Rule of fours

Godwin, Joscelyn. The real rule of four. New York Disinformation, 2004. 192p. ISBN 1-932857-08-7... 

A study of Hypnerotomachia Poliphili, using the novel by Ian Cauldwell The rule of four as a starting point. "You ve read The Rule of Four, now read about its source, the Hypnerotomachia Poliphili. The Rule of Four by Ian Caldwell and Dustin Thomason is a runaway international bestseller, topping the charts on both sides of the Atlantic. But the foundation of The Rule of Four, as all its readers know, is a little-known text from the fifteenth century, the Hypnerotomachia Poliphili. 

Erudite and engaging, The Real Rule of Four is the perfect companion piece to The Rule... 

Cauldwell, Ian and Dustin Thomason. The rule of four. Arrow Books, 2005. 527p. ISBN 0-09-945195-6... 

A petition for certiorari means that the petitioner is asking the court to use its discretionary power to review the case. The Supreme Court hears most cases on petition known as a writ of certiorari. Of the thousands of writs received in a given year, fewer than 100 are granted. To accept a case on a writ of certiorari, four out of the nine justices must agree (the so-called rule of four) that the petition should be granted. 

With the plating of fasteners, some special considerations apply, particularly in respect to threads (Ref 8). As might be expected, electroplated metals build up faster on apexes of the threads, and coverage can be minimal at the bottom of the grooves. ANSI Specification B 1.1 states that compared to flat surfaces, plating thickness builds up six times faster on the major diameter than the minor diameter and that this results in a fourfold buildup on the pitch diameter, as illustrated in Fig. S. This is known as the Rule of Four and Six. ... 

The area under a parabolic arc concave upward is bh, where b is the base of the figure and h is its height. The area of a parabolic arc concave downward is jh/t. The areas of parts of the figure diagrammed for Simpson s rule integration are shown in Fig. 1-3. The area A under the parabolic arc in Fig. 1-3 is given by the sum of four terms ... 

The economics of the various methods that are employed to sequence multicomponent columns have been studied. For example, the separation of three-, four-, and five-component mixtures has been considered (44) where the heuristics (rules of thumb) developed by earlier investigators were examined and an economic analysis of various methods of sequencing the columns was made. The study of sequencing of multicomponent columns is part of a broader field, process synthesis, which attempts to formalize and develop strategies for the optimum overall process (45) (see Separation systems synthesis). 

Distillation columns have four or more closed loops—increasing with the number of product streams and their specifications—all of which interact with each other to some extent. Because of this interaction, there are many possible ways to pair manipulated and controlled variables through controllers and other mathematical functions with widely differing degrees of effectiveness. Columns also differ from each other, so that no single rule of configuring control loops can be apphed successfully to all. The following rules apply to the most common separations. 

A brief overview of the form for rate equations reveals that temperature and concentration e Tects are strongly interwoven. This is so even if all four basic steps in the rules of Boudart (1968) are obeyed for the elementary steps. The expectations of simple unchanging temperature effects and strict even-numbered gas concentration dependencies of rate are not justified. 

All the well-characterized proteinases belong to one or other of four families serine, cysteine, aspartic, or metallo proteinases. This classification is based on a functional criterion, namely, the nature of the most prominent functional group in the active site. Members of the same functional family are usually evolutionarily related, but there are exceptions to this rule. We... 

The term (l/((Un) is sometimes ealled the equivalent time eonstant Tc for a seeond-order system. Note that In50 (2% toleranee) is 3.9, and ln20 (5% toleranee) is 3.0. Thus the transient period for both first and seeond-order systems is three times the time eonstant to within a 5% toleranee band, or four times the time eonstant to within a 2% toleranee band, a useful rule-of-thumb. 

The foregoing are but examples of the types of mechanics of materials approaches that can be used. Other assumptions of physical behavior lead to different expressions for the four elastic moduli for a unidirectionally reinforced lamina. For example, Ekvall [3-2] obtained a modification of the rule-of-mixtures expression for and of the expression for E2 in which the triaxial stress state in the matrix due to fiber restraint is accounted for ... 

Figure 2.9 shows a typical Gc topology, computed for a one-dimensional lattice consisting of four viu tices and evolving according to totalistic rule T2. 

A remarkable, but (at first sight, at least) naively unimpressive, feature of this rule is its class c4-like ability to give rise to complex ordered patterns out of an initially disordered state, or primordial soup. In figure 3.65, for example, which provides a few snapshot views of the evolution of four different random initial states taken during the first 50 iterations, we see evidence of the same typically class c4-like behavior that we have already seen so much of in one-dimensional systems. What distinguishes this system from all of the previous ones that we have studied, however, and makes this rule truly remarkable, is that Life has been proven to be capable of universal computation. 

Mirrors BBMCA rule (e), and its rotated equivalents, allows groups of particles to be built up to form stable configurations. Such configurations can then be used as mirrors to reflect balls, and thereby to act as signal routers. Figure 6.15, for example, shows the smallest possible fixed configuration consisting of four particles. Since adjacent squares remain uncoupled from one another, mirrors of arbitrary size can be built up from this basic four-particle mirror. 

Fig. 6.15 Smallest possible fixed mirror, formed by a stable arrangement of four particles. BBMCA rule (e) (see figure 6.12) is successively applied to even (i.e. thicic-lined) and odd (i.e. thin-lined) partitions of the lattice.

Consider a size N one-dimensional lattice with site variables Si t) = 1, i = On even (or odd) time steps, either even-indexed (or odd-indexed) sites evolve according to fixed probabilistic peripheral rules that is, according to rules that depend only on the values of a given site s neighboring sites. Such rules are completely specified by a set of four conditional probabilities, 0 < Ui < 1, i = T...4 ... 

In Woodcock, et al. s model, each combatant - or automaton - is endowed with a set of rules with which it can perform certain tasks. Rules are of four basic varieties ... 

In practice, oxidation numbers in all kinds of species are assigned according to a set of four arbitrary rules ... 

The four quantum numbers that characterize an electron in an atom have now been considered. There is an important rule, called the Pauli exclusion principle, that relates to these numbers. It requires that no two electrons in an atom can have the same set of four quan-... 

Each carbon atom forms a total of four covalent bonds. This is illustrated by the struc- Carbon always follows the octet rule in... 

Exdusion principle The rule stating that no two electrons can have the identical set of four quantum numbers, 141-142 Exhaustion, physical, 385 Exothermic reaction, 203 Exothermic Describes a process in which heat is evolved by a system AH is negative for an exothermic reaction, 208-210,212-213... 

The porphyrin ring system (the parent compound 1 is also known as porphin) consists of four pyrrole-type subunits joined by four methine ( = CH-) bridges to give a macrotetracycle. The macrocycle contains 227i-electrons from which 1871-electrons form a delocalized aromatic system according to Huckel s 4n + 2 rule for aromaticity. The aromaticity of the porphyrin determines the characteristic physical and chemical properties of this class of compounds. The aromatic character of porphyrins has been confirmed by determination of their heats of combustion.1"3 X-ray investigations4 of numerous porphyrins have shown the planarity of the nucleus which is a prerequisite for the aromatic character. 

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