Search results for "Mathematical analysis"

The isoperimetric inequality and the geodesic spheres. Some geometric consequences

1986

Recovery of time-dependent coefficients from boundary data for hyperbolic equations

2019

We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.

Comparison theorems for the volume of a geodesic ball with a product of space forms as a model

1995

We prove two comparison theorems for the volume of a geodesic ball in a Riemannian manifold taking as a model a geodesic ball in a product of two space forms.

A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold

1994

AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.

Rate of Mixing for the Geodesic Flow

2019

The main part of the chapter then consists in proving analogous bounds for the discrete-time and continuous-time geodesic ow for quotient spaces of simplicial and metric trees respectively.

Solving stochastic differential equations on Homeo(S1)

2004

Abstract The Brownian motion with respect to the metric H 3/2 on Diff( S 1 ) has been constructed. It is realized on the group of homeomorphisms Homeo( S 1 ). In this work, we shall resolve the stochastic differential equations on Homeo( S 1 ) for a given drift Z .

On Upper Conical Density Results

2010

We report a recent development on the theory of upper conical densities. More precisely, we look at what can be said in this respect for other measures than just the Hausdorff measure. We illustrate the methods involved by proving a result for the packing measure and for a purely unrectifiable doubling measure.

Fractional Fourier Transforms and Geometrical Optics

2010

The influence of the mean stress on fatigue life of 10HNAP steel under random loading

2001

Abstract This paper contains the results of uniaxial random load fatigue tests with different mean values performed on 10HNAP steel specimens. The experimental fatigue life was compared with the life determined according to different methods of amplitude transformation of the cycles. Cycles were counted with the rain flow algorithm and damage was cumulated with the Palmgren–Miner hypothesis. It has been shown that in the case of “symmetric” stress histories with zero expected values, the mean values of selected cycles do not strongly influence the calculated fatigue life and transformation of the cycle amplitudes; hence, no mean stress correction for cycle mean values different from zero is…

Spectral analysis of the Neumann-Poincaré operator and characterization of the stress concentration in anti-plane elasticity

2012

When holes or hard elastic inclusions are closely located, stress which is the gradient of the solution to the anti-plane elasticity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important to precisely characterize the blow-up of the gradient of such an equation. In this paper we show that the blow-up of the gradient can be characterized by a singular function defined by the single layer potential of an eigenfunction corresponding to the eigenvalue 1/2 of a Neumann–Poincare type operator defined on the boundaries of the inclusions. By comparing the singular function with the one corresponding to two disks osculating to the inclusions, we quant…