molecular eigenstates, likewise an expansion in the exact states can be used to prepare, for a short time, a zeroth-order state. If the perturbation V is small, and the model Hamiltonian Ho is a good approximation to //, then the initially prepared superposition of eigenstates will resemble a zeroth-order state. The dephasing of the exact molecular eigenstates in the wave packet superposition subsequently leads to an evolution of the initial zeroth-order electronic character, transforming into a different zeroth-order electronic state as a function of time. 

In the present chapter we summarize recent phylogenetic and floral structural findings for the Marantaceae. By using additional ecological and geographical data, we reconstruct the major character transformations per node and test the hypotheses of the pollination mechanism being (1) a key innovation for speciation or (2) exclusively a tool for optimization of the mating system. 

The polarizability is a tensor which, like a vector, has transformation properties under symmetry operations. The character transform-... 

The optical character of a-spherulites is controlled by the ratio of radial to tangential fibrils. Raising the temperature of crystallization leads to a reduction in the proportion of tangential ones [181] and, simultaneously, a positive to negative character transformation. No tangential fibrils form above 155°C [172]. It was also revealed that the thickness of tangential fibrils was lower than that of the radial ones. 

While the trivial and trade nomenclature in most cases has accidental character, the lUPAC Commission has worked out a series of rules [4] which allow the great majority of structures to be represented uniformly, though there still exists some ambiguity within this nomenclature. Thus, many structures can have more than one name. It is important that the rules of some dialects of the lUPAC systematic nomenclature are transformed into a program code. Thus, programs for generating the names from chemical structures, and vice versa (structures from names) have been created [5] (see Chapter II, Section 2 in the Handbook). 

The importance of the characters of the symmetry operations lies in the fact that they do not depend on the specific basis used to form them. That is, they are invariant to a unitary or orthorgonal transformation of the objects used to define the matrices. As a result, they contain information about the symmetry operation itself and about the space spanned by the set of objects. The significance of this observation for our symmetry adaptation process will become clear later. 

In doing so we have a < 2, (5 < 1. The character of the dependence of G on its arguments is completely determined by the transformation (4.169). It is of importance that the higher order terms have square growth in D u, D 17. Introduce the notation... 

The most important materials among nonlinear dielectrics are ferroelectrics which can exhibit a spontaneous polarization PI in the absence of an external electric field and which can spHt into spontaneously polarized regions known as domains (5). It is evident that in the ferroelectric the domain states differ in orientation of spontaneous electric polarization, which are in equiUbrium thermodynamically, and that the ferroelectric character is estabUshed when one domain state can be transformed to another by a suitably directed external electric field (6). It is the reorientabiUty of the domain state polarizations that distinguishes ferroelectrics as a subgroup of materials from the 10-polar-point symmetry group of pyroelectric crystals (7—9). 

To confirm that the matrix is amorphous following primary solidification, isothermal dsc experiments can be performed. The character of the isothermal transformation kinetics makes it possible to distinguish a microcrystalline stmcture from an amorphous stmcture assuming that the rate of heat released, dH/dt in an exothermic transformation is proportional to the transformation rate, dxjdt where H is the enthalpy and x(t) is the transformed volume fraction at time t. If microcrystals do exist in a grain growth process, the isothermal calorimetric signal dUldt s proportional to, where ris... 

Some weak electrophilic reagents, which are usually inert toward azoles, also react with quaternized azoles. Diazonium salts yield phenylhydrazones (Scheme 48) in a reaction analogous to the Japp-Klingemann transformation of /S-keto esters into phenylhydrazones in the dithiolylium series illustrated the product has bicyclic character. Cyanine dye preparations fall under this heading (see also Section 4.02.1.6.5). Monomethine cyanines are formed by reaction with an iodo quaternary salt, e.g. Scheme 49. Tri- and penta-methinecar-bocyanines (384 n = 1 and 2, respectively) are obtained by the reaction of two molecules of a quaternary salt with one molecule of ethyl orthoformate (384 n = 1) or/S-ethoxyacrolein acetal (384 n =2), respectively. 

Soft electrophiles will prefer carbon, and it is found experimentally that most alkyl halides react to give C-alkylation. Because of the n character of the HOMO of the anion, there is a stereoelectronic preference for attack of the electrophile approximately perpendicular to the plane of the enolate. The frontier orbital is ip2, with electron density mainly at O and C-2. The tpi orbital is transformed into the C=0 bond. The transition state for an 8 2 alkylation of an enolate can be represented as below. 

The transition state involves six partially delocalized electrons being transformed from one 1,5-diene system to another. The transition state could range in character from a 1,4-diradical to two nearly independent allyl radicals, depending on whether bond making or bond breaking is more advanced. The general framework for understanding the substituent effects is that the reactions are concerted with a relatively late transition state with well-developed C(l)—C(6) bonds. 

In the following table the characters of the principal isomerides and other transformation products of the cinchona alkaloids are summarised and references are given to the chief papers dealing with them, and upon which the foregoing account is based. The capital letters in brackets printed after the names of the substances refer to the formulae and explanatory footnote on p. 449. 

Chondrodendron polyanthum, 371 Chondrodendron tomentosum, 363, 371, 373, 377, 391 alkaloids, 376 Chondrodine, 363, 364 Chondrofoline, 364, 365 Chrycentrine, 172, 313 Chiysanthemine, 773 Chrysanthemum cineraricefoHum, 773 Chuchuara, 781 Chuehuhuasha, 781 Cicuta virosa, 13 Cinchamidine, 419, 429 Cinchene, 439 Cinchenine, 438, 439, 440 apoCinchenine, 440, 441 Cincholoipon, 438 Cincholoiponic acid, 438, 443 Cinchomeronic acid, 183 Cinchona alkaloid structure, synthesis, 457 Cinchona alkaloids, bactericidal action of some derivatives, 478 centres of asymmetry, 445 constitution, 435 formulae and characters of transformation products, 449, 451 general formula, 443 hydroxydihydro-bases, 448, 452-4 melting-points and specific rotations, 446... 

Thus, the Tsai-Wu tensor failure criterion is obviously of more general character than the Tsai-Hill or Hoffman failure criteria. Specific advantages of the Tsai-Wu failure criterion include (1) invariance under rotation or redefinition of coordinates (2) transformation via known tensor-transformation laws (so data interpretation is eased) and (3) symmetry properties similar to those of the stiffnesses and compliances. Accordingly, the mathematical operations with this tensor failure criterion are well-known and relatively straightforward. 

What are the mechanisms by which slow, laminar combustion can be transformed into an intense, blast-generating process This transformation is most strongly influenced by turbulence, and secondarily by combustion instabilities. A laminar-flame front propagating into a turbulent mixture is strongly affected by the turbulence. Low-intensity turbulence will only wrinkle the flame front and enlarge its surface area. With increasing turbulence intensity, the flame front loses its more-or-less smooth, laminar character and breaks up into a combustion zone. In an intensely turbulent mixture, combustion takes place in an extended zone in which... 

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