Off-diagonal condition

Rodrigues, Walter; García, Ana E. Delgado; Juriaans, S. O.; Silva, J. C.

doi:10.1007/s00605-022-01682-5

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…Ultrafilters of S parametrize prime and maximal ideals of K. It also holds that B(R) = B(C) (see [12]). In particular, the Heaviside function H / ∈ B(R), i.e., H 2 ̸ = H (see [25]).…”

Section: Preliminariesmentioning

confidence: 99%

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Fixed Point Theorems for Hypersequences and the Foundation of Generalized Differential Geometry: The Simplified Algebra

Juriaans,

Oliveira

2023

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We lay the foundations of a generalized geometry and prove a fixed point theorem for hypersequences in this generalized context. Given a classical riemannian manifold M we prove that it can be discretely embedded in a generalized manifold M * in such a way that the differential structure of the latter is a natural extension of the differential structure of the former. Furthermore, if Ω ⊂ R n then D ′ (Ω) is discretely embedded in G(Ω) and the elements of C ∞ (Ω) form a grid of equidistant points in G(Ω). Ergo, classical solutions to differential equations are scarce and association in G(Ω) is a topological and not an algebraic notion.

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“…Ultrafilters of S parametrize prime and maximal ideals of K. It also holds that B(R) = B(C) (see [12]). In particular, the Heaviside function H / ∈ B(R), i.e., H 2 ̸ = H (see [25]).…”

Section: Preliminariesmentioning

confidence: 99%

“…In [10], K 0 = {x ∈ K : x ≈ 0} was first formally given a notation as was K as = K + K 0 (see [37,Definition 1.6.5] where they were first defined). Here, we introduce the notation G(Ω) [25]). Confusion should not arise between G(Ω) 0 and G 0 (Ω), the original Colombeau algebra (see [37]).…”

Section: A Generalized Fixed Point Theoremmentioning

confidence: 99%

Fixed Point Theorems for Hypersequences and the Foundation of Generalized Differential Geometry: The Simplified Algebra

Juriaans,

Oliveira

2023

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New insights on the signature change via the Colombeau framework

Silva,

Carvalho,

Garcia

2024

Class. Quantum Grav.

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The no-boundary proposal by physicists Hartle and Hawking strives to build a model of the early Universe without the initial singularity. This approach introduces the concept of metric signature change, which has been addressed in various ways across the literature. Subsequently, Mansouri and Nozari tackled signature change by employing Colombeau formalism. However, in this context, the metric signature only changes for $t<0$ within the Euclidean regime, posing a challenge in providing coherent physical interpretations beforehand. To address this issue, this paper proposes a reinterpretation of the Mansouri-Nozari approach, ensuring that the sign change occurs for $t>0$ in the Euclidean regime. Our findings prove that the energy-momentum tensor does not vanish on the signature change surface, even when adopting conditions commonly used in the literature. Besides, we formulate a modified cosmology within the realm of signature change. We establish a constraint relating the state equation parameter and its singular part. Lastly, we determine an effective state equation parameter as a function of the redshift and its singular part.

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Off-diagonal condition

Cited by 2 publications

References 14 publications

Fixed Point Theorems for Hypersequences and the Foundation of Generalized Differential Geometry: The Simplified Algebra

Fixed Point Theorems for Hypersequences and the Foundation of Generalized Differential Geometry: The Simplified Algebra

New insights on the signature change via the Colombeau framework

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