Corollary orders

Overhage, J.M., Tiernery, W.M., Zhou, X. andMcDonald, C.J. (1997) A randomized trial of corollary orders to prevent errors of omission. Journal of the American Medical... 

Use of the isolation or pseudo-order technique. This approach is discussed in Chapter 2, where it was shown how a second-order reaction could be converted to a pseudo-first-order reaction by maintaining one of the reactant concentrations at an essentially eonstant level. The same method may be usefully applied to eomplex reactions. In this way, for example. Scheme XI can be studied under conditions such that it functions as Scheme IX. A corollary that must be kept in mind is that a reaction system that is observed to behave in accordance with (as an example) Scheme IX may actually be more complex than it appears to be, if an unsuspected reactant is present under pseudo-order conditions. 

Membrane proteins in many cases are randomly distributed through the plane of the membrane. This was one of the corollaries of the fluid mosaic model of Singer and Nicholson and has been experimentally verified using electron microscopy. Electron micrographs show that integral membrane proteins are often randomly distributed in the membrane, with no apparent long-range order. 

A corollary of this rule has us note that the orders in the rate law [Eq. (6-26)] are lower than those in the equilibrium constant expression for Eq. (6-25). This signals that an intermediate is produced but rapidly consumed. 

The problem of relationship between the activation parameters-the so called isokinetic relationship or compensation law—is of fundamental importance in structural chemistry, organic or inorganic. However, there are few topics in which so many misunderstandings and controversies have arisen as in connection with this problem. A critical review thus seems appropriate at present, in order to help in clarifying ideas and to draw attention to this treatment of kinetic or equilibrium data. The subject has already been reviewed (1-6), but sufficient attention has not been given to the statistical treatment which represents the heaviest problems. In this review, the statistical problems are given the first place. Theoretical corollaries are also dealt with, but no attempt was made to collect all examples from the literature. It is hoped that most of the important... 

That this should be so is a corollary of the Second Law of Thermodynamics which is concerned essentially with probabilities, and with the tendency for ordered systems to become disordered a measure of the degree of disorder of a system being provided by its entropy, S. In seeking their most stable condition, systems tend towards minimum energy (actually enthalpy, H) and maximum entropy (disorder or randomness), a measure of their relative stability must thus embrace a compromise between H and S, and is provided by the Gibb s free energy, G, which is defined by,... 

Thus, reactions affording either cyclopropanes or propylenes would most likely represent forms of termination of metathesis activity. As a corollary, any catalytic conversion of cyclopropanes to metathesis olefins via Eq. (26) would seem to require decomposition of the metal-carbene species in order to regenerate a naked metal species (M ) capable of further reactions with cyclopropanes. Of course, bimolecular carbene decomposition to yield an olefin as in Eq. (11) (e.g., ethylene from 2M=CH,) is one accepted process which could account for regeneration of M ... 

The functions of porous electrodes in fuel cells are 1) to provide a surface site where gas/liquid ionization or de-ionization reactions can take place, 2) to conduct ions away from or into the three-phase interface once they are formed (so an electrode must be made of materials that have good electrical conductance), and 3) to provide a physical barrier that separates the bulk gas phase and the electrolyte. A corollary of Item 1 is that, in order to increase the rates of reactions, the electrode material should be catalytic as well as conductive, porous rather than solid. The catalytic function of electrodes is more important in lower temperature fuel cells and less so in high-temperature fuel cells because ionization reaction rates increase with temperature. It is also a corollary that the porous electrodes must be permeable to both electrolyte and gases, but not such that the media can be easily "flooded" by the electrolyte or "dried" by the gases in a one-sided manner (see latter part of next section). 

The "principle of microscopic reversibility", which indicates that the forward and the reverse reactions must proceed through the same pathway, assures us that we can use the same reaction mechanism for generating the intermediate precursors of the "synthesis tree", that we use for the synthesis in the laboratory. In other words, according to the "principle of microscopic reversibility", [26] two reciprocal reactions from the point of view of stoichiometry are also such from the point of view of their mechanism, provided that the reaction conditions are the same or at least very similar. A corollary is that the knowledge of synthetic methods and reaction mechanisms itself -according to the electronic theory of valence and the theory of frontier molecular orbitals- must be applied in order to generate the intermediate precursors of the "synthesis tree" and which will determine the correctness of a synthesis design and, ultimately, the success of it. 

In terms of local order about the cations, it is generally argued that according to Pauhng s rules [257], M cations should not occupy adjacent sites (unless accompanied by vacant cation sites, i.e. a gibbsite unit within a brucite layer [56]) the corollaries of this are that the minimum possible f jg 2 and that when is exactly equal to 2 there is also... 

It is most remarkable that the entropy production in a nonequilibrium steady state is directly related to the time asymmetry in the dynamical randomness of nonequilibrium fluctuations. The entropy production turns out to be the difference in the amounts of temporal disorder between the backward and forward paths or histories. In nonequilibrium steady states, the temporal disorder of the time reversals is larger than the temporal disorder h of the paths themselves. This is expressed by the principle of temporal ordering, according to which the typical paths are more ordered than their corresponding time reversals in nonequilibrium steady states. This principle is proved with nonequilibrium statistical mechanics and is a corollary of the second law of thermodynamics. Temporal ordering is possible out of equilibrium because of the increase of spatial disorder. There is thus no contradiction with Boltzmann s interpretation of the second law. Contrary to Boltzmann s interpretation, which deals with disorder in space at a fixed time, the principle of temporal ordering is concerned by order or disorder along the time axis, in the sequence of pictures of the nonequilibrium process filmed as a movie. The emphasis of the dynamical aspects is a recent trend that finds its roots in Shannon s information theory and modem dynamical systems theory. This can explain why we had to wait the last decade before these dynamical aspects of the second law were discovered. 

Rule 3.7 (Corollary). If an ion is placed in an environment in which the average bond length is too long, i.e. in a cavity which is too large for the ion, the environment will distort in such a way as to increase the lengths of some bonds and decrease the lengths of others in order to raise the bond valence sum to the expected value. 

Metallic corrosion is a major engineering and economic problem. In North America and Europe, the cost of corrosion is on the order of 3-4% of gross domestic product (GDP). Not surprisingly, there is an abundance of good books on this topic.1 15 This chapter focuses mainly on corrosion of metals in aqueous systems, as this is the most commonly encountered problem and is a natural corollary of the material of the two preceding chapters. 

Fe2S2] clusters are part of the molybdenum containing hydroxylases. Typically, apart from molybdenum and two EPR-distinct iron-sulfur centres there can be FAD as additional cofactor. In Chlostridium purinolyticum a selenium-dependent purine hydroxylase has been characterized as molybdenum hydroxylase. The EPR of the respective desulfo molybdenum (V) signal indicated that the Mo-ligands should differ from those of the well known mammalian corollary xanthine oxidase.197 For the bacterial molybdenum hydroxylase quinoline oxidoreductase from Pseudomonas putida an expression system was developed in order to be able to construct protein mutants for detailed analysis. EPR was used to control the correct insertion of the cofactors, specifically of the two [Fe2S2] clusters.198... 

Theorem 3 and Corollary 2 transform the question of existence of Kekule structures in benzenoid systems to an algebraic problem. But it is also of little practical use, since the calculation of determinants of high orders is troublesome. 

---