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Lagrangians, SO(3)-Instantons and Mixed Equation
The mixed equation , defined as a combination of the anti-self-duality equation in gauge theory and Cauchy–Riemann equation in symplectic geometry, is...
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Direct minimizing method for Yang–Mills energy over SO(3) bundle
In this paper, we improve the known results on the direct minimizing method for Yang–Mills energy over closed four manifolds when the structure group...
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A Numerical Calculation Algorithm of the Inclination Function Based on the Representation of SO(3) Group
In the determination of the Earth gravity field in satellite geodesy, the inclination functions represent the projection of data observed along the...
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Representations of \(\mathrm{{SU} }(2)\) and \(\mathrm{{SO}}(3)\)
To study the irreducible representations of the Lie groups \(\mathrm{{SU}}(2)\)...
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A Second-Order SO(3)-Preserving and Energy-Stable Scheme for Orthonormal Frame Gradient Flow Model of Biaxial Nematic Liquid Crystals
In this paper, we present a novel second-order generalised rotational discrete gradient scheme for numerically approximating the orthonormal frame...
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On SO(3) as the Projective Group of the Space SO(3)
The fractional linear action of SO(3) on the projective space SO(3) is proven to be a (globally defined) projective action.
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Warum nehmen wir alles so genau?
Zu Beginn des Mathe-Studiums kommt es Ihnen vielleicht so vor, als würden Sie eine neue Sprache lernen: Viele neue Begriffe, deren Bedeutung Sie...
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Riemannian and Randers Einstein Metrics on SO(n) Which Are Non-naturally Reductive
In this article, we prove that there are at least two new non-naturally reductive Ad(SO( l ) × SO( k ) × SO( k ) × SO( k ))-invariant Einstein metrics on...
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Lie Groups \(\mathrm{SU}(2)\) and \(\mathrm{{SO}}(3)\)
In this chapter, we shall extend to compact topological groups many of the properties proved in the case of finite groups. Some properties will be...
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(2, 3)-Cordial Oriented Hypercubes
In this article we investigate the existence of (2, 3)-cordial labelings of oriented hypercubes. In this investigation, we determine that there...
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The \(SO(4)\) Verlinde Formula Using Real Polarizations
We adapt the construction of Jeffrey and Weitsman (Commun Math Phys 150:593–630, 1992) to interpret the...
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So viel Mathe muss sein! Gut vorbereitet in ein WiMINT-Studium
Mithilfe dieses Arbeitsbuches können sich Studieninteressierte auf die mathematischen Herausforderungen in einem WiMINT-Studium vorbereiten. Kurze,...
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Toric Manifolds over 3-Polytopes
In this note, we gather and review several facts about the existence of toric spaces over three-dimensional simple polytopes. First, over every...
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(2, 3)-Cordial Trees and Paths
Recently L. B. Beasley introduced (2, 3)-cordial labelings of directed graphs in [1]. He conjectured that every orientation of a path of length at...
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Curves in \(\mathbb {R}^3\)
For a closed curve \(\gamma \colon [a,b]\to \mathbb {R}^3\)...
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3. Skiing Between Fréz and Gard
In a skiing competition, participants take turns sliding down the slope, with the next contestant starting once the previous one reaches the finish...
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3. Skiing Between Fréz and Gard
In a skiing competition, participants take turns sliding down the slope, with the next contestant starting once the previous one reaches the finish...
