Abstract We prove Li-Yau-Kröger-type bounds for Neumann-type eigenvalues of the biharmonic operator on bounded domains in a Euclidean space. also sharp estimates lower order Steklov problem and Laplacian, which directly implies two Reilly-type inequalities corresponding first nonzero eigenvalue.

E.O. Kiktenko, 2, 3 A.S. Trushechkin, C.C.W. Lim, Y.V. Kurochkin, and A.K. Fedorov 5 Russian Quantum Center, Skolkovo, Moscow 143025, Russia Theoretical Department, DEPHAN, Skolkovo, Moscow 143025, Russia Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia Quantum Information Science Group, Computational Sciences and Engineering Division, Oak Ridge National Labo...

X iv :m at h/ 06 10 74 2v 2 [ m at h. C O ] 2 8 O ct 2 00 6 Clustering of spectra and fractals of regular graphs V. Ejov, J.A. Filar, S.K. Lucas, P. Zograf 1 School of Mathematics and Statistics, University of South Australia, Mawson Lakes SA 5095 Australia 2 Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, USA 3 St. Petersburg Department of Steklov In...

We describe geometric non-commutative formal groups in terms of a geometric commutative formal group with a Poisson structure on its splay algebra. We describe certain natural properties of such Poisson structures and show that any such Poisson structure gives rise to a non-commutative formal group. We describe geometric non-commutative formal groups in terms of a geometric commutative formal g...

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...

The infinite matrices in Witten’s vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s = 0 limit. We find that s = 1 eigenfunctions just acquire a p term, and x gets rep...

In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi{Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer bihar-monic potentials, of the Calderon projections and the Poincar e-Steklov operators for such domains are analysed. We derive direct boundary integra...

E.O. Kiktenko, 2, 3 N.O. Pozhar, 3 A.V. Duplinskiy, 4 A.A. Kanapin, 5 A.S. Sokolov, S.S. Vorobey, A.V. Miller, V.E. Ustimchik, M.N. Anufriev, 3 A.S. Trushechkin, R.R. Yunusov, V.L. Kurochkin, Y.V. Kurochkin, and A.K. Fedorov ∗ Russian Quantum Center, Skolkovo, Moscow 143025, Russia Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia Bauman Moscow State Technical...

The six-vertex model with domain wall boundary conditions (DWBC) on an N ×N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom) boundaries of the lattice is calculated. It is shown that this two-point boundary correlator is expressible in a very simple way in terms of the one-point bound...