Solution steps

The right-hand side in Equation (6.18) is known and hence its solution yields the error 5x in the original solution. The procedure can be iterated to improve the solution step-by-step. Note that implementation of this algorithm in the context of finite element computations may be very expensive. A significant advantage of the LU decomposition technique now becomes clear, because using this technique [A] can be decomposed only once and stored. Therefore in the solution of Equation (6.18) only the right-hand side needs to be calculated. 

FIGURE 20 7 The mecha nism of amide hydrolysis in acid solution Steps 1 through 3 show the for mation of the tetrahedral intermediate Dissociation of the tetrahedral inter mediate is shown in steps 4 through 6... 

Permeant movement is a physical process that has both a thermodynamic and a kinetic component. For polymers without special surface treatments, the thermodynamic contribution is ia the solution step. The permeant partitions between the environment and the polymer according to thermodynamic rules of solution. The kinetic contribution is ia the diffusion. The net rate of movement is dependent on the speed of permeant movement and the availabiHty of new vacancies ia the polymer. 

Step 3 Subtract the mass of solute (step 2) from the total mass (step 1) to find the mass of solvent in 1 L of solution,... 

Formulation of the Solution Steps for the Gauss-Newton Method Two Consecutive Chemical Reactions... 

A phosphitylation procedure was carried out in THF using tetrazole as the activator subsequent oxidation was performed by TBHP in THF (steps a and b). Simultaneous cleavage of 2-cyanoethyl and Fmoc groups was achieved by DBU in dichloromethane solution (step c). Finally the tert-butyl group was removed under acidic conditions by trifluoroacetic acid (TFA). In phosphitylation reactions leading to the phosphopeptides, symmetrically protected phosphoroamidites have formerly been used [53]. 

First phosphitylation was performed by 0-benzyl-bis(iV,iV,-diisopropyl)-phosphoroamidite in the presence of diisopropyl-ammonium tetrazolide at room temperature in dichloromethane solution (step a). The intermediate phosphoroamidite was coupled with a glycerol moiety in the presence of tetrazole in boiling CH2CI2 to give the benzyl phosphite (step b), which was oxidized by CPBA in CH2CI2 into the corresponding phosphate (step c). In the final step d total debenzylation was achieved by Pd/C transfer hydrogenol-ysis in the presence of formic acid and methanol at room temperature. 

Formation of the nucleoside phosphorodichloridite at -30 °C by PCI3 in CH2CI2 solution (step a) is followed by reaction with ethanol (step b). Subsequently dealkylation occurs with the assistance of hydrogen chloride formed in reaction (a) to give the desired 5 -nucleoside H-phosphonate (step c). It was found that a mixture of ethanol and tcrt-butanol (1 1) as alcoholysis agent prevented side reactions and gave a higher yield than when ethanol alone was used. 

The first coupling was performed in CH3CN or THF in the presence of EtN(i-Pr)2 at -38 °C in 3 h (step a). Formation of the intermediate took place by addition of elemental sulfur in carbon disulfide solution (step b). The desired phosphorodithioate analogue of phosphatidylcholine was prepared by treatment of the latter with choline tosylate in the presence of DBU. 

Dissolve menthol in peppermint oil at 25°C by slow stirring in another mixing vessel. Continue stirring until the solution becomes clear. Transfer the clean menthol solution (step 5) into step 4 while stirring at the set speed. Continue stirring for 1 hour. 

Solution, steps of purification of (cont.) by scavenging, 1093 by UV radiation, 1093 Solvation, 964... 

Isolation-Fractionation Scheme. Figure 1 illustrates the isolation-fractionation scheme devised and evaluated in this study. Step 1 The test solution was first acidified to pH 2 and passed through the XAD-8 column by gravity flow at a rate of 15 bed volumes/h. The last portion of the test solution remaining in the column was displaced from the resin by 1 bed volume of 0.01 N HC1 rinse, which was combined with the original test solution. Step 2 The hydrophobic acid fraction was desorbed with 0.25 bed volumes of 0.1 N NaOH followed by 1.5 bed volumes of OFW. Step 3 The test solution effluent from the XAD-8 (pH 2) was adjusted to pH 10 with 1 N NaOH and recycled through the XAD-8 column at a flow rate of 15 bed volumes/h. Following the sample, 2.5 bed volumes of OFW were used to rinse the XAD-8 column. The rinse was com-... 

While stirring, slowly add 40 ml methanol/ammonium acetate solution (step 1). 

Breaking up the solute into individual components (expanding the solute). Step 2... 

Dissolve 10 mg rifampicin (rifamycin SV) in 1.0 ml dimethyl sulfoxide. Prepare also a 5% (w/v) solution of trichloroacetic acid (TCA). 3-107. Place exactly 0.1 ml H-leucine solution (step 3-105) in a 125 ml Erlenmeyer flask and place the flask in the bath. 

Prepare the column sample by mixing 0.1 ml bromophenol blue (step 5-26) and 0.5 ml blue dextran solution (step 5-27). 

Place these tubes in a 1 liter Erlenmeyer flask full of destaining solution (step 6-7). Stir gently using a magnetic stirrer. This operation may be performed at room temperature, but destaining will be hastened if it is carried out at 37°C. 

Gels to be preserved are placed in tubes containing the 7.5% acetic acid solution (step 6-8). Keep stained gels out of direct sunlight or other strong light sources because they cause the stained bands to fade. 

Remove the supernatant solution using a Pasteur pipette. Take care to remove as much solution as possible. Wash the precipitate two or three times with 5 ml 0.85% saline solution. Some loss may occur at this point if great care is not exercised during the washing operations. The supernatant solutions derived from the washing operations may be discarded. 8-22. Place 0.2 ml of each supernatant solution (step 8-21) into 16 scintillation vials respectively and add 15 ml of an aqueous scintillation fluid to each. 

Let us consider a dilute solution of sodium chloride (Fig. 10-6). The process of conduction through this solution (step 3) is closely similar to that for molten sodium chloride. Here it is the dissolved sodium ions which move toward the cathode and the dissolved chloride ions which move toward the anode. By the motion of the ions in this way negative electric charge is carried toward the anode and away from the cathode. 

Simulated annealing A structure determination from diffraction data involves the development of an initial model, that is a structure solution step, and then completion and refinement of the model. Why are these steps distinct The answer is that today s structure refinement technology can operate effectively only when the starting model is relatively dose to the actual model crystallographic least squares techniques are unable to locate global... 

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