We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the timeand space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic ...

We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.

The objective of the current study was to evaluate the reproducibility of a reverse transcriptase PCR (RT-PCR)-based technique to differentiate viable and dead Salmonella cells in raw and sterilized milk. The microorganism was initially inoculated into the milk samples followed by incubating at 37°C for 4 h prior to inactivation by heat at 80°C for 10 min. The treated and non-treated samples we...

Localized cell shape change initiates epithelial folding, while neighboring cell invagination determines the final depth of an epithelial fold. The mechanism that controls the extent of invagination remains unknown. During Drosophila gastrulation, a higher number of cells undergo invagination to form the deep posterior dorsal fold, whereas far fewer cells become incorporated into the initially ...

Given a linear isometry A0 : Rn → Rn of finite order on Rn , a general 〈A0〉-invariant closed subset M of Rn is considered with Lipschitz boundary. Under suitable topological restrictions the existence of A0-invariant geodesics of M is proven.

[1] We have identified a dust storm deposit in the GISP2 ice core that most likely originated from the Great Plains region of the United States during the 1930’s ‘Dust Bowl’ era. These results indicate that the Central U.S. can be a significant source of dust to the Greenland ice sheet, especially when the source area is affected by intense drought conditions.

We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...

Infectious bursal disease (IBD) is an immunosuppressive, acute and highly contagious illness of growing-poultry stock infected with infectious bursal disease virus (IBDV). It is common in Pakistan, causing potential economic losses throughout the year. The objective of the study is to propose a rapid, sensitive and specific diagnostic tool, and compare it with existing commonly used reverse tra...