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371.
372.
In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold , admitting a non-constant smooth function f on M such that ?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented. 相似文献
373.
Theo Steininger Jait Dixit Philipp Frank Maksim Greiner Sebastian Hutschenreuter Jakob Knollmüller Reimar Leike Natalia Porqueres Daniel Pumpe Martin Reinecke Matev raml Csongor Varady Torsten Enßlin 《Annalen der Physik》2019,531(3)
NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy 3, a major upgrade to the original NIFTy framework. NIFTy 3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy 3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy 3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 . 相似文献
374.
375.
In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension in , and later this result has been extended to more general non-tangentially accessible domains and beyond.In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph Γ of dimension d in , , with a small Lipschitz constant. We construct a linear degenerate elliptic operator L such that the corresponding harmonic measure is absolutely continuous with respect to the Hausdorff measure on Γ. More generally, we provide sufficient conditions on the matrix of coefficients of L which guarantee the mutual absolute continuity of and the Hausdorff measure. 相似文献
376.
The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of embeds into the Bebutov flow, the -shift on . An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces. 相似文献
377.
We have synthesized a homologous series of azoesters consisting of a coumaryl moiety as the end group. Eleven derivatives of this series exhibit mesomorphism. The nematic mesophase is exhibited from ethyl homologue onward, while the smectic phase commences at the pentyl derivative and is exhibited along with the nematic phase up to the hexadecyl derivative. The N-I transition temperatures curves show the usual odd-even effect. All the compounds in this series are thermally stable and exhibit a wide mesomorphic range of nearly 120°C. Their thermal stabilities and other characteristics are discussed. 相似文献
378.
The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine-matics through translational and rot... 相似文献
379.
380.
Sehie Park 《Numerical Functional Analysis & Optimization》2013,34(1-2):101-110
In this paper we use fixed point and coincidence theorems due to Park [8] to give matching theorems concerning closed coverings of nonempty convex sets in a real topological vector space. Our new results extend previously given ones due to Ky Fan [2], [3], Shih [10], Shih and Tan [11], and Park [7]. 相似文献