Bernard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlass

Riemann, Georg Friedrich Bernhard; Weber, Heinrich; Dedekind, Richard; Noether, M.; Wirtinger, W.

doi:10.1017/cbo9781139568050

Cited by 29 publications

(35 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The surface is a periodic structure of connected tubes. It is topologically equivalent to a famous minimal surface which was introduced by Bernhard Riemann [16].…”

Section: Polarization Singularities: Simple Examplesmentioning

confidence: 99%

Topology of Generic Polarization Singularities in Birefringent Crystals

2009

View full text Add to dashboard Cite

An optical vortex incident on a birefringent crystal unfolds into a complex topological structure of lines of circular polarization (C-lines) and surfaces of linear polarization (L-surfaces). The incident beam splits into two orthogonally polarized beams of ordinary and extraordinary polarization. Extraordinary refraction causes a shift of the extraordinarily polarized beam even under normal incidence. This shift together with the different phase velocities of both beams is the origin of an intriguing pattern of polarization singularities. We measure spatially resolved the full set of Stokes parameters after the beam passed the crystal to determine experimentally the spatial structure of the polarization singularities in three dimensions, two spatial directions (x, y) and one (Λ) corresponding to the relative phase retardation between ordinary and extraordinary beam. The observed unfolding of the initial phase singularity is the most generic case of the generation of polarization singularities in uniaxial or biaxial birefringent crystals. It can be describe in a very general way in terms of Stokes parameters where the polarization singularities arise naturally from the zeros of the Stokes parameters.

show abstract

“…The surface is a periodic structure of connected tubes. It is topologically equivalent to a famous minimal surface which was introduced by Bernhard Riemann [16].…”

Section: Polarization Singularities: Simple Examplesmentioning

confidence: 99%

Topology of Generic Polarization Singularities in Birefringent Crystals

2009

View full text Add to dashboard Cite

show abstract

“…Riemann speculated that the absorbed aether is transferred into another world or dimension. 4 Quantum mechanics can be used to describe space-time as being "bitty" at extremely small scales, consisting of fluctuating and generating particle pairs that appear and disappear incredibly quickly. Instead of being "smooth," the vacuum is described as resembling a "quantum foam," which was devised by John Wheeler in 1955.…”

Section: Introductionmentioning

confidence: 99%

New aether sink model for gravity

Choisuren¹,

Bayarsaikhan²

2013

Physics Essays

View full text Add to dashboard Cite

This paper assumes that a perfect fluid aether flows into all material objects in the universe. A model for elementary fermions is developed by modifying the conventional conception of the perfect fluid aether. Consequently, a new aether sink model for gravity is proposed. The conventional concept of mass is extended within the framework of the proposed models. For a system that consists of two bodies of incomparable mass, the qualitative structure of a 2D-phase portrait of a spatial fluid (i.e., the perfect fluid aether) flow is predicted. In this flow, hyperbolic equilibrium points may coincide with the Lagrangian points. This paper suggests that a difference in the dynamic pressures of geodesic spatial fluid flows may generate inertial force, gravitational force, and centrifugal force and also the conventional equations for these forces are theoretically derived. The proposed models provide plausible explanations for gravitational anomalies such as the Pioneer anomaly and the correlation between earthquake activity and planetary positions, etc. V C 2013 Physics Essays Publication. [http://dx.Résumé: Cet article admet come hypothèse qu'un éther fluide parfait coule dans tous les corps matériels de l'univers. Un modèle pour les fermions élémentaires est développé en modifiant le concept conventionnel d'un éther fluide parfait. Conséquemment, l'on propose un Nouveau Modèle de Puits d'É ther pour la gravité. Le concept conventionnel de la masse est étendu dans le cadre des modèles proposés. Pour un système consistant de deux corps de masse incomparable, l'on prédit la structure qualitative de portrait de fluide spatial à deux dimensions de phase (c'est-àdire, l'éther fluide parfait). Dans ce flux, les points d'équilibre hyperbolique peuvent coïncider avec les points Lagrangiens. Cet article suggère qu'une différence entre les pressions dynamiques des flux spatiales géodésiques peut générer une force inertielle, une force gravitationnelle, et une force centrifuge, et les équations conventionnelles pour ces forces sont théoriquement dérivées. Les modèles proposés donnent des explications plausibles pour les anomalies gravitationnelles, telles que l'anomalie du Pioneer, et la corrélation entre l'activité de tremblement de terre et position des planètes, et caetera….

show abstract

“…It should be emphasized, that the definition of the fractional order derivative is not unique, several definitions e.g. the Feller, Fourier, Riemann, Caputo, Weyl, Riesz, Grünwald fractional derivative definitions coexist [21][22][23][24][25][26][27][28][29]. A direct consequence of this diversity is the fact, that the solutions e.g.…”

Section: Introductionmentioning

confidence: 99%

Higher-dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed Nilsson oscillator

Herrmann¹

2010

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

Fw 21.60.Cs Keywords:Perturbation and fractional calculus methods Nuclear shell models Ground state properties of nuclei a b s t r a c t Based on the Riemann and Caputo definitions of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higherdimensional representation of a fractional rotation group with mixed derivative types. An extended symmetric rotor model is derived, which predicts the sequence of magic proton and neutron numbers accurately. The ground state properties of nuclei are correctly reproduced within the framework of this model.

show abstract

Bernard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlass

Cited by 29 publications

References 0 publications

Topology of Generic Polarization Singularities in Birefringent Crystals

Topology of Generic Polarization Singularities in Birefringent Crystals

New aether sink model for gravity

Higher-dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed Nilsson oscillator

Contact Info

Product

Resources

About