Other Variants

There are at least as many variants of the basic CA algorithm as there are ways of generalizing the characteristics of a typical CA system. Here are a few general models  

Asynchronous CA. CA rules are typically defined so that all lattice sites update their values simultaneously throughout the lattice on each time step. A natural generalization is to lift this restriction by allowing asynchronous updates [inger84]. 

Coupled-map Lattices. Another obvious generalization is to lift the restriction that sites can take on only one of a few discrete values. Coupled-map lattices are CA models in which continuity is restored to the state space. That is to say, the cell values are no longer constrained to take on only the values 0 and 1 as in the examples discussed above, but can now take on arbitrary real values. First introduced by Kaneko [kaneko83]-[kaneko93], such systems are simpler than partial differential equations but more complex than generic CA. Coupled-map lattices are discussed in chapter 8. 

Probabilistic CA. Probabilistic CA are cellular automata in which the deterministic state-transitions are replaced with specifications of the probabilities of the cell-value assignments. Since such systems have much in common with certain statistical mechanical models, analysis tools from physics are often borrowed for their study. Probabilistic CA are introduced in chapter 8. 

Non-homogeneous CA. These are CA in which the state-transition rules are allowed to vary from cell to cell. The simplest such example is one where there are only two different rules randomly distributed throughout the lattice. Kauffman [kauff84] has studied the otlier extreme in whidi tlie lattice is randomly populated with all possible Boolean functions of k inputs. 

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Catalytic Processes. A second group of refining operations which contribute to gas production are the catalytic cracking processes, such as fluid-bed catalytic cracking, and other variants, in which heavy gas oils are converted into gas, naphthas, fuel oil, and coke (5). 

Besides the estabUshed audio CD and CD-ROM, there are other variants of optical storage disks with imprinted information which differ in the way the data are processed. 

One other variant in double-bond polymerisations may be mentioned here. Many conjugated dienes may be polymerised in such a way as to generate long chain molecules with residual double bonds in the chain. Well-known examples of such dienes are buta-1,3-diene and isoprene, which yield 1,4-polybutadiene and 1,4-polyisoprene respectively (Figure 2.4). Natural rubber has a formula corresponding to the 1,4-polyisoprene. 

IBM in California by Eigler and Schweizer (1990), who manipulated individual xenon atoms aeross a niekel (110) crystal surfaee. In the immediate aftermath of this achievement, many other variants of atom manipulation by STM have been published, and DiNardo surveys these. 

It was found inadvisable to use more than four molecules of form-amide [ (47) when R = H] per molecule of anthranilic acid and the condensation produces best results when the mixture is heated at 120 -130°C for 2 hr followed by further heating at 170°-180 C for 2 hr. Other variants of this reaction involve the use of ammonium o-acylaminobenzoates, anthranilic acid in the presence of nitriles and acetic anhydride, o-acetamidonitrile with acetic anhydride or hydrogen peroxide, anthranilic esters and aliphatic or aromatic amides or amidines, isatoic anhydride with amides or amidines, and anthranilic esters with aryl iminochlorides in acetoned The mechanism proposed by Bogert and Gotthelf has had experimental supporR and is represented in Scheme 12. 

Centronuclear myopathy with type 1 fiber hypotrophy is sometimes regarded as a separate entity because many cases show central nuclei only in the hypotrophic type 1 fibers, while the type 2 fibers are morphologically normal. Affected type 1 fibers are even more myotubelike than in other variants of the disorder, with the exception of the severe X-linked form, due to the persistence of a mitochondria-rich core within a peripheral ring of myofibrils. These features are clearly demonstrable using histochemical methods for the localization of SDH activity and myofibrillar ATPase, respectively. 

A detailed diseussion of these and other variants was given in (Ref.35). Attention must be called to the fact that these methods are not variational which causes the energies obtained with them to be lower than those obtained with the FCI method. The counterpart to this deffect is that excited states, open-shell systems, and radicals, can be calculated with as much ease as the ground state and closed-shell systems. Also, the size of the calculation is determined solely by the size of the Hilbert subspace chosen and does not depend in principle on the number of electrons since all happens as if only two electrons were considered. 

A. Claisen Rerrangements of Ketene Aminats and Imidates. A reaction that is related to the orthoester Claisen rearrangement utilizes an amide acetal, such as dimethylacetamide dimethyl acetal, in the exchange reaction with allylic alcohols.257 The products are y, 8-unsaturated amides. The stereochemistry of the reaction is analogous to the other variants of the Claisen rearrangement.258... 

SCA affects both males and females equally because it is not a sex-linked disease. Nine percent of African Americans possess the SCT and 1 in 600 has HbSS.5 Two thousand infants are identified with SCD annually in the United States.6 For every infant diagnosed with SCD, 50 are identified as carriers.6 HbSS (approximately 45%) is the most common genotypic expression, followed by HbSC (approximately 25%), HbS/5+-thalassemia (approximately 8%), and HbS/3° thalassemia (approximately 2%). Other variants account for less than 1% of patients.3,6... 

Several variations of the ADEQUATE experiment are possible. We will begin with the 1,1-ADEQUATE experiment, which exploits 1Jcn and 1/cc couplings to allow for the identification of adjacent neighbour carbons. Other variants of the experiment are 1, n-, n, 1-, and m,n-ADEQUATE 40 The schematic representation of the magnetization transfer in the various types of ADEQUATE experiments is shown in Figure 1. 

Other variants of this type of ring system are obtained by simple (S -type ) cyclization of the (3-hydroxypropyl-amino)thieno[2,3- /]pyrimidines 475 (Equation 202) <2000PS( 165)221 > and reaction of the parent aminopyrimidine with the enol ether 476 under microwave irradiation (Equation 203) <1999H(51)1819>. 

Whereas this important quotient is calculated solely from the product spectrum, process simplifications are a consequence of combining the rhodium catalyst with the special two-phase process. Compared with the conventional oxo process and with other variants (which, for example, include disadvantegeously thermal separation of the oxo reaction products from the catalyst) the procedure is considerably simplified (as shown in several papers, e.g., [2,12]). 

As in the first example, the time when the antioxidants are used up can be determined by measurement of the lag phase of oxygen consumption or of the generation of oxidation products. Although the measuring time is shorter than it is with the other variants mentioned, it still takes many minutes to obtain a result, obviously too long a period for routine tests. 

The electronic properties around the phosphorus atom can be varied by manipulation of the groups on that atom. MOD-DIOP (12c) was developed by Achiwa and used to reduce itaconic acids [68-72, 75, 103]. Some variations built on BCPM (18e), itself a variant of BPPM, such as the MOD-BCPM (18f) and MCCPM (18g) [88-93, 95-98, 104]. Other variants are PYRPHOS (21a also called DeguPHOS) [105, 106], DPCP (22) [107], NorPhos (23) [108], BDPP (24a) (also called SkewPHOS) [109-111], and PPCP (25) [112]. 

Each Hotel object is coupled to a room allocator object, to which it delegates decisions about allocating rooms. Separately, it is coupled to a staff payer, and the same is true for whatever other variant policies there may be. Different policies are implemented by different classes, which may be completely different in their internal structure. The only requirement is that all room allocator classes must implement the doAllocation( ) message—that is, they must conform to a single interface specification. 

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