Transformation probabilities

Some particles sputtered from the surface are neutral whereas others are charged. Molecular particles can be emitted either as intact molecules or fragmented. The probability of the desorption of A into the emission channel X is given by the transformation probability P (A -> X ) ... 

For post-ionized particles, it is possible to define a generalized transformation probability P (A Xf) ... 

A 1,8-naphthyridine, nalidixic acid (39), shows clinically useful antibacterial activity against Gram-negative bacteria as such, the drug is used in the treatment of infections of the urinary tract. Condensation of ethoxymethylenemalonate with 2-amino-6-methylpyridine (36) proceeds directly to the naphthyri-dine (38) the first step in this transformation probably involves an addition-elimination reaction to afford the intermediate, 37. W-Ethylation with ethyl iodide and base followed by saponification then affords nalidixic acid (39). 

Assignments I, J XO H A, P FNZ indices data vector scaling factor for ordinate intermediate results function to transform %-probability values to NPS-scale x is the independent variable in the polynomial. (See Section 5.1.1.)... 

Reaction of the heterocycle with 2-methylcyclopentane-1,3-dione in the presence of pyridine leads directly to tetracyclic intermediate 20. 5 The first step in this transformation probably consists in formation of the olefin 18 by elimination of dimethylamine. 

Before finding the Laplace-transformed probability density wj(s, zo) of FPT for the potential, depicted in Fig. A 1(b), let us obtain the Laplace-transformed probability density wx s, zo) of transition time for the system whose potential is depicted in Fig. Al(c). This potential is transformed from the original profile [Fig. Al(a)] by the vertical shift of the right-hand part of the profile by step p which is arbitrary in value and sign. So far as in this case the derivative dpoints except z = 0, we can use again linear-independent solutions U(z) and V(z), and the potential jump that equals p at the point z = 0 may be taken into account by the new joint condition at z = 0. The probability current at this point is continuous as before, but the probability density W(z, t) has now the step, so the second condition of (9.4) is the same, but instead of the first one we should write Y (0) + v1 (0) = YiiOje f1. It gives new values of arbitrary constants C and C2 and a new value of the probability current at the point z = 0. Now the Laplace transformation of the probability current is... 

FVP treatment of both isolated samples 300 and 301 resulted in a mixture containing 300 + 301 this finding revealed that these two compounds can be mutually transformed into each other under forced conditions. Upon some kinetic measurements (determination of a negative activation entropy), the authors concluded that the ring transformation probably proceeds via a concerted sigmatropic shift to an antiaromatic diazirine intermediate. 

A different approach towards titanium-mediated allene synthesis was used by Hayashi et al. [55], who recently reported rhodium-catalyzed enantioselective 1,6-addition reactions of aryltitanate reagents to 3-alkynyl-2-cycloalkenones 180 (Scheme 2.57). In the presence of chlorotrimethylsilane and (R)-segphos as chiral ligand, alle-nic silyl enol ethers 181 were obtained with good to excellent enantioselectivities and these can be converted further into allenic enol esters or triflates. In contrast to the corresponding copper-mediated 1,6-addition reactions (Section 2.2.2), these transformations probably proceed via alkenylrhodium species (formed by insertion of the C-C triple bond into a rhodium-aryl bond) and subsequent isomerization towards the thermodynamically more stable oxa-jt-allylrhodium intermediates [55],... 

Mechanistically, the present transformation probably comprises two steps. Mannich reaction of in situ-generated cyclohexadienol 103 with iminium ion 104 is followed by an intramolecular aza-Michael reaction to furnish isoquinuclidine 102 (Scheme 41). Three stereogenic centers are created in this process. 

Recently there has emerged the beginning of a direct, operational link between quantum chemistry and statistical thermodynamic. The link is obtained by the ability to write E = V Vij—namely, to write the output of quantum-mechanical computations as the standard input for statistical computations, It seems very important that an operational link be found in order to connect the discrete description of matter (X-ray, nmr, quantum theory) with the continuous description of matter (boundary conditions, diffusion). The link, be it a transformation (probably not unitary) or other technique, should be such that the nonequilibrium concepts, the dissipative structure concepts, can be used not only as a language for everyday biologist, but also as a tool of quantitation value, with a direct, quantitative and operational link to the discrete description of matter. 

This interpretation of the master equation means that is has an entirely different role than the Chapman-Kolmogorov equation. The latter is a nonlinear equation, which results from the Markov character, but contains no specific information about any particular Markov process. In the master equation, however, one considers the transformation probabilities as given by the specific system, and then has a linear equation for the probabilities which determine the (mesoscopic) state of that system. 

Substituted-4-oxo-4//-pyrido[l,2-a]pyrimidines of type 74 (6-R H) are transformed to l,4-dihydro-4-oxo-l,8-naphthyridines on the action of heat.bl)-71-7l, 1 29 1 33 323 325 Ring transformation is facilitated by the nearly coplanar disposition of the 4-CO group and the 6-substituent of the pyrido-[l,2-u]pyrimidines. The steric interaction of these groups is shown by the relatively long C-4—N-5 bond (e.g., 147 pm for ethyl 6-methyl-4-oxo-4/f-pyrido[l,2-u]pyrimidine-3-carboxylate, as determined by X-ray study326). The strain caused by this interaction is relieved when the C-4—N-5 bond cleaves. Ring transformation probably takes place via the reactive imino-ketene intermediate (75).130... 

In a rare example of the use of iodonium salts for heteroatom-heteroatom bond formation, diaryliodonium halides were employed with sodium 0,0-diethyl phosphoroselenolate for a one-pot synthesis of diaryl diselenides (Scheme 9) [27]. These transformations probably occur via arylation of the phosphoroselenolate salt with the diaryliodonium ions, hydrolysis of the resulting aryl phosphoroselenolates with sodium hydroxide, and air oxidation of the arene-selenide ions thus produced. 

The first-order model can also be used to examine sequences of transformations of the form A —> B —> C . For the simple example A —> B —> C, the concentration of the initial reactant A falls exponentially, that of the intermediate species B rises then falls, and that of C builds up as it is fed from B. These time-dependent changes are illustrated in Figure 23 using one set of transformation probabilities. 

A complex ring transformation, probably involving radical intermediates, occurs in the reaction of 2,4,6-triphenylthiopyrylium ion (9) with the 4-(diazomethyl)-4//-thiopyrans 349, 350, and 353, the reaction products being the bis(6//-pyrrolino[l,2-6]pyrazoles) 367-369, respectively (85T811). 

Ethoxyallylation. Treatment of the cyano ketone 1 with this acetal in refluxing benzene furnishes 2 in 76% yield. This transformation probably involves a Claisen rearrangement of the mixed acetal a. 

Another advantageous route to 107 is the pyrolysis of 2-dialkylamino-4-(a-bromoalkyl)-l,3-dithiolan-2-ylium obtained in almost quantitative yield by bromination of allyl dithiocarbamates (104). Intermediates 105 have been isolated and characterized. " Their transformation probably involves an initial 1,2-dehydrobromination giving 106, which undergoes 1,3-hydrogen shift. 

The ion 20 is losing CO to be transformed probably into the azatropilium ion 92. The mass spectra of m- and p-nitrotoluenes yielded only M—NO and M— NO ions. Nitroxylenes and polynitrotoluenes yielded ions [122]. 

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