An Illustrative Example

An Illustrative Example. Consider the following simple reaction scheme with first-order chain branching and termination. Suppose X denotes the chain carrier and that its initiation reaction is of constant rate (k)  

This relation will determine the position of the pressure-temperature ignition limits for the system. In cases where the L.H.S. of (26) is greater than the right we shall have stable reaction and conversely when the R.H.S. is the larger the reaction will proceed to explosion. Gray concludes from his analysis that  

Gray and Yang proposed the simple kinetic mechanism discussed here as a basis to explain the multiple limits found in the hydrogen-oxygen reaction. At the present time too few direct measur nents of reactant temperatures have been made in this system to justify this proposal. However, experimental confirmation of some of the qualitative aspects has been found in a similar gas-phase oxidation, that of hydrogen sulphide.-  

My colleagues at Safety Performance Solutions use both education and training to teach safety coaching skills. They start with education, teaching the basic principles behind a behavior-based approach to coaching. Then they use group exercises to implement a training process. 

Altirough tire title of this section is Behavior-Based Safety Training, I hope it is dear that botir training and education are needed. First, people need to understand and believe in the theory and principles rmderlying the behavior-based approach to preventing injuries. This is commonly referred to as education. 

Understanding, belief, or awareness is not sufficient, however, to implement a particular behavior-based safety process. People need to learn the specific behaviors or activities required for successful implementation. This requires training and should include behavior-based observation and feedback. In other words, participants need to practice the behaviors called for by the intervention process and then receive constructive behavior-focused feedback from objective and vigilant observers. 

Education can influence behaviors indirectly i/the education process changes an attitude, intention, belief, or value which is perceived as linked to a certain behavior. Training can also influence attitudes, intentions, beliefs, or values indirectly if the behavior change is accepted by the participant and perceived as related to a particular attitude, intention, belief, or value. The bottom line is that a strategic combination of both education and training is needed to improve both behavior and attitude. 

We have already covered a variety of situational factors that influence the occurrence of safe or at-risk behavior. This included a sequence of questions to ask in order to decide whether instructional intervention is needed, whether another approach to corrective action would be more cost-effective—from redesigning a task to clarifying expectations and providing behavior-based feedback. Here we examine some basic principles about behavior and behavior-change techniques that should influence your choice of an improvement intervention. We begin with a distinction among other-directed, self-directed, and automatic behavior (Watson and Tharp, 1997). 

Our approach to two-phase problems begins with an illustrative example dealing with solidification in a stagnant liquid. 

Consider a liquid initially at temperature Tx suddenly brought into contact with a plane wall at constant temperature T, . Here we consider the case of a liquid at the melting point solidifying on an isothermal subcooled wall (Fig. 11.1). We wish to find the thickness of the solidified layer, S(t). 

The problem is in terms of a clearly defined penetration depth (instantaneous thickness of the solidified liquid), and it is well suited for an integral formulation. For an expanding control volume which encloses the solid, the conservation of mass becomes 

A first-order polynomial profile for the solid satisfying the boundary conditions 

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Desulfurization will become mandatory when oxidizing catalysts are installed on the exhaust systems of diesel engines. At high temperatures this catalyst accelerates the oxidation of SO2 to SO3 and causes an increase in the weight of particulate emissions if the diesel fuel has not been desulfurized. As an illustrative example, Figure 5.22 shows that starting from a catalyst temperature of 400°C, the quantity of particulates increases very rapidly with the sulfur content. 

An illustrative example is provided by investigating the possible momenta for a single particle travelling in the v-direction, p First, one writes the equation that defines the eigenvalue condition... 

The field of gas phase reaction dynamics has been extensively reviewed elsewhere [1, 2 and 3] in considerably greater detail than is appropriate for this chapter. Here, we begin by simnnarizing the key theoretical concepts and experimental teclmiques used in reaction dynamics, followed by a case study , the reaction F + H2 HF + H, which serves as an illustrative example of these ideas. 

As an illustrative example, consider the vibrational energy relaxation of the cyanide ion in water [45], The mechanisms for relaxation are particularly difficult to assess when the solute is strongly coupled to the solvent, and the solvent itself is an associating liquid. Therefore, precise experimental measurements are extremely usefiil. By using a diatomic solute molecule, this system is free from complications due to coupling... 

In other words, (n VQ ) is imaginary, making real. As an illustrative example, n) may assumed to be given by Eq. (24), in which case... 

Essential Dynamics In most applications details of individual MD trajectories are of only minor interest. An illustrative example due to Grubmuller [10] is documented in Figure 3. It describes the dynamics of a polymer chain of 100 CH2 groups. Possible stepsizes for numerical integration are confined... 

Having found a place (the sp -sp bon d t to establish the boundary between classical atom s and quantum atoms, the next cpiesiion is how to cap the quantum atoms. Let s first of all look at an illustrative example of the problem. ... 

As an illustrative example we consider the Galerkin finite element solution of the following differential equation in domain Q, as shown in Figure 2.20. 

In Chapter 4 the development of axisymmetric models in which the radial and axial components of flow field variables remain constant in the circumferential direction is discussed. In situations where deviation from such a perfect symmetry is small it may still be possible to decouple components of the equation of motion and analyse the flow regime as a combination of one- and two-dimensional systems. To provide an illustrative example for this type of approximation, in this section we consider the modelling of the flow field inside a cone-and-plate viscometer. 

An illustrative example generates a 2 x 2 calibration matrix from which we can determine the concentrations xi and X2 of dichromate and permanganate ions simultaneously by making spectrophotometric measurements yi and j2 at different wavelengths on an aqueous mixture of the unknowns. The advantage of this simple two-component analytical problem in 3-space is that one can envision the plane representing absorbance A as a linear function of two concentration variables A =f xuX2). 

The amount of HEU that becomes avadable for civdian use through the 1990s and into the twenty-first century depends on the number of warheads removed from nuclear arsenals and the amount of HEU in the weapons complex that is already outside of the warheads, ie, materials stockpdes and spent naval reactor fuels. An illustrative example of the potential amounts of weapons-grade materials released from dismanded nuclear weapons is presented in Table 7 (36). Using the data in Table 7, a reduction in the number of warheads in nuclear arsenals of the United States and Russia to 5000 warheads for each country results in a surplus of 1140 t of HEU. This inventory of HEU is equivalent to 205,200 t of natural uranium metal, or approximately 3.5 times the 1993 annual demand for natural uranium equivalent. 

There seem to be few limits to the kind of fragment extruded (Scheme 29), or to the nature of reactions preceding the fragmentation step. An illustrative example is the formation of a zwitterionic isomer before loss of ethylene (Scheme 30 Section 5.14.4.2.4) (70JOC584, B-73MI50301). 

As an illustrative example, consider the simplified block diagram for a representative decoupling control system shown in Fig. 8-41. The two controlled variables Ci and Co and two manipulated variables Mi and Mo are related by four process transfer functions, Gpn, Gpi9, and pie, Gpii denotes the transfer function between Mi... 

This reaction is especially well suited for the reduction of tertiary aldehydes which have no activated a-hydrogens. In this case only two deuteriums are incorporated in place of the carbonyl oxygen. The reduction of 12-methoxypodocarpa-8,ll,13-trien-17-al (82) provides an illustrative example. After back exchange of the aromatic deuteriums, the isotopic purity of the resulting dideuterio reduction product (83) is 92%. ... 

The treatment of ketoximes with lithium aluminum hydride is usually a facile method for the conversion of ketones into primary amines, although in certain cases secondary amine side products are also obtained. Application of this reaction to steroidal ketoximes, by using lithium aluminum deuteride and anhydrous ether as solvent, leads to epimeric mixtures of monodeuterated primary amines the ratio of the epimers depends on the position of the oxime function. An illustrative example is the preparation of the 3(x-dj- and 3j5-di-aminoandrostane epimers (113 and 114, R = H) in isotopic purities equal to that of the reagent. 

The use of the amide ions in these reactions leads sometimes to unexpected side reactions, since besides addition amide ions can also act as a deprotonation agent. An illustrating example is the formation of... 

The Diels-Alder reaction,is a cycloaddition reaction of a conjugated diene with a double or triple bond (the dienophile) it is one of the most important reactions in organic chemistry. For instance an electron-rich diene 1 reacts with an electron-poor dienophile 2 (e.g. an alkene bearing an electron-withdrawing substituent Z) to yield the unsaturated six-membered ring product 3. An illustrative example is the reaction of butadiene 1 with maleic anhydride 4 ... 

The versatility of the Diels-Alder reaction becomes especially obvious, when considering the hetero-variants. One or more of the carbon centers involved can be replaced by hetero atoms like nitrogen, oxygen and sulfur. An illustrating example is the formation of the bicyclic compound 31, by an intramolecular hetero-Diels-Alder reaction ... 

As an illustrating example for the application of the Friedel-Crafts acylation in the synthesis of complex molecules, its use in the synthesis of [2.2.2]cyclophane 13 by Cram and Truesdale shall be outlined. The reaction of [2.2]paracyclo-phane 10 with acetyl chloride gives the acetyl-[2.2]paracyclophane 11, which is converted into the pseudo-geminal disubstituted phane 12 by a Blanc reaction, and further to the triple bridge hydrocarbon 13 ... 

For the performance of an enantioselective synthesis, it is of advantage when an asymmetric catalyst can be employed instead of a chiral reagent or auxiliary in stoichiometric amounts. The valuable enantiomerically pure substance is then required in small amounts only. For the Fleck reaction, catalytically active asymmetric substances have been developed. An illustrative example is the synthesis of the tricyclic compound 17, which represents a versatile synthetic intermediate for the synthesis of diterpenes. Instead of an aryl halide, a trifluoromethanesul-fonic acid arylester (ArOTf) 16 is used as the starting material. With the use of the / -enantiomer of 2,2 -Z7w-(diphenylphosphino)-l,F-binaphthyl ((R)-BINAP) as catalyst, the Heck reaction becomes regio- and face-selective. The reaction occurs preferentially at the trisubstituted double bond b, leading to the tricyclic product 17 with 95% ee. °... 

An illustrative example for the generation of cyclopentenes from vinylcyclopropanes is the formation of bicyclo[3.3.0]oct-l-ene 10 from 1,1-dicyclopropylethene 9 by two consecutive vinylcyclopropane cyclopentene rearrangements. ... 

An illustrative example for the usefulness of the Weiss reaction for the construction of complex cyclopentanoid carbon skeletons is the synthesis of the all -cis [5.5.5.5]fenestrane 7 after Cook et al., starting from the a-diketone ... 

This chapter is organized as follows the experimental and theoretical techniques are presented briefly in Sections 5.2 and 5.3. In Section 5.4 some materials aspects and concepts arc introduced, where /ro/z.v-poly acetylene is used as an illustrative example. A series of illustrative examples on surfaces and interfaces arc... 

An illustrative example of the Michael reaction is that of the thiirene dioxide 19b with either hydroxylamine or hydrazine to give desoxybenzoin oxime (87) and desoxybenzoin azine (88), respectively, in good yields6 (see equation 29). The results were interpreted in terms of an initial nucleophilic addition to the a, j8-unsaturated sulfone system, followed by loss of sulfur dioxide and tautomerization. Interestingly, the treatment of the corresponding thiirene oxide (18a) with hydroxylamine also afforded 86 (as well as the dioxime of benzoin), albeit in a lower yield, but apparently via the same mechanistic pathway6. 

An illustrative example of the potency of the second-generation Ru catalyst C is found in Paquette s highly efficient total synthesis of the natural products teubrevin G (122) and teubrevin H (123), which feature a cyclooctane core fused and spiroannulated to smaller oxygen-containing rings [76]. In the retrosyn-thetic analysis, the viability of an RCM step for annulation of a cyclooctenone ring to the furan played a central role. 

An illustrative example of an alternative strategy (cf Fig. 11c) involving the use of a novel traceless linker is found in the multistep synthesis of 6-epi-dysidiolide (363) and several dysidiolide-derived phosphatase inhibitors by Waldmann and coworkers [153], outlined in Scheme 70. During the synthesis, the growing skeleton of 363 remained attached to a robust dienic linker. After completion of intermediate 362, the terminal olefin in 363 was liberated from the solid support by the final metathesis process with concomitant formation of a polymer-bound cyclopentene 364. Notably, during the synthesis it turned out that polymer-bound intermediate 365a, in contrast to soluble benzoate 365b, produced diene 367 only in low yield. After introduction of an additional linker (cf intermediate 366), diene 367 was released in distinctly improved yield by RCM. 

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