The integral assembly map in algebraic K-theory is split injective for any geometrically finite discrete group with finite asymptotic dimension. The goal of this paper is to apply the techniques developed by the first author in [3] to verify the integral Novikov conjecture for groups with finite asymptotic dimension as defined by M. Gromov [9]. Recall that a finitely generated group Γ can be vi...

Let V be a noncompact complete Riemannian manifold. We find a geometric condition which assures that the essential spectrum of the Laplacian on V contains a half-line, by means of fiber bundle structures and the asymptotic behavior of mean curvatures on the ends of V , and give lower bounds of the essential spectrum. Our criteria can be applied to locally symmetric spaces of finite volume and m...

The single 3-brane brane world at six dimension is examined when the extra dimensions are not compact. Although the warp factor diverges at the asymptotic region of the extra dimension, the normalizable zero mode and higher KK spectrum exist in the gravitational fluctuation. We compute the zero mode analytically and KK spectrum numerically. It is explicitly proven that our solution does not obe...

The Fuč́ık spectrum for systems of second order ordinary differential equations with Dirichlet or Neumann boundary values is considered: it is proved that the Fuč́ık spectrum consists of global C surfaces, and that through each eigenvalue of the linear system pass exactly two of these surfaces. Further qualitative, asymptotic and symmetry properties of these spectral surfaces are given. Finally, ...

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic...

in this paper we discuss on the fixed points of asymptotic contractions and boyd-wong type contractions in uniform spaces equipped with an e-distance. a new version ofkirk's fixed point theorem is given for asymptotic contractions and boyd-wong type contractions is investigated in uniform spaces.

A surface functional theory for p-dimensional extended objects, the p-branes , was proposed in previous papers. The eld equations for toroidal p-branes was exactly solved in d = p+2 dimensions, yielding equally spaced mass-squared spectrum with massless states. In this paper, we obtain the asymptotic distribution of mass spectrum in the point-particle limit of the theory with sphere-like membra...

The spectrum of complex PT-symmetric potential, V (x) = igx, is known to be null. We enclose this potential in a hard-box: V (|x| ≥ 1) = ∞ and in a softbox: V (|x| ≥ 1) = 0. In the former case, we find real discrete spectrum and the exceptional points of the potential. The asymptotic eigenvalues behave as En ∼ n. The solvable purely imaginary PT-symmetric potentials vanishing asymptotically kno...

The spectrum of complex PT-symmetric potential, V (x) = igx, is known to be null. We enclose this potential in a hard-box: V (|x| ≥ 1) = ∞ and in a softbox: V (|x| ≥ 1) = 0. In the former case, we find real discrete spectrum and the exceptional points of the potential. The asymptotic eigenvalues behave as En ∼ n. The solvable purely imaginary PT-symmetric potentials vanishing asymptotically kno...