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

Giant oscillations of the current in a dirty 2D electron system flowing perpendicular to a lateral barrier under magnetic field

The charge transport in a dirty 2-dimensional electron system biased in the presence of a lateral potential barrier under magnetic field is theoretically studied. The quantum tunneling across the barrier provides the quantum interference of the edge states localized on its both sides that results in giant oscillations of the charge current flowing perpendicular to the lateral junction. Our theoretical analysis is in a good agreement with the experimental observations presented in Ref.8. In particular, positions of the conductance maxima coincide with the Landau levels while the conductance itself is essentially suppressed even at the energies at which the resonant tunneling occurs and hence these puzzling observations can be resolved without taking into account the electron-electron interaction.Comment: 6 pages, 4 figure

Hitchin Systems - Symplectic Hecke Correspondence and Two-dimensional Version

The aim of this paper is two-fold. First, we define symplectic maps between Hitchin systems related to holomorphic bundles of different degrees. We call these maps the Symplectic Hecke Correspondence (SHC) of the corresponding Higgs bundles. They are constructed by means of the Hecke correspondence of the underlying holomorphic bundles. SHC allows to construct B\"{a}cklund transformations in the Hitchin systems defined over Riemann curves with marked points. We apply the general scheme to the elliptic Calogero-Moser (CM) system and construct SHC to an integrable \SLN Euler-Arnold top (the elliptic \SLN-rotator). Next, we propose a generalization of the Hitchin approach to 2d integrable theories related to the Higgs bundles of infinite rank. The main example is an integrable two-dimensional version of the two-body elliptic CM system. The previous construction allows to define SHC between the two-dimensional elliptic CM system and the Landau-Lifshitz equation.Comment: 39 pages, the definition of the symplectic Hecke correspondence is explained in details, typos corrected, references adde

Allelic Frequency of Kappa-Casein Locus (Asp148/Ala) in F1: Simmental (Bos Taurus) X Ongole Grade (Bos Indicus)

This study was conducted to detect the genetic variants (single nucleotide polymorphism) of kappa-casein locus (Asp148/Ala) in F1: Simmental (Bos taurus) x Ongole grade (Bos indicus), SIMPO. Genomic DNA was isolated from blood sample of 40 SIMPO (21 males and 19 females). A 780 bp specific fragment of kappa-casein gene spanning from the forth exon region (517 bp) to forth intron (263 bp) was successfully amplified. The result of the PCR-RFLP (Polymerase Chain Reaction - Restriction Fragment Length Polymorphisms) analysis using HindIII enzyme showed that two genotypes (AA and AB) were found at this locus in SIMPO. The frequencies of A and B alleles in SIMPO were 0.79 and 0.21, respectively. The frequency lies between B. taurus (Simmental) and B. indicus group