Step-wise

Step-wise equilibria may also be expressed in this way, e.g. 

MA( , ) + A. MA n-[MA( , )][A] Ky, Kfy being called the step-wise stability constants. Overall stability constants, designated may be evaluated by multiplication of the individual stability constants, e.g. 

Since the electron density p(x) oc /(v)p, where /(v) is die electron wavefiinction, this implies that the electron wavefiinction varies in a similarly step-wise fashion at the interface. This indicates that d i //dx, where s indicates that the derivative is evaluated at the surface, becomes infinite. Since the electron kinetic... 

Recent developments m calorimetry have focused primarily on the calorimetry of biochemical systems, with the study of complex systems such as micelles, protems and lipids using microcalorimeters. Over the last 20 years microcalorimeters of various types including flow, titration, dilution, perfiision calorimeters and calorimeters used for the study of the dissolution of gases, liquids and solids have been developed. A more recent development is pressure-controlled scamiing calorimetry [26] where the thennal effects resulting from varying the pressure on a system either step-wise or continuously is studied. 

The effective moment of inertia / and the friction coefficient / could easily be estimated. The force constant k associated with the relative motion of the lobes was determined from an empirical energy function. To do so, the molecule was opened in a step-wise fashion by manipulating the hinge region and each resulting structure was energy minimized. Then, the interaction energy between the two domains was measured, and plotted versus 0. 

The procedures are based on an imaginary emptying of the pores by the step-wise lowering of relative pressure, from the point already referred to where the mesopore system is taken as being full up a relative pressure of 0-95po is frequently adopted as starting point with isotherms having a hysteresis loop of Type A or Type E. (With Type B, as will appear later, the validity of pore size calculations is doubtful.)... 

The PES found by Smedarchina et al. [1989] has two cis-form local minima, separated by four saddle-points from the main trans-form minima. The step-wise transfer (trans-cis, cis-trans) - because of endoergicity of the first stage - displays Arrhenius behavior even at T < T. . The concerted transfer of two hydrogen atoms was supposed to become prevalent at sufficiently low temperatures. However, because of too high a barrier for the concerted trans-trans transition, this... 

On the other hand, it is clear that in the classical regime, T> (T i is the crossover temperature for stepwise transfer), the transition should be step-wise and occur through one of the saddle points. Therefore, there should exist another characteristic temperature. r 2> above which there exist two other two-dimensional tunneling paths with smaller action than that of the one-dimensional instanton. It is these trajectories that collapse to the saddle points atlT = T i. The existence of the second crossover temperature, 7, 2, for two-proton transfer has been noted by Dakhnovskii and Semenov [1989]. 

As we stated earlier, the moleeular weight advaneement in phenolies oeeurs through a step-wise eondensation proeess. Depending on the intermediates involved the moleeule eondensed out of the strueture may be either water or formaldehyde. An overview of this proeess was provided in Seheme 3. 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

You may also decide to implement integration step-wise, where each step integrates a whole division. This approach can be successful if PSM and ESH is managed at divisional level. This has the advantage of requiring fewer resources, but will lengthen the time required to achieve all the benefits. 

You might have projected that some benefits would be available across the company within 12 months of project initiation. However, you have now concluded that the project will be implemented step-wise one division at a time. The result of this is that although the first benefits will still be seen within one year, the total benefit will not be seen until the third year. 

Thiohydantoin 9 was obtained from the treatment of carbonyl 1 with carbon disulfide and ammonium cyanide in aqueous methanol. The transformation could also be carried out step-wise, that is, treatment of 1 with ammonium cyanide to form aminonitrile 10 followed by reaction with carbon disulfide to produce thiohydantoin 9. Alternatively, 5,5-disubstituted 4-thiohydantoins could be prepared by the reaction of ketones with ammonium monothiocarbamate and sodium cyanide. ... 

The mechanism of the cycloaddition reaction of benzaldehyde 2a with Danishefsky s diene 3a catalyzed by aluminum complexes has been investigated theoretically using semi-empirical calculations [14]. It was found that the reaction proceeds as a step-wise cycloaddition reaction with the first step being a nucleophilic-like attack of Danishefsky s diene 2a on the coordinated carbonyl compound leading to an aldol-like intermediate which is stabilized by interaction of the cation with the oxygen atom of the Lewis acid. The next step is the ring-closure step, giving the cycloaddition product. 

Fig. 8.13 Schematic representation of the change in energies for the concerted hetero-Diels-Alder reaction of benzaldehyde with Danishefsky s diene and the step-wise reaction...

Fig. 8.14 The calculated transition-state structures along the reaction path for the step-wise formation of the hetero-Diels-Alder...

The effect of the partial condenser is indicated in Figure 8-13 and is otherwise represented by the relations for the rectifying and stripping sections as just given. The key point to note is that the product is a vapor that is in equilibrium with the reflux to the column top tray, and hence the partial condenser is actually serving as an external tray for the system and should be considered as the top tray when using the equations for total reflux conditions. This requires just a little care in step-wise ctdculation of the column performance. 

From Graph, L/V = 0.653 was plotted based on feed at its boiling point. No. of theoretical plates (step-wise graph) =11.3... 

Point F on the figure represents conditions in the kettle or still with Xj, yj, or Xq, yo- Line DF represents slope of the operating line at minimum reflux. The step-wise development from point D cannot cross the intersection, F, where the slope intersects the equilibrium line, and leads to an infinite condition, as point F is approached. Thus, an infinite number of theoretical trays/stages is required, and... 

Continue step-wise calculations until the ratio of light to heavy key on a tray equals (or nearly so) that ratio in the liquid portion of the feed. This is then considered the feed tray. 

A graphical solution is presented by Edmister [18] and handled like step-wise distillation. 

Because the packed tower is a continuous contacting device as compared to the step-wise plate tower, performance capacity is expressed as the number of transfer units, N, the height of the transfer unit, H.T.U., and mass transfer coefficients K a and Kj a. Figure 9-68 identifies the key symbols and constant flow material balance. 

Ploty, from y bottoms to y overhead versus l/(y - y). The position of y-feed can be noted on the graph, and the integration so arranged as to reveal the split betiveen rectifying and stripping transfer units. The total number by this method should check closely with the graphical step-wise method. 

A student is asked to calculate the amount of heat involved in changing 10.0 g of liquid bromine at room temperature (22.5°C) to vapor at 59.0°C. To do this, one must use Tables 8.1 and 8.2 for information on the specific heat, boiling point, and heat of vaporization of bromine. In addition, the following step-wise process must be followed. 

A method which appears to be essentially equivalent to the best ABL method was patented by Brennecke (Ref 10) who claims better utilization of the spent acid and solvent and better yield in a repetitive, step-wise procedure. Another modification patented by Rolewicz et al (Ref 12) utilizes mixed acid and methylene chloride extrn and appears to be little different from the above methods, except that the nitric acid is made oxide-free. A method of obtaining 98.4% pure Petrin from its mixts with PETN and PE dinitrate is claimed by Brennecke (Ref 16)... 

Minagawa, M. and Wada, E. 1984 Step-wise enrichment of N along food chains further evidence and the relationship between 5 N and animal age. Geochimica et Cosmochimica Acta 48 1135-1140. 

Fig.2. Dynamic response of output voltage with Step-wise current loads.

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