Bakers’ transformation

Fig. 7.2 The top figure indicates a mixing protocol of mixing by stretching-cutting-stacking, yielding 2n+1 layers after n steps, in this case, n — 1. The bottom figure shows a stretching-folding bakers transformation yielding 1+2 layers, in this case, n — 2.

Figure E7.2 compares a stepwise increase in interfacial area in simple shear flow with optimal initial orientation, and simple shear flow where, at the beginning of each step, the interfacial area element is placed 45° to the direction of shear. The figure shows that, whereas in the former case the area ratio after four shear units is 4.1, in the latter case the ratio is 6.1, with a theoretical value of 7.3 when the 45° between the plane and direction of shear is maintained at all times. We note, however, that it is quite difficult to generate steady extensional flows for times sufficiently long to attain the required total elongational strain. This is why a mixing protocol of stepwise stretching and folding (bakers transformation) is so efficient. Not only does it impose elongational stretching, but it also distributes the surface area elements over the volume.

This is a version of the disk simulator but using a grid in the conformal space given by the Verbrugge/Baker transformation, as discussed in Chap. 12, page 224. 

Figure 3-34 Proportional base drive circuits (a) the Baker clamp (b) transformer-coupled proportional base drive.

Guirao and Bach (1979) used the flux-corrected transport method (a finite-difference method) to calculate blast from fuel-air explosions (see also Chapter 4). Three of their calculations were of a volumetric explosion, that is, an explosion in which the unbumed fuel-air mixture is instantaneously transformed into combustion gases. By this route, they obtained spheres whose pressure ratios (identical with temperature ratios) were 8.3 to 17.2, and whose ratios of specific heats were 1.136 to 1.26. Their calculations of shock overpressure compare well with those of Baker et al. (1975). In addition, they calculated the work done by the expanding contact surface between combustion products and their surroundings. They found that only 27% to 37% of the combustion energy was translated into work. 

Bioprocess plants are an essential part of food, fine chemical and pharmaceutical industries. Use of microorganisms to transform biological materials for production of fermented foods, cheese and chemicals has its antiquity. Bioprocesses have been developed for an enoimous range of commercial products, as listed in Table 1.1. Most of the products originate from relatively cheap raw materials. Production of industrial alcohols and organic solvents is mostly originated from cheap feed stocks. The more expensive and special bioprocesses are in the production of antibiotics, monoclonal antibodies and vaccines. Industrial enzymes and living cells such as baker s yeast and brewer s yeast are also commercial products obtained from bioprocess plants. 

Very little information exists in the literature on the transformation and degradation of methyl parathion in air. An early study indicated that direct photolysis of methyl parathion may occur however, the products of this photolysis were not determined (Baker and Applegate 1974). A later study found a transformation product of methyl parathion, methyl paraoxon, in air samples taken from areas where methyl parathion had been applied. Formation of methyl paraoxon was attributed to the vapor phase oxidation of methyl parathion (Seiber et al. 1989). Recent monitoring studies in California have also found both methyl parathion and methyl paraoxon (Baker et al. 1996). 

Direct photolysis does not appear to be a significant transformation process in soils. Only 5-17% of the methyl parathion concentration was lost over 50-60 days (half-life equal to 330 days) during a photolysis study (Baker and Applegate 1970). 

GERWIN B J, SPILLARE E, FORRESTER K, LEHMAN T A, KISPERT J, WELSH J A, PFEIFER A M, LECHNER J F, BAKER s J, VOGELSTEIN B et al. (1992) Mutant p53 can induce tumorigenic conversion of human bronchial epithelial cells and reduce their responsiveness to a negative growth factor, transforming growth factor beta 1 , Proc Natl Acad Sci USA, 89, 2759-63. 

Csuk, R. and Glaenzer, B.I. (1991) Baker s yeast mediated transformations in organic chemistry. Chemical Reviews (Washington, DC, United States), 91 (1), 49-97. 

Y )- Benzyl morpholine is a potent appetite suppressant drug. The synthesis of 2-(/ )-benzyl-morpholine began with the reduction of the unsaturated bromocinnamaldehyde to the corresponding saturated (X)-bromo-alcohol by baker s yeast, with a very low ee of 63%. However, an efficient transformation can be achieved by controlling the substrate concentration with the addition of hydrophobic resin Amberlite XAD-1180 [26]. With a resin-to-substrate ratio of one and an initial substrate concentration of 5 gL, the saturated (X)-bromo-alcohol was recovered at nearly quantitative yield and 98.6% ee. 

Newkome, G.R., Moorefield, C.N., Keith, J.M., Baker, G.R., and Escamilla, G.H. (1994) Chemistry of micelles. 37. Internal chemical transformations in a precursor of a unimolecular micelle boron supercluster via site-specific addition of BioH14 to cascade molecules. Angew. Chem., Int. Ed. Engl. 33, 666-668. 

Schliephake K, Mainwaring DE, Lonergan GT, Jones KI, Baker WL (2000) Transformation and degradation of the disazo dye Chicago sky blue by a purified laccase from Pycnoporus cinnabarinus. Enzyme Microb Biotechnol 27 100-107... 

Very few enzyme-catalysed reactions involving the reduction of alkenes have achieved any degree of recognition in synthetic organic chemistry. Indeed the only transformation of note involves the reduction of a, (3-unsaturated aldehydes and ketones. For example, bakers yeast reduction of (Z)-2-bromo-3-phenylprop-2-enal yields (S)-2-bromo-3-phenylpropanol in practically quantitative yield (99 % ee) when a resin is employed to control substrate concen-tration[50]. Similarly (Z)-3-bromo-4-phenylbut-3-en-2-one yields 2(5), 3(,S)-3-bromo-4-phenylbutan-2-ol (80% yield, >95% ee)[51]. Carbon-carbon double bond reductases can be isolated one such enzyme from bakers yeast catalyses the reduction of enones of the type Ar—CH = C(CH3)—COCH3 to the corresponding (S)-ketones in almost quantitative yields and very high enantiomeric excesses[52]. 

Enzyme reductions of carbonyl groups have important applications in the synthesis of chiral compounds (as described in Chapter 10). Dehydrogenases are enzymes that catalyse, for example, the reduction of carbonyl groups they require co-factors as their co-substrates. Dehydrogenase-catalysed transformations on a practical scale can be performed with purified enzymes or with whole cells, which avoid the use of added expensive co-factors. Bakers yeast is the whole cell system most often used for the reduction of aldehydes and ketones. Biocatalytic activity can also be used to reduce carbon carbon double bonds. Since the enzymes for this reduction are not commercially available, the majority of these experiments were performed with bakers yeast1 41. 

A Non-farnesylated Ha-Ras Protein Can Be Palmitoyl-ated and Trigger Potent Differentiation and Transformation, M. A. Booden, T. L. Baker, P. A. Solski, C. J. Der,... 

Fermenting baker s yeast transformed 2-butanone oxime containing 44% excess of the ( )-isomer into optically active (R)-2-aminobutane in 58% enantiomeric excess. The chiral amine was also obtained in 24% e.e. from the oxime acetate but the oxime methyl ether gave a racemic product (equation 2)16. 

Hoke, S.H.IL Morand, K.L. Greis, K.D. Baker, T.R. Harbol, K.L. Dobson, R.L.M. Transformations in Pharmaceutical Research and Development, Driven by Innovations in Multidimensional Mass Spectrometry-Based Technologies. Int. J. Mass Spectrom. 2001, 212, 135-196. 

In the MPC theory, the problem is not even posed. One starts defining the purely mathematical concept of dynamical system without any reference to a representation of reality. (The baker s transformation or the Bernoulli shift are obvious examples.) From here on, one proves mathematically the existence of a class of abstract dynamical systems (K-flows) that are intrinsically stochastic —that is, that possess precise mathematical properties (including a temporal symmetry breaking that can be revealed by a change of representation). 

At the time of publication of La Nouvelle Alliance the Prigoginian theory was still at the MPC stage. It is thus significant that aU general statements be illustrated only by the baker s transformation. It is only in Les Lois du Chaos (1994) and in La Fin des Certitudes (1996) that the Large Poincare Systems (LPS) show up. As stated in Section I.D 4, this concept results from the quest of real physical systems satisfying the criteria of intrinsic stochasticity. In this case, however, Prigogine and Petrosky were led to introduce a true modification... 

Our interest in the synthesis of deoxy- and deoxy-amino sugars of the L-series originates from studies (1 ) on the products obtained by the action of fermenting baker s yeasts on such aromatic, a,/9-unsaturated aldehydes as cinnamaldehyde (la) and a-methylcinnamaldehyde (lb ). The transformation proceeds as indicated in Eq. 

Note that in contrast to a general similarity transformation (e.g., as found in the usual coupled-cluster theory) the canonical transformation produces a Hermitian effective Hamiltonian, which is computationally very convenient. When U is expressed in exponential form, the effective Hamiltonian can be constructed termwise via the formally infinite Baker-Campbell-Hausdorff (BCH) expansion,... 

Yokelson, R. J J. G. Goode, R. A. Susott, R. E. Babbitt, D. E. Ward, S. P. Baker, W. M. Hao, and D. W. T. Griffith, Smoke Chemistry Measurements by Airborne Fourier Transform Infrared Spectroscopy (AFTIR), IGAC International Symposium on Atmospheric Chemistry and Future Global Environment, Nagoya, Japan, November 11-13, 1997b. 

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