The validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

Characterization of Mycobacterium leprae RecA intein, a LAGLIDADG homing endonuclease, reveals a unique mode of DNA-binding, helical distortion and cleavage, compared to a canonical LAGLIDADG homing endonuclease

Mycobacterium leprae, which has undergone reductive evolution leaving behind a minimal set of essential genes, has retained intervening sequences in four of its genes implicating a vital role for them in the survival of the leprosy bacillus. A single in-frame intervening sequence has been found embedded within its recA gene. Comparison of M. leprae recA intervening sequence with the known intervening sequences indicated that it has the consensus amino acid sequence necessary for being a LAGLIDADG-type homing endonuclease. In light of massive gene decay and function loss in the leprosy bacillus, we sought to investigate whether its recA intervening sequence encodes a catalytically active homing endonuclease. Here we show that the purified M. leprae RecA intein (PI-MleI) binds to cognate DNA and displays endonuclease activity in the presence of alternative divalent cations, Mg2+ or Mn2+. A combination of approaches including four complementary footprinting assays such as DNase I, Cu/phenanthroline, methylation protection and KMnO4, enhancement of 2-aminopurine fluorescence and mapping of the cleavage site revealed that PI-MleI binds to cognate DNA flanking its insertion site, induces helical distortion at the cleavage site and generates two staggered double-strand breaks. Taken together, these results implicate that PI-MleI possess a modular structure with separate domains for DNA target recognition and cleavage, each with distinct sequence preferences. From a biological standpoint, it is tempting to speculate that our findings have implications for understanding the evolution of LAGLIDADG family of homing endonucleases

Rapid distortion of axisymmetric turbulence

A generalization of the isotropic theory of Batchelor & Proudman (1954) is developed to estimate the effect of sudden but arbitrary three-dimensional distortion on homogeneous, initially axisymmetric turbulence. The energy changes due to distortion are expressed in terms of the Fourier coefficients of an expansion in zonal harmonics of the two independent scalar functions that describe the axisymmetric spectral tensor. However, for two special but non-trivial forms of this tensor, which represent possibly the simplest kinds of non-isotropic turbulence and specify the angular distribution but not the wavenumber dependence, the energy ratios have been determined in closed form. The deviation of the ratio from its isotropic value is the product of a factor containing R, the initial value of the ratio of the longitudinal to the transverse energy component, and another factor depending only on the geometry of the distortion. It is found that, in axisymmetric and large two-dimensional contractions, the isotropic theory gives nearly the correct longitudinal energy, but (when R > 1) over-estimates the increase in the transverse energy; the product of the two intensities varies little unless the distortion is very large, thus accounting for the stress-freezing observed in rapidly accelerated shear flows.Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement. The different ansatzes predict results in broad qualitative agreement with a simple strategem suggested by Reynolds & Tucker (1975), but the quantitative differences are not always negligible.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Tendency to promote ferroelectric distortion in Pr-modified PbTiO3

Structural, microstructural, and dielectric studies have been carried out on Pr-modified PbTiO3. A comparative analysis with La-modified PbTiO3 suggests that for chemical modification by same amount, the Pr-modified system has larger tetragonal strain and Curie point. No clear feature of relaxor ferroelectric state is observed for Pr concentration as high as x=0.35, suggesting that Pr modification is less effective, as compared to La-modification, in inducing a relaxor ferroelectric state. Results suggest that inspite of increased chemical disorder, Pr modification partly tends to restore the ferroelectric distortion of the lattice through partial occupancy of the Pr4+ ions on the Ti4+ sites.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Space-Vector-Based Hybrid Pulsewidth Modulation Techniques for Reduced Harmonic Distortion and Switching Loss

Novel switching sequences can be employed in spacevector-based pulsewidth modulation (PWM) of voltage source inverters. Differentswitching sequences are evaluated and compared in terms of inverter switching loss. A hybrid PWM technique named minimum switching loss PWM is proposed, which reduces the inverter switching loss compared to conventional space vector PWM (CSVPWM) and discontinuous PWM techniques at a given average switching frequency. Further, four space-vector-based hybrid PWM techniques are proposed that reduce line current distortion as well as switching loss in motor drives, compared to CSVPWM. Theoretical and experimental results are presented.

Hydration and distortion of peptide helices in crystals. α-Helical structure of a dodecapeptide, Boc-(Ala-Leu-Aib)4-OMe

The dodecapeptide Boc-(Ala-Leu-Aib)(4)-OMe crystallized with two independent helical molecules in a triclinic cell. The two molecules are very similar in conformation, with a 3(10)-helix turn at the N-terminus followed by an alpha-helix, except for an elongated N(7)...O(3) distance in both molecules. All the helices in the crystal pack in a parallel motif. Eleven water sites have been found in the head-to-tail region between the apolar helices that participate in peptide-water hydrogen bonds and a network of water-water hydrogen bonds. The crystal parameters are as follows: 2(C58H104N12O15)+ca. 10H(2)O, space group P1 with a = 12.946(2), b = 17.321(3), c = 20.465(4) Angstrom, alpha = 103.12(2), beta = 105.63(2), gamma = 107.50(2)degrees, Z = 2, R = 10.9% for 5152 data observed > 3 sigma(F), resolution 1.0 Angstrom. In contrast to the shorter sequences [Karle et al. (1988)Proc. Natl. Acad. Sci. USA 85, 299-303] and Boc-(Ala-Leu-Aib)(2)-OMe [Karle et al. (1989) Biopolymers 28, 773-781], no insertion of a water molecule into the helix is observed. However, the elongated N---O distance between Ala(7) NH and Aib(3) CO in both molecules (molecule A, 3.40 Angstrom; molecule B, 3.42 Angstrom) is indicative of an incipient break in the helices. (C) Munksgaard 1994.