Iterated Differential Forms IV: C-Spectral Sequence

For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the algebra of secondary iterated differential forms on (O,C). This allows to develop secondary tensor analysis on generic diffieties, some simplest elements of which are sketched here. The presented here general theory will be specified to infinite jet spaces and infinitely prolonged PDEs in subsequent notes.Comment: 8 pages, submitted to Math. Dok

Dipole-Quadrupole Theory of Surface Enhanced Infrared Absorption and Appearance of Forbidden Lines in the SEIRA Spectra of Symmetrical Molecules

The paper presents main aspects of the Dipole-Quadrupole theory of Surface Enhanced Infrared Absorption (SEIRA). It is pointed out the possibility of appearance of the lines, caused by totally symmetric vibrations transforming after the unit irreducible representation, which are forbidden in usual infrared absorption spectra in molecules with sufficiently high symmetry. Observation of such lines in the SEIRA spectra of diprotonated and ethylene, adsorbed on and on mordenites is pointed out. The results well agree with our ideas about surface enhanced optical processes, based on the conception of a strong quadrupole light-molecule interaction, which allows us to develop the SERS and SEHRS theories.Comment: 15 pages,3 figures, 1 tabl

Glycerol as an Energy Source for Ruminants: a Meta-Analysis of in Vitro Experiments

Glycerol or glycerin is generally recognized as a safe compound to be used in animal feed, especially for ruminants. A number of in vitro studies related to glycerol supplementation in ruminant ration have been published but to date the results have not been summarized. The objective of this study was, therefore, to evaluate in vitro digestibility, ruminal fermentation characteristics, total gas and methane production through the meta-analysis approach. Meta-analysis was applied to 13 experiments and 42 treatments dealing with glycerol supplementation in ruminants. Data were analyzed by general linear model procedure in which the glycerol levels and the different studies were treated as fixed effects. Results revealed that glycerol supplementation did not affect the in vitro digestibility and total VFA production, but significantly decreased molar proportion of acetate and iso-valerate (P<0.05). In contrast, molar proportion of propionate, butyrate, and valerate significantly increased, and thus the ratio of acetate to propionate declined linearly (P<0.05). Methane production decreased linearly and accompanied with an increase of total gas production with increasing levels of glycerol supplementation (P<0.05). It is concluded that the use of glycerol as an energy substitution in animal feed has no detrimental effects in the rumen and environmentally friendly

On the initial condition for evolution of the perturbative QCD Pomeron in the nucleus

It is shown that subdominant terms found in the reggeized gluon diagram technique, to be added to Pomeron fan diagrams with the 3P interaction, can be exactly taken into account by taking the initial condition for evolution in the Glauber form. This demonstrates complete equivalence of the dipole picture and the reggeized gluon approach not only on the leading level but also on the subleading level.Comment: 5 pages in LaTe

2 and 3-dimensional Hamiltonians with Shape Invariance Symmetry

Via a special dimensional reduction, that is, Fourier transforming over one of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape invariance symmetry. Using this symmetry we have obtained their eigenspectrum. In the mean time we show equivalence of shape invariance symmetry and Lie algebraic symmetry of these Hamiltonians.Comment: 24 Page

Massive Fields of Arbitrary Integer Spin in Symmetrical Einstein Space

We study the propagation of gauge fields with arbitrary integer spins in the symmetrical Einstein space of any dimensionality. We reduce the problem of obtaining a gauge-invariant Lagrangian of integer spin fields in such background to an purely algebraic problem of finding a set of operators with certain features using the representation of high-spin fields in the form of some vectors of pseudo-Hilbert space. We consider such construction in the linear order in the Riemann tensor and scalar curvature and also present an explicit form of interaction Lagrangians and gauge transformations for massive particles with spins 1 and 2 in terms of symmetrical tensor fields.Comment: 15 pages, latex, no figures,minor change

On Chebyshev polynomials and torus knots

In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s,2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, with the help of q,p-numbers, the generalized two-variable Alexander polynomials, and prove their direct connection with the HOMFLY polynomials and the skein relation of the latter.Comment: 6 pages (two-column UJP style

The Quantum Hall Effect: Unified Scaling Theory and Quasi-particles at the Edge

We address two fundamental issues in the physics of the quantum Hall effect: a unified description of scaling behavior of conductances in the integral and fractional regimes, and a quasi-particle formulation of the chiral Luttinger Liquids that describe the dynamics of edge excitations in the fractional regime.Comment: 11 pages, LateX, 2 figures (not included, available from the authors), to be published in Proceedings of the International Summer School on Strongly Correlated Electron Systems, Lajos Kossuth University, Debrecen, Hungary, Sept 199

Operator-Schmidt decomposition of the quantum Fourier transform on C^N1 tensor C^N2

Operator-Schmidt decompositions of the quantum Fourier transform on C^N1 tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1>N2. The first known special case, N1=N2=2^n, was computed by Nielsen in his study of the communication cost of computing the quantum Fourier transform of a collection of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis, University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in their study of strength measures of quantum operations. [M.A. Nielsen et. al, (accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the Schmidt decompositions presented here, it follows that in all cases the communication cost of exact computation of the quantum Fourier transform is maximal.Comment: 9 pages, LaTeX 2e; No changes in results. References and acknowledgments added. Changes in presentation added to satisfy referees: expanded introduction, inclusion of ommitted algebraic steps in the appendix, addition of clarifying footnote