Intertwining number

The number of helical turns in these structures is larger than those found so far in two-sheet p helices. The pectate lyase p helix consists of seven complete turns and is 34 A long and 17-27 A in diameter (Figure 5.30) while the p-helix part of the bacteriophage P22 tailspike protein has 13 complete turns. Both these proteins have other stmctural elements in addition to the P-helix moiety. The complete tailspike protein contains three intertwined, identical subunits each with the three-sheet p helix and is about 200 A long and 60 A wide. Six of these trimers are attached to each phage at the base of the icosahedral capsid. 

Shock-induced solid state chemistry represents the most complex fundamental problem ever encountered in shock-compression science. All the mechanical and physical complications of other work are present, yet the additional chemical complications are added. Indeed, all mechanical, physical, and chemical aspects of the problem are intimately intertwined. Chemical investigations promise to provide a description of shock compression that differs considerably from that to which we have become accustomed. Nevertheless, a full description of the process requires contributions from a number... 

The basic parameter characterizing supercoiled DNA is the linking number (L). This is the number of times the two strands are intertwined, and, provided both strands remain covalently intact, L cannot change. In a relaxed circular... 

Although blood pressure control follows Ohm s law and seems to be simple, it underlies a complex circuit of interrelated systems. Hence, numerous physiologic systems that have pleiotropic effects and interact in complex fashion have been found to modulate blood pressure. Because of their number and complexity it is beyond the scope of the current account to cover all mechanisms and feedback circuits involved in blood pressure control. Rather, an overview of the clinically most relevant ones is presented. These systems include the heart, the blood vessels, the extracellular volume, the kidneys, the nervous system, a variety of humoral factors, and molecular events at the cellular level. They are intertwined to maintain adequate tissue perfusion and nutrition. Normal blood pressure control can be related to cardiac output and the total peripheral resistance. The stroke volume and the heart rate determine cardiac output. Each cycle of cardiac contraction propels a bolus of about 70 ml blood into the systemic arterial system. As one example of the interaction of these multiple systems, the stroke volume is dependent in part on intravascular volume regulated by the kidneys as well as on myocardial contractility. The latter is, in turn, a complex function involving sympathetic and parasympathetic control of heart rate intrinsic activity of the cardiac conduction system complex membrane transport and cellular events requiring influx of calcium, which lead to myocardial fibre shortening and relaxation and affects the humoral substances (e.g., catecholamines) in stimulation heart rate and myocardial fibre tension. 

Just as in everyday life, in statistics a relation is a pair-wise interaction. Suppose we have two random variables, ga and gb (e.g., one can think of an axial S = 1/2 system with gN and g ). The g-value is a random variable and a function of two other random variables g = f(ga, gb). Each random variable is distributed according to its own, say, gaussian distribution with a mean and a standard deviation, for ga, for example, (g,) and oa. The standard deviation is a measure of how much a random variable can deviate from its mean, either in a positive or negative direction. The standard deviation itself is a positive number as it is defined as the square root of the variance ol. The extent to which two random variables are related, that is, how much their individual variation is intertwined, is then expressed in their covariance Cab ... 

The scale of the cells within the multifilament strand is controlled by two factors (1) the number of primary filaments bundled into the second feedrod, and (2) the size of the extrusion die used to form the second filament. The number of filaments bundled into the second feedrod is determined by both the size of the primary filaments and the size of the second feedrod. The decreasing ratio of extrusion die sizes results in a dramatic increase in the number of cells within a strand. In addition to making finer cell sizes possible, it is also much easier to lay coarse multifilament strands into a die than it is to lay small fibers. The strands lay straight and flat, whereas fibers tend to curl up and become intertwined. However, despite the fine cell size, the coarseness of the strands limits their use to architectures in which the scale of a cluster of cells is no less than 0.75 mm. 

Structural studies of the oxy-Cope catalytic antibody system reinforce the idea that conformational dynamics of both protein and substrate are intimately intertwined with enzyme catalysis, and consideration of these dynamics is essential for complete understanding of biologically catalyzed reactions. Indeed, recent single molecule kinetic studies of enzyme-catalyzed reactions also suggest that different conformations of proteins are associated with different catalytic rates (Xie and Lu, 1999). In addition, a number of enzymes are known to undergo conformational changes on binding of substrate (Koshland, 1987) that lead to enhanced catalysis two examples are hexokinase (Anderson and Steitz, 1975 Dela-Fuente and Sols, 1970) and triosephosphate isomerase (Knowles, 1991). 

Seven position titles—trustee, director, curator, conservator, exhibition specialist, restorer, and caretaker—are most often encountered in museums. People in these positions are expected to carry out the functions of acquisition, study, conservation, and presentation with due consideration of the impact of these functions on preserving the collection. Indeed, only with the combined effort of these workers can preservation be guaranteed. Often one person must carry out more than one function in other cases, a number of people share one function. In all instances, however, their responsibilities do intertwine, so that everyone concerned must work together in good faith. 

Since electrochemical methods are described in Volume 7, Chapter 7.1, emphasis will be placed on the thermal and photochemical activation of electron-transfer oxidation. Even with this restriction the scope of electron-transfer oxidation is too extensive to be covered completely in a single chapter. Therefore the approach here is to present those fundamental aspects that allow electron-transfer oxidations to be developed for synthetic transformations. Hopefully this format will encourage the creative chemist to devise myriad oxidative syntheses from a limited number of principles. Fortunately, there are already available a variety of recent monographs with each presenting a restricted coverage to permit the inclusion of detailed and useful examples. For the convenience of the reader these articles are listed as references 17 to 32, with the chapter titles included where appropriate. Taken all together they offer the reader an interesting panoply of electron-transfer oxidations that are intertwined by the principles outlined herein. 

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