219 resultados para Locally Compact Group
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It is shown that prop-2-ynyl esters are useful protecting groups for carboxylic acids and that they are selectively deprotected in the presence of other esters on treatment with tetrathiomolybdate under mild conditions.
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With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.
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The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.
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We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.
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We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.
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Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
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Among the various substituted coumarins investigated only 7-acetoxycoumarin is observed to photodimerize topochemically in the crystalline state and this observation may be of importance in the context of "crystal engineering".
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Metabolism of linalyl acetate by Pseudomonas incognita isolated by enrichment culture on the acyclic monoterpene alcohol linalool was studied. Biodegradation of linalyl acetate by this strain resulted in the formation of linalool, linalool- 8-carboxylic acid, oleuropeic acid, and A5-4-acetoxy-4-methyl hexenoic acid. Cells adapted to linalyl acetate metabolized linalyl acetate-8-aldehyde to linalool- 8-carboxylic acid, linalyl acetate-8-carboxylic acid, A5-4-acetoxy-4-methyl hexenoic acid, and geraniol-8-carboxylic acid. Resting cell suspensions previously grown with linalyl acetate oxidized linalyl acetate-8-aldehyde to linalyl acetate-8- carboxylic acid, A5-4-acetoxy-4-methyl hexenoic acid, and pyruvic acid. The crude cell-free extract (10,000 g of supernatant), obtained from the sonicate of linalyl acetate-grown cells, was shown to contain enzyme systems responsible for the formation of linalyl acetate-8-carboxylic acid and linalool-8-carboxylic acid from linalyl acetate. The same supernatant contained NAD-linked alcohol and aldehyde dehydrogenases involved in the formation of linalyl acetate-8-aldehyde and linalyl acetate-8-carboxylic acid, respectively. On the basis of various metabolites isolated from the culture medium, resting cell experiments, growth and manometric studies carried out with the isolated metabolites as well as related synthetic analogs, and the preliminary enzymatic studies performed with the cellfree extract, a probable pathway for the microbial degradation of linalyl acetate with the acetoxy group intact is suggested.
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Treatment of morphine in aqueous HCl at 70° with KIO3 yields a monochloromorphine, identified as 1-chloromorphine by spectroscopic means and by the fact that it, and its methyl ether 1-chlorocodeine, are different from 2-chloromorphine and 2-chlorocodeine prepared from 2-aminomorphine of unequivocally established structure. Formation of 1-chloromorphine and the previously known 1-bromomorphine involves entry of the halogen into the position meta to the free phenolic hydroxyl. Possible mechanistic interpretations of this unusual orientation are discussed.
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Among the various substituted coumarins investigated only 7-acetoxycoumarin is observed to photodimerize topochemically in the crystalline state and this observation may be of importance in the context of "crystal engineering".
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The crystal structure of the cyclic peptide disulfide Boc-Cys-Pro-Aib-Cys-NHMe has been determined by X-ray diffraction. The peptide crystallizes in the space group P212121, with A = 8.646(1), B = 18.462(2), C = 19.678(3)Å and Z = 4. The molecules adopt a highly folded compact conformation, stabilized by two intramolecular 4→ 1 hydrogen bonds between the Cys (1) and Pro (2) CO groups and the Cys (4) and methylamide NH groups, respectively. The backbone conformational angles for the peptide lie very close to those expected for a 310 helix. The S-S bridge adopts a right handed twist with a dihedral angle of 82°. The structure illustrates the role of stereochemically constrained residues, in generating novel peptide conformations. Aib, α-aminoisobutyric acid; Z, benzyloxycarbonyl; Boc, t-butyloxycarbonyl; OMe, methyl ester; OBz, benzyl ester; NHMe, N-methylamide; Tosyl, p-toluenesulfonyl.
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Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.
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We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.
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It is demonstrated that Kibble’s method of gauging the Poincaré group can be applied to the gauging of the conformal group. The action of the gauge transformations is the action of general spacetime diffeomorphisms (or coordinate transformations) combined with a local action of an 11-parameter subgroup of SO(4,2). Because the translational subgroup is not an invariant subgroup of the conformal group the appropriate generalisation of the derivative of a physical field is not a covariant derivative in the usual sense, but this does not lead to any inconsistencies.