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

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

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

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

Structural, elastic, and electronic properties of newly discovered Li2PtSi3 superconductor: Effect of transition metals

First-principles calculations within the density functional theory (DFT) with GGA-PBE exchange-correlation scheme have been employed to predict the structural, the elastic and the electronic properties of newly discovered lithium silicide superconductor, Li2PtSi3, for the first time. All the theoretical results are compared with those calculated recently for isostructural Li2IrSi3. The present study sheds light on the effect of replacement of transition metal element Ir with Pt on different mechanical, electronic, and superconducting properties. The effect of spin-orbit coupling on electronic band structure was found to be insignificant for Li2PtSi3. The difference in superconducting transition temperatures of Li2PtSi3 and Li2IrSi3 arises primarily due to the difference in electronic energy density of states at the Fermi level. Somewhat reduced Debye temperature in Li2PtSi3 plays a minor role. We have discussed the implications of the theoretical results in details in this study.Comment: Submitted for publicatio