M. A. Jafarizadeha, M. Mirzaeea, M. Rezaee · 2008
The intimate connection between the Banach space wavelet reconstruction method on homogeneous spaces with both singular and nonsingular vacuum vectors, and some of well known quantum tomographies, such as: Moyal-representation for a spin, discrete phase space tomography, tomography of a free particle, Homodyne tomography, phase space tomography and SU(1,1) tomography is explained. Also both the atomic decomposition and banach frame nature of these quantum tomographic examples is explained in details.
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Ramiro de la Vega, Kenneth Kunen · ArXiv.org · 2003
Under the continuum hypothesis, there is a compact homogeneous strong S-space.
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Nature · 1894
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Henson, C. Ward, Iovino, José, Kechris, Alexander S. et al. · CaltechAUTHORS (California Institute of Technology) · 2003
We cannot end before at least briefly discussing one other spectacular result of the 90's. \n \nWe recall that the homogeneous Banach space problem (P5) is: If X is isomorphic to all Y ⊆ X, is X isomorphic to l2? This was solved by combining two beautiful pieces of work, Gowers' dichotomy theorem (Theorem 3.1) and the following theorem of Komorowski and Tomczak-Jaegermann [KT1, KT2]. A nice exposition somewhat simplifying the argument appears in [TJ1].
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N Van den Bergh · AIP conference proceedings · 2012
All Petrov type D Killing spinor space-times admitting a homogeneous conformal representant are constructed.
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Evert Slob, Maarten Mulder · Geophysics · 2016
ABSTRACT We have developed explicit expressions and the corresponding computer code for all homogeneous space Green’s functions for coupled electromagnetic fields and poroelastic waves. The Green’s functions are derived from the basic equations in closed form in the wavenumber- and space-frequency domains. They are given for point sources of any type. This adds several Green’s functions to what has been published before. These Green’s functions can be used in integral equation formulations, for numerical model validation, and for studying earthquake-related electrokinetic effects. The wavenumber domain code for all Green’s functions is given with the numerical test on the basic equations to demonstrate correctness. The numerical codes to compute them in the space-frequency domain are also given. A numerical inverse fast Fourier transformation routine is used to provide space-time domain results. At seismic frequencies, the fast P-wave is radiated with the largest amplitude in all fields, except for the magnetic fields where no P-waves are generated. At ultrasonic frequencies and in the particle and filtration velocity fields generated by an electric current source, the slow P-wave has the strongest amplitude. In the filtration velocity and particle velocity, the slow P-wave is, respectively, three orders and one order of magnitude stronger than the fast P-wave.
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Cambridge University Press eBooks · 2003
We recall that the homogeneous Banach space problem (P5) is: If X is isomorphic to all Y ⊆ X, is X isomorphic to l2? This was solved by combining two beautiful pieces of work, Gowers' dichotomy theorem (Theorem 3.1) and the following theorem of Komorowski and Tomczak-Jaegermann [KT1, KT2]. A nice exposition somewhat simplifying the argument appears in [TJ1].
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Yi Zhu · Journal of the Institute of Mathematics of Jussieu · 2017
By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface over an algebraically closed field, a variety whose geometric generic fiber is a projective homogeneous space admits a rational point if and only if the elementary obstruction vanishes.
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R. F. Polishchuk · 1973
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William Thomson · Proceedings of the Royal Society of London · 1894
Abstract 1. The homogeneous division of any volume of space means the dividing of it into equal and similar parts, or cells, as I shall call them, all sameways oriented. If we take any point in the interior of one cell or on its boundary, and corresponding points of all the other cells, these points form a homogeneous assemblage of single points, according to Bravais’ admirable and important definition. The general problem of the homogeneous partition of space may be stated thus.
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Richard Tolimieri · Geometriae Dedicata · 1972
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M. K. Gupta, Suman Sharma, Fatemah Mofarreh et al. · Mathematics · 2023
The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsler spaces, are one of the major issues in Finsler geometry. In this paper, we have obtained the expression for S-curvature in homogeneous Finsler space with a generalized Matsumoto metric and demonstrated that the homogeneous generalized Matsumoto space with isotropic S-curvature has to vanish the S-curvature. We have also derived the expression for the mean Berwald curvature by using the formula of S-curvature.
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RECERCAT (Consorci de Serveis Universitaris de Catalunya) · 2021
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Robert L. Bryant, Luis A. Florit, Wolfgang Ziller · Advances in Mathematics · 2025
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M. Rosenbaum, Michael P. Ryan, L. C. Shepley · Journal of Mathematical Physics · 1979
A space-time homogeneous model is one in which the metric and the connection are invariant under a four-dimensional transitive Lie group. The Einstein-Cartan theory describes the effect of spin on geometry. The field equations require a stress-energy tensor and a spin tensor for a perfect fluid, and we give the required forms here. The main part of this paper is a presentation of several classes of space-time homogeneous solutions of the Einstein-Cartan equations for perfect fluid cosmological models.
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Waldo Arriagada, Jorge Huentutripay · SHILAP Revista de lepidopterología · 2017
In this article we define and characterize the homogeneous Orlicz space $\mathscr{D}^{1,\Phi}_{\rm o}(\mathbb{R}^{N})$ where $\Phi:\mathbb{R}\to [0,+\infty)$ is the N-function generated by an odd, increasing and not-necessarily differentiable homeomorphism $\phi:\mathbb{R}\to\mathbb{R}$. The properties of $\mathscr{D}^{1,\Phi}_{\rm o}(\mathbb{R}^{N})$ are treated in connection with the $\phi$-Laplacian eigenvalue problem $$ -\hbox{div}\Big(\phi(|\nabla u|)\frac{\nabla u}{|\nabla u|}\Big) =\lambda\,g(\cdot)\phi(u)\quad\text{in }\mathbb{R}^N $$ where $\lambda\in\mathbb{R}$ and $g:\mathbb{R}^N\to\mathbb{R}$ is measurable. We use a classic Lagrange rule to prove that solutions of the $\phi$-Laplace operator exist and are non-negative.
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Robert L. Bryant, Luis A. Florit, Wolfgang Ziller · arXiv (Cornell University) · 2024
We classify curvature homogeneous hypersurfaces in S^4 and H^4. In higher dimesnsion one only has the FKM examples and an isolate one by Tsukada of a hypersurface in H^5. Besides some simple examples, we show that there exists an isolated hypersurface with a circle of symmetries and and a one parameter family admitting no continuous symmetries. Outside the set of minimal points, which only exists in the case of S^4, every example is locally and up to covers of this form.
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Thorne Shipley · Annual Meeting Optical Society of America · 1989
In 1965 (Science 150, 348-350) I first showed that stereoscopic depth contours could be generated across large homogeneous central regions of visual space and that these contours were real in that they reversed directly when the sign of the disparity in the frame also reversed, provided that the inducing frame(s) was of sufficient strength. I left the issue unsettled as to what that strength must consist of. Much work has been done by others since, but no one seems to have advanced significantly on this key issue. It thus seemed worthwhile to devise some new targets and to repeat and extend the early measurements. These contours seem limited to a range of ~5° of visual angle, and they are most robust, paradoxically perhaps, when they pass directly across the foveal region, hence, between the two interhemispherical cortical projection areas. Consequently, neural processes must extend over these ranges, and any adequate model of stereopsis must take account of this impressive low frequency global event. The contrast to high spatial frequency stereoacuity processes seems worthy, also, of reemphasis.
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Hardy Littlewood Maximal Operator, Yoshihiro Sawano, Yoshihiro Sawano · 2003
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Xinpeng Liu, J. Nellie Liang, Chenshuo Zhang et al. · 2025
Analyses of human motion kinematics have achieved tremendous advances. However, the production mechanism, known as human dynamics, is still undercovered. In this paper, we aim to push the understanding of data-driven human dynamics forward. We identify a major obstacle to this as the heterogeneity of existing human motion understanding efforts. Specifically, heterogeneity exists in not only the diverse kinematics representations and hierarchical dynamics representations but also the data from different domains, namely biomechanics and reinforcement learning. With an in-depth analysis of the existing heterogeneity, we propose to emphasize the beneath homogeneity: all of them represent the homogeneous fact of human motion, though from different perspectives. Given this, we propose Homogeneous Dynamics Space (HDyS) as a fundamental space for human dynamics by aggregating heterogeneous data and training a homogeneous latent space with inspiration from the inverse-forward dynamics procedure. HDyS achieves decent mapping between human kinematics and dynamics by leveraging the heterogeneous representations and datasets. We demonstrate the feasibility of HDyS with extensive experiments and applications. The project page is https://foruck.github.io/HDyS.
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