Cyclic sequence

Scheme 2. The cyclic sequence of hydrogen bonds in diol structures...

What is the difference between the systems initiator-RH and initiator- RH Oz that is responsible for the initiation of the chain reaction It is apparent that, in contrast to the former system, the radical R in the latter system is regenerated via a cyclic sequence of chemical conversions. The analysis of this system and other similar systems suggests that a chain reaction can be sustained only in a system where radicals are involved in a cyclic sequence of conversions with the conservation of free valence. It is the multiple repetition of conversion cycles that leads to the chain reaction [2,3]. 

A reaction mechanism may involve one of two types of sequence, open or closed (Wilkinson, 1980, pp. 40,176). In an open sequence, each reactive intermediate is produced in only one step and disappears in another. In a closed sequence, in addition to steps in which a reactive intermediate is initially produced and ultimately consumed, there are steps in which it is consumed and reproduced in a cyclic sequence which gives rise to a chain reaction. We give examples to illustrate these in the next sections. Catalytic reactions are a special type of closed mechanism in which the catalyst species forms reaction intermediates. The catalyst is regenerated after product formation to participate in repeated (catalytic) cycles. Catalysts can be involved in both homogeneous and heterogeneous systems (Chapter 8). 

Although one can probably find exceptions, most equilibrium calculations involving flue gas slurries are performed with temperature as a known variable. With temperature known, the numerical values of the appropriate equilibrium constants can be immediately calculated. The remaining unknown variables to be determined are the activities, activity coefficients, molalities, and the gas phase partial pressures. The equations used to determine these variables are formulated from among the equilibrium expressions presented in Table 1, the expressions for the activity coefficients, ionic strength, material balance expressions, and the electroneutrality balance. Although there are occasionally exceptions, the solution sequence generally is an iterative or cyclic sequence. 

The success of these model experiments led Bonner and coworkers to propose a mechanism involving repetitive cyclic sequences of partial polymerization followed by partial depolymerizaton in which the latter is caused by hydrolysis. Thus, this process is driven by environmental dry and wet cycles that could ultimately have led to homochiral polypeptides on early Earth. [97] Brach and Spach [95] have also proposed a mechanism involving partial hydrolysis for the enantiomeric enrichment of polypeptides having (3-sheet secondary structures. 

We think about metabolic pathways as linear or cyclical sequences of reactions as described in Chapter 1. Individual reactions within a pathway are often dependant upon at least one other reaction. For example, we know from our studies of enzyme kinetics in Chapter 2 that the rate of an enzyme catalysed reaction is determined in part by the concentration of substrate. Remember, the substrate for one reaction is usually the product of a previous reaction, so the activity of an enzyme is affected by the activity of the preceding enzyme in the sequence. 

The scientific research method consists of a cyclic sequence of experimental and logical steps designed to yield knowledge about the world by using conjecture and appeals to experience. The first step in the sequence is to divide the world into a conveniently sized part called the study system and a complementary part called the environment. A study system and its complement are created by and for the convenience of the investigator only. A study system can be of any size and type as long as it is known where in the universe it comes from and exactly where it fits in it. 

This is not a restatement of the old observation that science is influenced diffusely and subtly by the prevailing value system of societv(22). It is to say that value-laden judgments are specific, readily identifiable and necessary parts of the cyclic sequence of activities that make up the scientific research method. Such judgments are the scientists means of coping with experimental uncertainty, i.e., the decision rules for testing statistical hypotheses (g.). ... 

Urea is produced only in the liver, in a cyclic sequence of reactions (the urea cycle) that starts in the mitochondria and continues in the cytoplasm. The two nitrogen atoms are derived from NH4 " (the second has previously been incorporated into aspartate see below). The keto group comes from hydrogen carbonate (HC03 ), or CO2 that is in equilibrium with HC03. ... 

The cyclical sequence of Gi, S, G2 and M phases describes a standard cell cycle (Fig. 13.1). Rapidly dividing cells in mammals require 12-24 h for completion of a cell cycle. 

The cyclic sequence of Reactions 5 and 6 can be accelerated by adding a species which promotes the formation of Co(III) from Co(II). In the oxidation of alkylaromatic hydrocarbons ozone (7), acetaldehyde (8), and methyl ethyl ketone (4) act as promoters in this way. 

Nitric acid can also catalyze the oxidation by oxidizing Co (II) to Co (III), thus facilitating the cyclic sequence of Reactions 5 and 6. 

The s process terminates at 209Bi because of the cyclic sequence ... 

One often finds cyclic sequences for which conditions are a set of inequalities. These are stable cycles, since in the space of the delays (which has 2n dimensions if there are n variables), there is a 2 -dimen-sional manifold within which the conditions are fulfilled if one stands in that domain, one can change the value of one or more delay and yet remain within the range of the constraints. In other words, these cycles are, within certain limits, stable toward alterations of the time delays. There exist even cycles which, once reached, persist whatever the values of the time delays. This situation takes place each time one deals with a cycle for which each state has only one possible next state (only one dash). 

For other cyclic sequences, one finds among the conditions one (or more) equality between combinations of delays. These are unstable cycles because, starting from the conditions which would permit the system to go through them, the slightest modification of the value of one of the delays involved in the equality would induce the system to leave this trajectory. Another way to characterize this situation is to remark that in the 2n-dimensional space of the delays there is only a 2n - 1 manifold (hypersurface) within which the conditions are fulfilled. 

The sum of the many organic reactions that take place in cells is called metabolism. These reactions usually occur in long sequences, which may be either linear or cyclic. In a linear sequence, the product of one reaction serves as the starting material for the next. In a cyclic sequence, a series of reactions regenerates the first reactant and produces other products along the way. 

The earlier PSA units typically utilized 2,3, or 4 adsorber beds in a cyclic sequence in which one of the beds was always on an adsorption step while the other bed or beds were being regenerated. However, these systems were inherently inefficient for two reasons. First, the blowdown from adsorption pressure to the low waste pressure caused large losses of the desired product gas which was stored in the bed at high pressure. Second, some pure product gas was cycled to waste since it was used to purge a regenerating bed. 

Every summand in the denominator is the spanning tree weight. Let us recall that, in this case, the sense of the spanning tree is a non-cyclic sequence of reactions with the help of which a given intermediate is formed of all others. Hence it can easily be shown that (a) every summand of the denominator Z.XDX and of the matching parameter Pt cannot simultaneously contain weights for the direct and reverse reactions of the same step (b)... 

As an external observer, this means not positioned on the surface itself, we can have two positions relative to the surface we can be on the inside or the outside . Suppose we are on the outside and look at a graph on the surface, then for every vertex, we can write down a cyclic sequence (clockwise or counterclockwise) of... 

The solution of the puzzle is according to modern views that in the case of a cyclic process the only possible stationary value of the rotational flow in a cyclic sequence is zero, which is known as the principle (or axiom) of microscopic reversibility. 

The time is ripe for truly exciting developments in the reactivity of dinuclear transition metal compounds. The potential for cyclic sequences of reactions, as is required for catalytic reactions, has already been realized. (1) It has been shown, by Muetterties, et al. (53), that alkynes can be selectively hydrogenated to alkenes (cU 2H-addition) by Cp2Mo2(C0) the rate determining step involves CO dissociation from the acetylene adducts Cp2MO2(C0) (R2C2). (2) We have found that... 

Possible intermediates of the form M=N—NH3 have been observed and characterized they are stable when M = W but react to form NH3 when M = Mo. In a cyclic sequence of reactions that can be driven chemically or electrochemically, protonation of bound N2 occurs in a stepwise manner, with electrons flowing from the metal atom as protons are picked up from solution. 

The symbol R is assigned if the cyclic sequence of priority numbers, proceeding from highest priority, is clockwise when the viewer is looking down the vector from the tetrahedral centre to the least preferred substituent (the substituent having the priority number with the highest numerical value, i.e. 4). An anticlockwise cyclic sequence is assigned the symbol S. 

Houdry s Catofin and similar processes employ a cyclic sequence of steps—process, purge, air regeneration, purge, hydrogen reduction, and back to process. 

---