scholarly journals Topological Operators on Cell Complexes in Arbitrary Dimensions

2012 ◽  
pp. 98-107 ◽  
Author(s):  
Lidija Čomić ◽  
Leila De Floriani
Keyword(s):  
Cell Complexes ◽  
Arbitrary Dimensions

Topological modifications and hierarchical representation of cell complexes in arbitrary dimensions

2014 ◽  
Vol 121 ◽  
pp. 2-12 ◽  
Author(s):  
Lidija Čomić ◽  
Leila De Floriani ◽  
Federico Iuricich ◽  
Ulderico Fugacci
Keyword(s):  
Hierarchical Representation ◽  
Cell Complexes ◽  
Arbitrary Dimensions

scholarly journals The Kerr-Schild double copy in Lifshitz spacetime

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Gökhan Alkaç ◽  
Mehmet Kemal Gümüş ◽  
Mustafa Tek
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Charge Density ◽  
Localized Source ◽  
Curvature Term ◽  
Constant Charge Density ◽  
Arbitrary Dimensions ◽  
Double Copy ◽  
Theory Solution ◽  
Constant Charge

Abstract The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

scholarly journals A New General Method for Constructing Confidence Sets in Arbitrary Dimensions: With Applications

1995 ◽  
Vol 23 (4) ◽  
pp. 1408-1432 ◽  
Author(s):  
A. DasGupta ◽  
J. K. Ghosh ◽  
M. M. Zen
Keyword(s):  
Confidence Sets ◽  
Arbitrary Dimensions ◽  
General Method

scholarly journals Dyonic objects and tensor network representation

2020 ◽  
pp. 2050336
Author(s):  
A. Belhaj ◽  
Y. El Maadi ◽  
S-E. Ennadifi ◽  
Y. Hassouni ◽  
M. B. Sedra
Keyword(s):  
Particle Physics ◽  
Network Representation ◽  
Tensor Network ◽  
Arbitrary Dimensions

Motivated by particle physics results, we investigate certain dyonic solutions in arbitrary dimensions. Concretely, we study the stringy constructions of such objects from concrete compactifications. Then, we elaborate their tensor network realizations using multistate particle formalism.

scholarly journals UNIVERSAL CALABI–YAU ALGEBRA: TOWARDS AN UNIFICATION OF COMPLEX GEOMETRY

2003 ◽  
Vol 18 (30) ◽  
pp. 5541-5612 ◽  
Author(s):  
F. ANSELMO ◽  
J. ELLIS ◽  
D. V. NANOPOULOS ◽  
G. VOLKOV
Keyword(s):  
Lie Algebras ◽  
Complex Geometry ◽  
Algebraic Approach ◽  
Higher Dimensions ◽  
Normal Algebra ◽  
Natural Extensions ◽  
Recurrence Formulae ◽  
Different Dimensions ◽  
Arbitrary Dimensions

We present a universal normal algebra suitable for constructing and classifying Calabi–Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions, related to Batyrev's reflexive polyhedra, and their n-ary combinations. It also includes a "dual" construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of Calabi–Yau spaces in arbitrary dimensions with Weierstrass, K3, etc., fibrations. Our approach also yields simple algebraic relations between chains of Calabi–Yau spaces in different dimensions, and concrete visualizations of their singularities related to Cartan–Lie algebras. This Universal Calabi–Yau algebra is a powerful tool for deciphering the Calabi–Yau genome in all dimensions.

scholarly journals Bott characteristics of cell complexes

1983 ◽  
Vol 86 (4) ◽  
pp. 493-499
Author(s):  
Jack Weinstein
Keyword(s):  
Cell Complexes

scholarly journals Exactly solvable models in arbitrary dimensions

1998 ◽  
Vol 238 (4-5) ◽  
pp. 213-218 ◽  
Author(s):  
Ranjan Kumar Ghosh ◽  
Sumathi Rao
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Exactly Solvable ◽  
Arbitrary Dimensions

scholarly journals On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations

2014 ◽  
Vol 46 (3) ◽  
pp. 622-642 ◽  
Author(s):  
Julia Hörrmann ◽  
Daniel Hug
Keyword(s):  
Euclidean Space ◽  
Asymptotic Behaviour ◽  
Explicit Formula ◽  
Dimensional Euclidean Space ◽  
Arbitrary Dimensions ◽  
Zero Cell ◽  
Parametric Class

We study a parametric class of isotropic but not necessarily stationary Poisson hyperplane tessellations in n-dimensional Euclidean space. Our focus is on the volume of the zero cell, i.e. the cell containing the origin. As a main result, we obtain an explicit formula for the variance of the volume of the zero cell in arbitrary dimensions. From this formula we deduce the asymptotic behaviour of the volume of the zero cell as the dimension goes to ∞.

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