Search results for "fundamental"

The Second Main Theorem

1998

Hadamard-type theorems for hypersurfaces in hyperbolic spaces

2006

Abstract We prove that a bounded, complete hypersurface in hyperbolic space with normal curvatures greater than −1 is diffeomorphic to a sphere. The completeness condition is relaxed when the normal curvatures are bounded away from −1. The diffeomorphism is constructed via the Gauss map of some parallel hypersurface. We also give bounds for the total curvature of this parallel hypersurface.

Canonical Brownian Motion on the Diffeomorphism Group of the Circle

2002

AbstractFor infinitesimal data given on the group of diffeomorphism of the circle with respect to the metric H3/2, the associated Brownian motion has been constructed by Malliavin (C.R. Acad. Sci. Parist.329 (1999), 325–329). In this work, we shall give another approach and prove the invariance of heat measures under the adjoint action of S1.

Feuilletages Riemanniens singuliers

2006

Abstract We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular. To cite this article: V. Miquel, R.A. Wolak, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The General Stokes’s Theorem

2012

Let ω be a differential form of degree k - 1 and class C 1 in a neighborhood of a compact regular k-surface with boundary M of class C 2. The general Stokes’s theorem gives a relationship between the integral of ω over the boundary of M and the integral of the exterior differential dω over M. It can be viewed as a generalization of Green’s theorem to higher dimensions, and it plays a role not unlike that of the fundamental theorem of calculus in an elementary course of analysis. Particular cases of the general Stokes’s theorem that are of great importance are the divergence theorem, which relates a triple integral with a surface integral and what we know as the classical Stokes’s theorem, w…

Non linear representations of Lie Groups

1977

International audience

5 QCD on the Lattice

2008

Since Wilson’s seminal papers of the mid-1970s, the lattice approach to Quantum Chromodynamics has become increasingly important for the study of the strong interaction at low energies, and has now turned into a mature and established technique. In spite of the fact that the lattice formulation of Quantum Field Theory has been applied to virtually all fundamental interactions, it is appropriate to discuss this topic in a chapter devoted to QCD, since by far the largest part of activity is focused on the strong interaction. Lattice QCD is, in fact, the only known method which allows ab initio investigations of hadronic properties, starting from the QCD Lagrangian formulated in terms of quark…

Quantum technologies and the elephants

2021

Extraordinary progress in quantum sensors and technologies opens new avenues for exploring the Universe and testing the assumptions forming the basis of modern physics. This QST focus issue: focus on quantum sensors for new-physics discoveries is a next-decade roadmap on developing a wide range of quantum sensors and new technologies towards discoveries of new physics. It covers the next generation of various technologies, including atomic and nuclear clocks, atomic and diamond-based magnetometers, atom and laser interferometers, control of trapped atoms, ions, and molecules, optomechanical systems, and many others. In this editorial, we outline major problems of fundamental physics we aim …

A novel numerical meshless approach for electric potential estimation in transcranial stimulation

2015

In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.

Parameters affecting the fundamental period of infilled RC frame structures

2015

Despite the fact that the fundamental period appears to be one of the most critical parameters for the seismic design of structures according to the modal superposition method, the so far available in the literature proposals for its estimation are often conflicting with each other making their use uncertain. Furthermore, the majority of these proposals do not take into account the presence of infills walls into the structure despite the fact that infill walls increase the stiffness and mass of structure leading to significant changes in the fundamental period numerical value. Toward this end, this paper presents a detailed and in-depth analytical investigation on the parameters that affect…