Three-step

A timestep of size At with the Verlet method ( velocity Verlet ) takes iqo,Po) to (51,pi) and can be divided into three steps (1) a kick ... 

The symmetry T p) = T[—p) implies that reversing the order of these three steps and changing the sign of r and p results in exactly the same method. In other words, Verlet is time-reversible. (In practice, the equations are usually reduced to equations for the positions at time-steps and the momenta at halfsteps, only, but for consideration of time-reversibility or symplecticness, the method should be formulated as a mapping of phase space.)... 

The training of a Kohonen network is performed in three steps. 

The explorative analysis of data sets by visual data mining applications takes place in a three-step process During the first step (overview), the user can obtain an overview of the data and maybe can identify some basic relationships between specific data points. In the second step (filtering), dynamic and interactive navigation, selection, and query tools will be used to reorganize and filter the data set. Each interaction by the user will lead to an immediate update of the data scene and will reveal the hidden patterns and relationships. Finally, the patterns or data points can be analyzed in detail with specific detail tools. 

The general procedure in a QSPR approach consists of three steps structure representation descriptor analysis and model building (see also Chapter X, Section 1.2 of the Handbook). 

Model building consists of three steps training, evaluation, and testing. In the ideal case the whole training data set is divided into three portions, the training, the evaluation set, and the test set. A wide variety of statistical or neural network... 

Building a QSPR model consists of three steps descriptor calculation, descriptor analysis and optimization, and establishment of a mathematical relationship between descriptors and property. 

This coding is performed in three steps (cf Chapter 8) First the 3D coordinates of the atoms arc calculated using the structure generator CORINA (COoRdlNAtes). Subsequently the program PETRA (Parameter Estimation for the Treatment of Reactivity Applications) is applied for calculating physicochemical properties such as charge distribution and polarizability. The 3D information and the physicochemical atomic properties are then used to code the molecule. 

After diagonalization of the EHT matrix, the lowest 4 orbitals have an energy sum of about —70 eV. The electronic energy for these doubly occupied orbitals is 2(—70) = — 140 eV. The energy gain of the molecule relative to its atoms is —140 — ( — 110) = —30eV = —690 kcal mol (1 eV = 23 kcal mol ) therefore, the molecule is stable relative to its atoms. We can envision an energy cycle with three steps (Eig. 7-5) ... 

Frequently the three steps can be combined without isolation of the intermediates. 

It turns out that the last three steps can be accomphshed simply by boiling with cone. HBr. 

Clearly it is the same as the three step synthesis, 73%. So it is better to assemble two more or less equal parts of a molecule separately and join them together at the end. Let s look at this in practice. What three alternative disconnections are immediately obvious on TM 311 ... 

Homologues in principle can also be prepared from RCH(Br)-C(8r)=CH2 but for the synthesis of these starting compounds three steps have to be carried out. The dehalogenation procedure has also been used in the preparation of di- and tri-fluoroal1enes. ... 

Then N-Boc-O-benzylserine is coupled to the free amino group with DCC. This concludes one cycle (N° -deprotection, neutralization, coupling) in solid-phase synthesis. All three steps can be driven to very high total yields (< 99.5%) since excesses of Boc-amino acids and DCC (about fourfold) in CHjClj can be used and since side-reactions which lead to soluble products do not lower the yield of condensation product. One side-reaction in DCC-promoted condensations leads to N-acylated ureas. These products will remain in solution and not reaa with the polymer-bound amine. At the end of the reaction time, the polymer is filtered off and washed. The times consumed for 99% completion of condensation vary from 5 min for small amino acids to several hours for a bulky amino acid, e.g. Boc-Ile, with other bulky amino acids on a resin. A new cycle can begin without any workup problems (R.B. Merrifield, 1969 B.W. Erickson, 1976 M. Bodanszky, 1976). 

The 5-oxohexanal 27 is prepared by the following three-step procedure (1) 1,2-addition of allylmagnesium bromide to an a, / -unsaturated aldehyde to give the 3-hydroxy-1,5-diene 25, (2) oxy-Cope rearrangement of 25 to give 26, and (3) palladium catalyzed oxidation to afford 27. The method was applied to the synthesis of A -2-octalone (28), which is difficult to prepare by the Robinson annulation[25]. 

The synthesis of these disubstituied thioureas takes place in three steps. First the alkyl bromide is prepared by the action of hydrobromic acid on the corresponding alcohol (518). Then the dialkylcyanamide is obtained by treatment at 25°C with calcium cyanamide. The yields are of the order of 30 to 60%. Thioureas are obtained in a third step from the cyanamide by reaction at 40 C with HjS in the presence of pyridine. Yields ranged from 57 to 90% (518),... 

These common features suggest that carbocations are key intermediates m alcohol dehydra tions just as they are m the reaction of alcohols with hydrogen halides Figure 5 6 portrays a three step mechanism for the acid catalyzed dehydration of tert butyl alcohol Steps 1 and 2 describe the generation of tert butyl cation by a process similar to that which led to its for matron as an intermediate m the reaction of tert butyl alcohol with hydrogen chloride... 

Instead of the three step mechanism of Figure 6 9 the following... 

IS reversible with respect to reactants and products so each tiny increment of progress along the reaction coordinate is reversible Once we know the mechanism for the for ward phase of a particular reaction we also know what the intermediates and transition states must be for the reverse In particular the three step mechanism for the acid catalyzed hydration of 2 methylpropene m Figure 6 9 is the reverse of that for the acid catalyzed dehydration of tert butyl alcohol m Figure 5 6... 

The synthesis of compound C was achieved by using compounds A and B as the source of all carbon atoms Suggest a synthetic sequence involving no more than three steps by which A and B may be converted to C... 

R B Woodward was one of the leading organic chemists of the middle part of the twenti eth century Known pnmanly for his achievements in the synthesis of complex natural products he was awarded the Nobel Pnze in chemistry in 1965 He entered Massachusetts Institute of Tech nology as a 16 year old freshman in 1933 and four years later was awarded the Ph D While a student there he earned out a synthesis of estrone a female sex hormone The early stages of Woodward s estrone synthesis required the conversion of m methoxybenzaldehyde to m methoxy benzyl cyanide which was accomplished in three steps... 

Suggest a reasonable three step sequence showing all necessary reagents for the preparation of m methoxybenzyl cyanide from m methoxybenzaldehyde... 

Mechanism of Acid-Catalyzed Hydration Three steps are involved m acid catalyzed hydration (Figure 17 7 on page 718) The first and last are rapid proton transfers between... 

Steps 1-3 Acid catalyzed nucleophilic addition of 1 mole of ethanol to the carbonyl group The details of these steps are analogous to the three steps of acid catalyzed hydration in Figure 17 7 The product of these three steps is a hemiacetal... 

The ketone shown was prepared in a three step sequence from ethyl trifluoroacetate The first step in the sequence involved treating ethyl tnfluoroacetate with ammonia to give a compound A Compound A was in turn converted to the desired ketone by way of a compound B Fill in the missing reagents in the sequence shown and give the structures of compounds A and B... 

There are three steps in carrying out any quantum mechanical calculation in HyperChem. First, prepare a molecule with an appropriate starting geometry. Second, choose a calculation method and its associated (Setup menu) options. Third, choose the type of calculation (single point, geometry optimization, molecular dynamics, Langevin dynamics, Monte Carlo, or vibrational analysis) with the relevant (Compute menu) options. 

A solution can be diluted by a factor of 200 using readily available pipets (f-mL to fOO-mL) and volumetric flasks (fO-mL to fOOO-mL) in either one, two, or three steps. Limiting yourself to glassware listed in Table 4.2, determine the proper combination of glassware to accomplish each dilution, and rank them in order of their most probable uncertainties. 

In the sections that follow, these three steps are considered for the sampling of liquids (including solutions), gases, and solids. 

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

Another example of vims clearance is for IgM human antibodies derived from human B lymphocyte cell lines where the steps are precipitation, size exclusion using nucleases, and anion-exchange chromatography (24). A second sequence consists of cation-exchange, hydroxylapatite, and immunoaffinity chromatographies. Each three-step sequence utilizes steps based on different properties. The first sequence employs solubiUty, size, and anion selectivity the second sequence is based on cation selectivity, adsorption, and selective recognition based on an anti-u chain IgG (24). 

Steps. A pressure-swing cycle has at least three steps adsorption, blowdown, and repressurization. Although not always necessary, a purge step is normally used. In finely tuned processes, cocurrent depressurization and pressure-equalization steps are frequendy added. 

Apart from the cleanout procedure, the analytical work performed during the production of a bulk pharmaceutical in a three-step synthesis includes 15 different analyses having deterrnination of 22 parameters for raw materials 15 different analyses having deterrnination of 17 parameters in process controls and 11 different analyses having deterrnination of 19 parameters for the product. 

Preparation of other fluorosilicone monomers follows methods similar to that described above. For example, 2,4,6-trimethyl-2,4,6-tris(3,3,4,4,5,5,6,6,6-nona- uorohexyl)cyclotrisiloxane [38521-58-3] is produced from 3,3,4,4,5,5,6,6,6-nona-fluorohexene [19430-93 ] and methyldichlorosilane in three steps (3). 

The expansion process consists of three steps creating small discontinuities or cells in a fluid or plastic phase causing these cells to grow to a desired volume and stabilizing this cellular stmcture by physical or chemical means. 

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