Simple Rearrangement Research Articles

Reactions of polyfluoro-arenols and -heteroarenols with activated dimethyl sulphoxide. Facile [2,3]-sigmatropic rearrangement reactions giving de-aromatised products

Pentafluorophenol reacted with the reagent dimethyl sulphoxide–dicyclohexylcarbodi-imide–orthophosphoric acid below room temperature to give the ether (1), the [2,3]-rearrangement product (2), and (3) a derivative of (2). Under similar conditions, 2,3,5,6-tetrafluorophenol gave (7) and (8), and 1,3,4,5,6,7,8-heptafluoro-2-naphthol gave (12) and (13). Reaction of polyfluoroarenols with dimethyl sulphoxide–trifluoroacetic anhydride at low temperatures followed by deprotonation with triethylamine resulted in more efficient rearrangement reactions; 4-bromo-3,5,6-trifluoropyridin-2-ol gave the ether (14) and the products of rearrangement both to carbon and nitrogen, (15)(after hydrolysis) and (16) respectively; 2,4,5,6-tetrafluoropyridin-3-ol resulted in the overall replacement of the 2-fluorine by CHO (17) and by CH(SMe)2(18); and with 2,5,6-trifluoropyrimidin-4-ol and 5-fluoro-4,6-dimethoxypyrimidine-2-ol, simple rearrangement products (21) and (22) were obtained. Hydrolysis of (21) gave the 5-fluorouracil derivative (23). Sodium borohydride reduction and Raney nickel desulphurisations of some of the rearrangement compounds gave phenolic products. Reaction of the sulphone from (13) with base (DBU) effected the overall efficient replacement of the 1-fluorine in the 2-naphthol by CHO (35) and by CH(SO2Me)2(36).

Thermodynamics of intermediate ion–molecule complexes or kinetics of competing reactions? The reactions of low-energy isobutylamine and neopentylamine molecular ions

Metastable isobutylamine molecular ions fragment predominantly by loss of either C2H5 or C3H7 radicals. In contrast, the principal reaction of the closely related metastable neopentylamine ions is loss of C4H7 radicals. Claims that competition between simple cleavage and rearrangement is governed in these systems by the heats of formation of transient ion–molecule complexes are shown to be unjustified. It is proposed that, in both systems, rearrangement predominates over ‘simple cleavage’ for low-energy ions, but that crossing of the k(E)vs. E curves occurs at slightly higher energies for neopentylamine than for isobutylamine. Reversible isomerization of the molecular ions to stable distonic isomers is suggested. These isomers are considered to be important intermediates in the rearrangement–fragmentation processes. The involvement of distonic isomers complicates a description of the competing reactions in terms of simple cleavage vs. rearrangment. α-Cleavage for the distonic ions is in fact a rearrangement reaction.

Germanium film on SiO2 with a 〈100〉 texture deposited by the rf sputtering technique

Germanium (Ge) films on SiO2 with 〈100〉 texture deposited by a sputtering technique and the texture enhancement by a subsequent solid-state thermal annealing are demonstrated for the first time. A 0.6-μm-thick Ge film on a surface oxidized Si wafer deposited by the rf sputtering technique at 600 °C produces a 〈100〉 texture, and the preferential orientation of the film is enhanced by a conventional grain growth process at 900 °C (approximately 0.95Tm, where Tm is the melting point in the Kelvin scale) for 1 h, while the crystallographic texture of the films has never changed at 650 °C (0.75Tm) annealing. The texture enhancement is interpreted by the existence of 〈100〉 oriented precursors and a simple coalescence and rearrangement model.

A Two-Stage Rearrangeable Broadcast Switching Network

A new rearrangeable broadcast switching network has been invented. In its simplest form, the network has two stages. For larger networks, the switches in each stage can be replaced with two-stage networks to reduce crosspoint cost. The invention is based on an innovative approach of connecting each inlet channel to a multiplicity of first-stage switches according to a predetermined connection pattern. The network grows easily and has simple path hunt and rearrangement algorithms. It provides a general solution for any nonblocking broadcast switching application. Fewer crosspoints are required than in any other known two- or three-stage rearrangeable broadcast network. The connection arrangement exemplifies a topic heretofore unaddressed in combinatorial theory.

Solving embedded generalized network problems

A complete, unified description is given of the design and implementation of a fast and efficient program which solves linear programming problems with network substructures. The very efficient generalized network procedures which have recently been developed are extended in this paper to produce an algorithm, called E mnet, which can solve generalized network problems with additional constraints and additional (complicating) variables. The only requirement on the network substructure is that it contain, at most two nonzero entries in each column. This requirement is the most general possible for network substructures. Many large linear programming problems can be placed in this form by a simple rearrangement of its rows and columns. Preliminary computational experience indicates E mnft is about five times faster than M inos. The algorithm presented should provide a very efficient and fast solution for many linear programming problems involving production scheduling, distribution, facility location and personnel assignment. These problems tend to contain large embedded network substructures.

Polymerization of glycidol and its derivatives: A new rearrangement polymerization

AbstractAnionic (KOH) polymerization of glycidol, or its trimethylsilyl ether (TMSGE) followed by hydrolysis, gives a low molecular weight, largely amorphous polymer that is not the reported 1,3‐polyglycidol but, based on 13C‐NMR, largely a 1,4‐poly(3‐hydroxyoxetane) with much branching. This result is achieved by a simple rearrangement of the usual, propagating secondary oxyanion to a primary one. Substantial amounts of four dimers (5–10%), four trimers, and some tetramers were also found. One dimer was isolated and shown to be glycidyl glycerin, the usual thermal dimer from glycidol. Possible structures of the other dimers are proposed. The polymerization appears to begin with the rapid formation of the glycidoxy anion , formed by base abstraction of a proton from glycidol and by nucleophilic displacement of the SiMe3 group from TMSGE. Other bases such as KOtert‐Bu give similar 1,4 polymer for glycidol but, with TMSGE, there is considerable 1,3 polymerization. Detailed mechanisms are proposed. The polymer perpared from R‐TMSGE with KOH was highly crystalline, high melting (166°C), H2O soluble, isotactic poly(3‐hydroxyoxetane). The cationic polymerization of tert‐butyl glycidyl ether (TBGE) and TMSGE gave low molecular weight 1,3 polyethers. The TBGE polymer was all head‐to‐tail whereas the polyglycidol from TMSGE contained extensive head‐to‐head chain units with considerable branching. Mechanisms for these interesting differences are proposed.

An Analysis of Backtracking with Search Rearrangement

The search rearrangement backtracking algorithm of Bitner and Reingold [Comm. ACM, 18 (1975), pp. 651–655] introduces at each level of the backtrack tree a variable with a minimal number of remaining values; search order may differ on different branches. For conjunctive normal form formulas with v variables, s literals per term $(s \geqq 3)$, and $v^\alpha $ terms $((s/2) < \alpha < s)$, the average number of nodes in a search rearrangement backtrack tree is $\exp [\Theta (v^{(s - \alpha - 1)/(s - 2)} )]$ (i.e., for some positive constants $a_1 ,a_2 $, and $v_0 $, when $v \geqq v_0 $ the number of nodes is between $\exp (a_1 v^{(s - \alpha - 1)/(s - 2)} )$ and $\exp (a_2 v^{(s - \alpha - 1)/(s - 2)} )$. For $1 < \alpha \leqq s/2$ the average number of nodes is between $\exp [\Theta (v^{(s - \alpha - 1)/(s - 2)} )]$ and $\exp [\Theta ((\ln v)^{(s - 1)/(s - 2)} v^{(s - \alpha - 1)/(s - 2)} )]$. This compares with $\exp [\Theta (v^{(s - \alpha )/(s - 1)} )]$ for ordinary backtracking. For $1 < \alpha < s$, simple search rearrangement has approximately the same effect on speeding up backtracking as does reducing the problem complexity by decreasing the number of literals per term by one. Thus simple search rearrangement backtracking leads to a dramatic improvement in the expected running time.

Concentration dependence of diffusion in liquid crystals. A new experimental approach

The impurity diffusion of a chiral species into an aligned nematic film displays a unique textural behavior. A dynamical analysis of this type of texture provides a new approach to study the concentration dependence of the diffusion coefficients in liquid crystals. By a simple variable rearrangement in the solution to the Fick’s Law, we evaluated the diffusion coefficients from the linear portion of the typical x2k/t - ln t plot at various measurable concentrations (pitches). The results showed an inverse law between the diffusion coefficient and the concentration of the diffusion profile. Extrapolation to zero concentration would give a good approximation to the self-diffusion coefficient of the nematic solvent.

Search rearrangement backtracking and polynomial average time

The average time required for simple search rearrangement backtracking is compared with that for ordinary backtracking when each algorithm is used to find all solutions for random conjunctive normal form predicates. The sets of random predicates are characterized by v: the number of variables, t(v): the number of clauses, and p(v): the probability that a literal appears in clause. For large v if vp(v)<- 1n2 both backtracking methods require exponential time if and only if the average number of solutions per problem is exponential. Any backtracking method which finds all solutions to problems has this limitation. For vp(v)> 1n 2, there is a difficult region where the average number of solutions per problem is exponentially small, but backtracking requires an exponentially large time. The difficult region for search rearrangement backtracking is only slightly smaller than the difficult region for ordinary backtracking. It is conjectured that search rearrangement backtracking is exponentially faster than ordinary backtracking for nearly all of the difficult region. It is proved that there is no major advantage in using search rearrangement backtracking outside of the difficult region.

Carbonium ion rearrangements controlled by the presence of a silyl group

Tertiary alcohols with a λ-silyl group ( 3) generally undergo a simple carbonium ion rearrangement in acid giving a single alkene product ( 4) with loss of the silyl group.

Recent advances in negative ion mass spectrometry.

The paper describes theoretical and applied applications of negative ion chemistry carried out at Adelaide during the past five years. kinetic energy release in negative metastable ion decompositions is described, with particular reference to simple cleavage reactions, rearrangement reactions, and reactions which proceed by dual mechanisms. The application of deuterium isotope effects as a mechanistic probe is illustrated by reference to the elimination of ketene from quinone acetate negative ions. Charge stripping of a negative ion yields a decomposing positive ion, which produces a dissociative charge inversion spectrum of the negative ion. This technique allows the study of positive ions not available by conventional ionization; it provides a fingerprint for the parent positive ion produced in the collision process, and it may be used to determine the structure of the precursor negative ion. Finally, a combination of a negative ion spectrum and a charge inversion spectrum may be used as an analytical technique for the structure determination of unknown molecules.

INTERACTION EFFECTS IN MARINE SEISMIC SOURCE ARRAYS*

AbstractPast design of marine source arrays has been based on one or more of the following principles: simultaneous operation of multiple identical sources to increase radiated signal strength by simple addition; superposition of wavelets of different fundamental frequency to achieve a total pulse of desired, front‐loaded form (e.g. mixed volume air‐gun arrays); horizontal spacing of units or groups to achieve spatial filtering effects. The phenomenon of interaction between sources, affecting the loading experienced by each, has usually been ignored, or else avoided by wide spacing of units. However, interactions can significantly affect the efficiency and frequency response, in a way that can be favourable.Calculations are presented for sources emitting continuous or long duration signals, showing the energy efficiency as a function of frequency for arrays in a variety of configurations. Interaction effects are significant for inter‐source spacings smaller than or comparable with the wavelength—not, as is often stated, up to a distance related to the radii of the sources. The results show that potential exists for tailoring the frequency response of a source system, according to the application, by simple spatial rearrangement of units.Similar effects occur with interacting impulsive sources, but it is shown that different criteria apply for the optimum arrangements of units.

Iron and ruthenium carbonyls of 6,7-dimethylene- exo-3-oxatricyclo[3.2.1.0 2.4]octane. Protic acid additions to an epoxide ring homoconjugated to a η 4-(diene)Fe(CO) 3 function. Crystal structures of (C 9H 10O)Fe(CO) 3 and (C 10H 14O 2)Fe(CO) 3

The reaction of the epoxydiene 6,7-dimethylene- exo-3-oxatricyclo[3.2.1.0 2.4]octane (I) with iron and ruthenium carbonyls in various solvents yields the (η 4-1,3-diene)M(CO) 3 exo (II, M = Fe; IV, M = Ru). The endo-Fe(CO) 3 isomer (III) was obtained only in small yield from the reaction of I with Fe 2(CO) 9 or Fe(CO) 5 in n-pentane. The exo configuration of II was ascertained by an X-ray crystal structure determination. It reacts cleanly and rapidly with HCl in ether giving the exo-2-chloro-5,6-dimethylene- syn-7-norbornanol- endo-iron tricarbonyl complex (V), while the endo isomer III does not react to any significant extent under the same conditions. A simple Wagner-Meerwein rearrangement can explain the formation of V from II + HCl, although participation of the (diene)Fe(CO) 3 moiety cannot be excluded. When treated with HSO 3F/SO 2ClF/CD 2Cl 2, II furnished a stable cationic complex whose 1H and 13C NMR spectra suggest delocalisation of the homoconjugated positive charge by the (diene)Fe(CO) 3 function. Quenching of the cation with methanol yielded the exo-2-methoxy-5,6-dimethylene- syn-7-norbornanol- endo-iron tricarbonyl complex (X) whose structure was established by single crystal X-ray diffraction.

An Approach to the Interpretation of the Mass Spectra of Aliphatic Acids

Abstract A method of comparing the sum of the total energies of fragment molecules has been applied to the interpretation of simple cleavage and rearrangement reactions in electron-impact mass spectrometry for the straight chain aliphatic acids.

Integrating-input technique for c.c.d.

A simple rearrangement of the usual waveforms and voltage levels on the input terminals of a charge-coupled device can be used to integrate the input signal during the intersample interval. The method automatically provides a lowpass filter characteristic matched to the sampling time and tends to suppress high-frequency components and hence reduces aliasing problems. Adequate linearity and dynamic range are demonstrated.

A further note on backwards Markovian models (Corresp.)

Given a wide-sense forwards Markovian model, namely a state-space system driven by a white-noise process that is uncorrelated with the random initial state of the system, several papers have shown how to obtain a corresponding {\sl backwards} Markovian model: a system driven backwards in time from a 'terminal' state by a white-noise process that is uncorrelated with this state, and such that the joint second-order statistics of the backwards-model state and output processes equal those of the corresponding forwards-model processes. A very direct derivation is presented that shows in effect how a simple rearrangement of the forwards

Generalization of Cooperative Behavior Across Classroom Situations

Three behavior-disordered preschoolers who had low rates of cooperative behavior served as subjects in a classroom setting. Observations were made throughout phases of Baseline, Intervention I, Reversal, and Intervention II, and within a multiple baseline design. For participation in a low-frequency assembly task, children gained access time to high-frequency activities. Data were also collected during free-play occasions during which contingencies were not manipulated. Results indicated an increase in cooperative behavior and proximity within task-specific (e.g., assembly) situations. There was additional evidence of generalization of such behavior during free-play periods. The outcomes indicate the feasibility of group behavior change by simple systematic contingency rearrangement of existing classroom activities. Results also support generalization of programmed gains to nonprogrammed behavior classes within the same environment.

On the Computation of the Discrete Cosine Transform

An N -point discrete Fourier transform (DFT) algorithm can be used to evaluate a discrete cosine transform by a simple rearrangement of the input data. This method is about two times faster compared to the conventional method which uses a 2N -point DFT.

Thermodynamic data from the thermochromic effect. An undergraduate physical chemistry experiment

This experiment is good for basic physical chemistry undergraduate courses because it can be completed in three hours and it requires a minimum of calculation since the reaction is a simple unimolecular rearrangement.

Photolysis of diterpenoid quinones

Photolysis of the diterpene quinone royleanone in benzene gave predominantly products resulting from both side-chain rearrangement and formation of an ether bridge to C-1. It is proposed that these arose by very specific transfer of two hydrogen atoms in a highly oriented complex between ground state royleanone and photo-excited royleanone. In contrast 7α-acetoxyroyleanone gave products of simple side chain rearrangement, with or without loss of acetic acid, probably via a spirocyclopropyl intermediate.Royleanone methyl ether gave mainly an oxetanol in benzene but a methylenedioxy com-pound and an acetoxymethoxy compound in acetic acid. It is suggested that these arise from diradical and zwitterionic intermediates.