Search results for "auch"
showing 10 items of 221 documents
Solving the Cut-Off Wave Numbers in Partially filled Rectangular Waveguides with Ferrite by the Cauchy Integral Method
2005
The modal analysis of the off-centered rectangular waveguide loaded with a vertical slab of ferrite material, biased in the y-direction by a DC magnetic field, leads to the resolution of a transcendent equation whose infinite solutions are the TE/sub m0/ cutoff wave numbers in the guide. The method based on the Cauchy integral (Delvest L.M. and Lyness, J.N., 1967) is becoming very popular for solving such equations. This powerful method is described for solving the propagation constant in a partially ferrite filled waveguide. The method is used to calculate the propagation constant of the fundamental TE mode for some configurations used in the literature about ferrites. Results obtained in …
Topologies on Partial O*-Algebras
2002
In this chapter, we introduce some basic locally convex topologies on partial O*-algebras and we establish general properties of these topologies. In Section 4.1, we compare the graph topologies induced by different O-families on the same domain (and the corresponding families of bounded subsets). In the case where the domain D M of an O-family M is a (quasi-) Frechet space, the structure of bounded subsets in D M can be described in a rather explicit way. Section 4.2 and Section 4.3 are devoted to the topologization of (partial) O*-algebras. Section 4.2 deals with locally convex topologies, the so-called uniform topologies τ u , τ u , τ * u and quasiuniform topologies τ qu , and Section 4.…
Verhulst model with Lévy white noise excitation
2008
The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Levy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise, (ii) noise with a probability density of increments expressed in terms of Gamma function, and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induc…
Ancient proteins resolve the evolutionary history of Darwin's South American ungulates.
2015
No large group of recently extinct placental mammals remains as evolutionarily cryptic as the approximately 280 genera grouped as 'South American native ungulates'. To Charles Darwin, who first collected their remains, they included perhaps the 'strangest animal[s] ever discovered'. Today, much like 180 years ago, it is no clearer whether they had one origin or several, arose before or after the Cretaceous/Palaeogene transition 66.2 million years ago, or are more likely to belong with the elephants and sirenians of superorder Afrotheria than with the euungulates (cattle, horses, and allies) of superorder Laurasiatheria. Morphology-based analyses have proved unconvincing because convergences…
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.
Infinite Dimensional Holomorphy
2019
We give an introduction to vector-valued holomorphic functions in Banach spaces, defined through Frechet differentiability. Every function defined on a Reinhardt domain of a finite-dimensional Banach space is analytic, i.e. can be represented by a monomial series expansion, where the family of coefficients is given through a Cauchy integral formula. Every separate holomorphic (holomorphic on each variable) function is holomorphic. This is Hartogs’ theorem, which is proved using Leja’s polynomial lemma. For infinite-dimensional spaces, homogeneous polynomials are defined as the diagonal of multilinear mappings. A function is holomorphic if and only if it is Gâteaux holomorphic and continuous…
Principal Values of Cauchy Integrals, Rectifiable Measures and Sets
1991
The extensive studies started by A. P. Calderon in the sixties and continued by many authors up today have revealed that the Cauchy integrals $$ {C_{\Gamma }}f(z) = \int_{\Gamma } {\frac{{f\left( \zeta \right)d\zeta }}{{\zeta - z}}} $$ behave very well on sufficiently regular, not necessarily smooth, curves F, see [CCFJR], [D] and [MT].
Holomorphic Functions on Polydiscs
2019
This is a short introduction to the theory of holomorphic functions in finitely and infinitely many variables. We begin with functions in finitely many variables, giving the definition of holomorphic function. Every such function has a monomial series expansion, where the coefficients are given by a Cauchy integral formula. Then we move to infinitely many variables, considering functions defined on B_{c0}, the open unit ball of the space of null sequences. Holomorphic functions are defined by means of Frechet differentiability. We have versions of Weierstrass and Montel theorems in this setting. Every holomorphic function on B_{c0} defines a family of coefficients through a Cauchy integral …
On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients
2017
International audience; The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space problem we establish energy estimates with finite loss of derivatives, which is linearly increasing in time. This implies well-posedness in H ∞ , if the coefficients enjoy enough smoothness in x. From this result, by standard arguments (i.e. extension and convexification) we deduce also local existence and uniqueness. A huge part of the analysis is devoted to give an appropriate sense to the Cauchy problem, which is not evide…
Lévy flights and Lévy-Schrödinger semigroups
2010
We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.