Equivariant Reduction to Torus of a Principal Bundle

Let M be an irreducible projective variety, over an algebraically closed field k of characteristic zero, equipped with an action of a connected algebraic group S over k. Let E _G be a principal G-bundle over M equipped with a lift of the action of S on M, where G is a connected reductive linear algebraic group. Assume that E _G admits a reduction of structure group to a maximal torus TG. We give a necessary and sufficient condition for the existence of a T-reduction of E _G which is left invariant by the action of S on E _G .     

400-photon-per-pulse ultrashort pulse autocorrelation measurement with aperiodically poled lithium niobate waveguides at 1.55 microm

We demonstrate ultrasensitive intensity autocorrelation measurements of subpicosecond optical pulses in the telecommunication band by using aperiodically poled lithium niobate (A-PPLN) waveguides. The tightly confined optical beam in the waveguides and the chirped poling period facilitate simultaneous high second-harmonic generation (SHG) efficiency and broad phase-matching (PM) bandwidth. The resulting measurement sensitivity is 3.2 x 10(-7) mW2, approximately 500 times better than the previous record for intensity autocorrelations. We also show that chirped A-PPLN waveguides retain nearly the same SHG efficiency as the unchirped guide as long as the PM bandwidth is not significantly broader than the input spectrum.     

Direct imaging of multimode interference in a channel waveguide

By use of a near-field scanning optical microscope in collection mode, multimode interference was directly measured in an annealed proton-exchanged LiNbO3 waveguide. Periodic transitions from a single-peaked Gaussianlike intensity distribution to a double-peaked intensity distribution were observed. The intensity distribution along the waveguide was calculated, and the results agree well with the experimental observation.     

Magnetoelectric characterization of xNi0.75Co0.25Fe2O4-(1−x)BiFeO3 nanocomposites

Magnetoelectric (ME) nanocomposites containing Ni_0.75Co_0.25Fe₂O₄-BiFeO₃ phases were prepared by citrate sol-gel process. X-ray diffraction (XRD) analysis showed phase formation of xNi_0.75Co_0.25Fe₂O₄-(1−x)BiFeO₃ (x=0.1, 0.2, 0.3 and 0.4) composites on heating at 700 °C. Transmission electron microscopy revealed the formation of powders of nano order size and the crystal size was found to vary from 30 to 85 nm. Dispersion in dielectric constant (ε) and dielectric loss (tan δ) in the low-frequency range have been observed. It is seen that nanocomposites exhibit strong magnetic properties and a large ME effect. On increasing Ni_0.75Co_0.25Fe₂O₄ contents in the nanocomposites, the saturation magnetization (M_S) and coercivity (H_C) increased after annealing at 700 °C. The large ME output in the nanocomposites exhibits strong dependence on magnetic bias and magnetic field frequency. The large value of ME output can be attributed to small grain size of ferrite phase of nanocomposite being prepared by citrate precursor process.     

10 Gbps optical soliton transmission link using in-line SOA on standard SMF at 1.3 μm

In this paper, 10 Gbps optical soliton transmission link using in-line semiconductor optical amplifiers (SOAs) for already installed standard single mode fibers (SMF) at 1.3 μm wavelength has been reported. The pattern effect and the impact of chirp on pulse propagation after amplification have been investigated. The observations are based on modeling and simulation optical soliton transmission link. Optical soliton pulse transmission over distances of the order of several hundreds of kilometers has been shown with and without initial chirp.     

Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling

Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we consider ranked set sampling, in which ranking of units are done based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We then estimate the mean of the study variate Y by the BLUE based on the measurements made on the units of the ranked set sampling regarding the study variable Y, when (X ,Y) follows a Morgenstern type bivariate exponential distribution. We then consider unbalanced multistage ranked set sampling and estimate the mean of the study variate Y by the BLUE based on the observations made on the units of multistage ranked set sample regarding the study variable Y. Efficiency comparison is also made on all estimators considered in this work.     

Intramolecular Wittig Reaction: A New Synthesis of (S)‐Pyrrolam A

A straightforward synthesis of (S)‐pyrrolam A is described. The synthesis involves in situ generation of the phosphorane 3 , followed by an intramolecular Wittig reaction to furnish (S)‐pyrrolam A.