Step operators

In a batch process, the main steps operate discontinuously. In contrast with a continuous process, a batch process does not deliver its product continuously but in discrete amounts. This means that... 

This definition implies that the direction of the vector d was taken into account and that the coefficient c(i,j,fd)sndc(j,i,f,-d) may be different. So, the symmetrical matrix consists of a two step operation ... 

The first stage of the operation error analysis is to determine if any of the error categories in Figure 5.7 apply to the task, subtask, or task step being analyzed. For example, at the level of individual task steps, operations would... 

Plutonium pyrochemical processes are now the principal tools at Los Alamos for producing large amounts of high purity plutonium metal from impure metal and oxide scrap. Pyrochemical processing was selected because of its cost effectiveness. The processes are highly compact and require little floor space and manpower to operate. The processes are also operationally efficient in that one or two steps can be used to supplant multi-step operations found in the classical aqueous chemistry flow streams. The... 

The score vector, zx, is found in a two-step operation to guarantee that the covariance of the scores is maximized. Once z, i, i, and qx have been found, the procedure is repeated for the residual matrices ExA and Ev i to find z2,ol2,u2, and q2. This continues until the residuals contain no... 

As pointed out in Chapter 1, in a batch process the main steps operate discontinuously. This means that temperature, concentration, mass and other properties vary with time. Also as pointed out in Chapter 1, most batch processes are made up of a series of batch and semicontinuous steps. A semicontinuous step operates continuously with periodic start-ups and shutdowns. 

We can make polyurethanes via one- or two-step operations. In the single-stage process, diols and isocyanates react directly to form polymers. If we wish to make thermoplastic linear polymers, we use only diisocyanates. When thermosets are required, we use a mixture of diisocyanates and tri- or polyisocyanates residues of the latter becoming crosslinks between chains. In the first step of the two-stage process, we make oligomers known as prepolymers, which are terminated either by isocyanate or hydroxyl groups. Polymers are formed in the second step, when the isocyanate terminated prepolymers react with diol chain extenders, or the hydroxyl terminated prepolymers react with di- or polyisocyanates. 

A general idea related to the preparation of protein-like copolymers through the co-polymerization or co-polycondensation of the mixtures of comonomers with differing hydrophilicity/hydrophobicity has been described in Sect. 2.1. Scheme 4 demonstrates the multi-step operations used in the first successful realization [26,27] of such an approach in a free radical polymerization process. 

In the RTN approach, the process and the plant are represented by networks of different types of nodes which are connected by arcs. The nodes represent states (materials, products), tasks (production steps, operations), or resources (machines, pieces of equipment). 

Production planning has to determine on the detailed level which production step (operation) has to be carried out at which time and on which resource. For this purpose a resource allocation problem has to be solved (this is denoted as a scheduling problem in mathematical theory). It is natural to desire this allocation to be optimal in a certain sense (minimal number of setups and/or violations of requirements dates, etc.). 

This four step operation to convert ketones to vinylcyclobutanones (Eq. 53)... 

Noteworthy is the fact that one can utilize the appropriate bromopyrrole (e.g., 48) in conjunction with the desired Grignard reagent in a one-step operation to afford the corresponding substituted pyrroles (e.g., 49) [43]. The mixed pyrrole-pyridine heterocycle 50 was made in this fashion [45]. 

For this reaction, the early investigations of Reppe pointed out the need for catalyst precursors to operate at high pressure [2], It is necessary to work at 150-300 bar of CO in order to stabilize the two catalytic species [Co(H)(CO)4] or [Ni(H)(X)(CO)2] that adopt a mechanism analogous to the cobalt-catalyzed hydroformylation [44,45]. Many industrial applications have been reported [28,46,47] for the synthesis of plasticizers and detergents. Similarly, the two-step methoxycarbonylation of 1,3-butadiene has been explored by BASF and other companies to produce dimethyl 1,6-hexanedioate (adipate) directly from the C4 cut [28,48]. The first step operates at 130 °C and... 

Tryptamine. CA, 79, 14632 (1973). This is a fast one step operation, giving a good 70% yield. Condensation of PhNHNH2 (phenylhydrazine) with CICH2CH2CH2CHO (n-butyryl chloride, 2-chloroethyl vinyl ether) in refluxing aqueous EtOH for 6 hours gives 70% tryptamine. 

Despite the rich chemistry of 45 [18], the only method for accessing this compound is the oxidation of the corresponding alcohol derived from 2-methyl-2-propen-l-ol or other sources, which can be obtained through multi-step operations. In contrast to the known methods, 45 can be readily derived from 44 and 50 by a simple one-pot operation. Since the propargylic alcohol 50 a is readily accessed from a ketone or aldehyde, realization of the transformation of 50 to 45 through a one-pot procedure provides a novel method for carbonyl olefmation of ketones or aldehydes. 

Domino reactions attract significant attention due to their ability to allow for multi-step operations in one pot. Two classes of domino transformations are known for the PK reaction. The first involves the use of a dual-catalyst system, while the second uses a single catalyst with modification of the reaction parameters to control reactivity. 

The following two-step operation was chosen as an example of the former case. The first step involves an allylation to generate the 1,6-enyne intermediate 1, via the reaction between a metal n -allyl complex derived from 52 and propargyl anion 51, followed by the PK-type reaction to furnish the bicyclopentenone 2 (Scheme 11.13). Since these two specific reactions have opposing electronic requirements (the first prefers Lewis basic character, while the second can be facilitated by Lewis acidic catalysts), finding the right combination of catalysts was the key to success. 

Epoxides are useful synthetic intermediates, and the conversion of an alkene to an epoxide is often part of a more extensive molecular transformation.85 In many instances, advantage is taken of the high reactivity of the epoxide ring to introduce additional functionality. Because epoxide ring opening is usually stereospecific, such reactions can be used to establish stereochemical relationships between adjacent substituents. Such two- or three-step operations can accomplish specific oxidative transformations of an alkene that may not easily be accomplished in a single step. Scheme 12.13 provides a preview of the type of reactivity to be discussed. 

SOPs detailing step-by-step operational procedures for specific items of equipment (e.g. autoclaves, homogenizers, freeze-dryers, pH meters, product labelling machines, etc.) ... 

Halogenation and dehydrohalogenation have been performed as a one-step operation from aldoximes using NCS in the presence of base such as pyridine (67), NBS and triethylanfine (68), or a heterogeneous base such as basic alumina or Florisil (69). Solvent-free reaction conditions also proved useful for the preparation... 

For example, when the mixed solution of Ag(CN)2 and Au(CN)2 is irradiated by y-radiolysis at increasing dose, the spectrum of pure silver clusters is observed first at 400 nm, because Ag is more noble than Au due to the CN ligand. Then, the spectrum is red-shifted to 500 nm when gold is reduced at the surface of silver clusters in a bilayered structure [102], as when the cluster is formed in a two-step operation [168] (Table 5). However, when the same system is irradiated at a high dose rate with an electron beam, allowing the sudden (out of redox thermodynamics equilibrium) and complete reduction of all the ions prior to the metal displacement, the band maximum of the alloyed clusters is at 420 nm [102]. 

Data mining can, therefore, be considered as a three-step operation. Prior to any analysis, the collected data is preprocessed to integrate the warehouse, and some verification is performed to maintain the data level for example, integration,... 

In Great Britain, the Imperial Chemical Industries, Ltd., has developed a fluidized coal gasification process (32) using combustion of part of the fuel with air to supply the heat necessary for the endothermic steam-carbon reaction. This procedure is divided into three steps carbonization, air-blowing, and steam-blowing. The first and third steps operate with fluidized beds, and the second with a dilute suspension. Powdered coal is fed into the carbonization vessel, where it is heated by combustion of some of the carbonization gases. The powdered char is blown into a feed hopper connected with the air-... 

Much writing is saved by introducing the step operator E, defined by its effect on an arbitrary function /(n) ... 

Since the step operator E here only acts on smooth functions it may be replaced with a Taylor expansion... 

Ex and EY are, of course, the step operators acting on nx and nY. The equation is nonlinear, which makes an -expansion necessary. 

Beeause the processing of natural substances often involves multi-step operations, costs arc generally considered to be higher than a majority of synthesized compounds. A number of natural flavors and essences are given in Table 2. which illustrates the very wide range of ingredient... 

---