Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area-minimizing hypersurfaces exist. Below this value, in contrast, we construct examples.Comment: 31 pages. Comments are welcome

Hot Spots on the Fermi Surface of Bi2212: Stripes versus Superstructure

In a recent paper Saini et al. have reported evidence for a pseudogap around (pi,0) at room temperature in the optimally doped superconductor Bi2212. This result is in contradiction with previous ARPES measurements. Furthermore they observed at certain points on the Fermi surface hot spots of high spectral intensity which they relate to the existence of stripes in the CuO planes. They also claim to have identified a new electronic band along Gamma-M1 whose one dimensional character provides further evidence for stripes. We demonstrate in this Comment that all the measured features can be simply understood by correctly considering the superstructure (umklapp) and shadow bands which occur in Bi2212.Comment: 1 page, revtex, 1 encapsulated postscript figure (color

Minimal graphic functions on manifolds of non-negative Ricci curvature

We study minimal graphic functions on complete Riemannian manifolds \Si with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with such growth via splitting for tangent cones of \Si at infinity. When, in contrast, we do not impose any growth restrictions for minimal graphic functions, we also obtain a Liouville type theorem under a certain non-radial Ricci curvature decay condition on \Si. In particular, the borderline for the Ricci curvature decay is sharp by our example in the last section.Comment: 38 page

The Schwaigerian driver transfer technique and the Thevenin's and the Norton's theorem Final report

Graphical technique for analyzing series-parallel networks by rectangular diagrams in solving power distribution problem

Features of pulsed synchronization of a systems with a tree-dimensional phase space

Features of synchronization picture in the system with the limit cycle embedded in a three-dimensional phase space are considered. By the example of Ressler system and Dmitriev - Kislov generator under the action of a periodic sequence of delta - function it is shown, that synchronization picture significantly depends on the direction of pulse action. Features of synchronization tons appeared in these models are observed.Comment: 16 pages, 11 figure

Dynamical evolution of scalar perturbation in Ho\v{r}ava-Lifshitz black-hole spacetimes

We study the dynamical evolution of a massless scalar perturbation in the Ho\v{r}ava-Lifshitz black-hole spacetimes with the coupling constants $\lambda={1/3}$, $\lambda={1/2}$ and $\lambda=3$, respectively. Our calculation shows that, for the three cases, the scalar perturbations decay without any oscillation in which the decay rate imprints the parameter of the Ho\v{r}ava-Lifshitz black hole. The results are quite different from those in the Schwarzschild AdS black hole and can help us understand more about the Ho\v{r}ava-Lifshitz gravity.Comment: 14 pages, 5 figure

Three realizations of quantum affine algebra Uq(A2(2))U_q(A_2^{(2)})

In this article we establish explicit isomorphisms between three realizations of quantum twisted affine algebra $U_q(A_2^{(2)})$: the Drinfeld ("current") realization, the Chevalley realization and the so-called $RLL$ realization, investigated by Faddeev, Reshetikhin and Takhtajan.Comment: 15 page

On the \phi(1020)f_0(980) S-wave scattering and the Y(2175) resonance

We have studied the \phi(1020)f_0(980) S-wave scattering at energies around threshold employing chiral Lagrangians coupled to vector mesons through minimal coupling. The interaction kernel is obtained by considering the f_0(980) as a K\bar{K} bound state. The Y(2175) resonance is generated in this approach by the self-interactions between the \phi(1020) and the f_0(980) resonances. We are able to describe the e^+e^-\to \phi(1020)f_0(980) recent scattering data to test experimentally our scattering amplitudes, concluding that the Y(2175) resonance has a large \phi(1020)f_0(980) meson-meson component.Comment: 20 pages, 8 figure