Results 21 to 30 of about 4,769 (119)

Measures for a Transdimensional Multiverse

, 2010
The multiverse/landscape paradigm that has emerged from eternal inflation and string theory, describes a large-scale multiverse populated by "pocket universes" which come in a huge variety of different types, including different dimensionalities.
A. De Simone ., A. Guth, A. Linde, A. Vilenkin, A.D. Linde, A.D. Linde, A.H. Guth, Alexander Vilenkin, B. Fiol, B. Freivogel, C. Krishnan, D. Schwartz-Perlov, D.N. Page, Delia Schwartz-Perlov, I.-S. Yang, J. Garriga, J. Garriga, J. Garriga, J.J. Blanco-Pillado, J.J. Blanco-Pillado, J.J. Blanco-Pillado, L. Dyson, L. Susskind, L. Susskind, M. Rees, M. Tegmark, R. Bousso, R. Bousso, R. Easther, S.M. Carroll   +29 more
core   +1 more source

New asymptotic Anti-de Sitter solution with a timelike extra dimension in 5D relativity

, 2017
In 5D relativity, the usual 4D cosmological constant is determined by the extra dimension. If the extra dimension is spacelike, one can get a positive cosmological constant $\Lambda$ and a 4D de Sitter (dS) space.
Han, Yu, Liu, Molin, Shi, Yingying, Zhao, Zonghua   +3 more
core   +1 more source

Vertical Deformation Mapping: Steering Optimiser Toward Flat Minima

CAAI Transactions on Intelligence Technology, EarlyView.
ABSTRACT Standard deep learning optimisation is typically conducted on shape‐fixed loss surfaces. However, shape‐fixed loss surfaces may impede optimisers from reaching flat regions closely associated with strong generalisation. In this work, we propose a new paradigm named deformation mapping to deform the loss surface during optimisation.
Liangming Chen, Longbang Wang, Man‐Fai Leung, Jianfeng Li, Long Jin   +4 more
wiley   +1 more source

Some open problems and conjectures on submanifolds of finite type: recent development [PDF]

, 2014
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29].
Chen, Bang-Yen
core   +1 more source

The geometric Cauchy problem for developable submanifolds

, 2019
Given a smooth distribution $\mathscr{D}$ of $m$-dimensional planes along a smooth regular curve $\gamma$ in $\mathbb{R}^{m+n}$, we consider the following problem: To find an $m$-dimensional developable submanifold of $\mathbb{R}^{m+n}$, that is, a ruled
Raffaelli, Matteo
core   +1 more source

Rational points on even‐dimensional Fermat cubics

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract We show that even‐dimensional Fermat cubic hypersurfaces are rational over any field of characteristic not equal to three, by constructing explicit rational parameterizations with polynomials of low degree. As a byproduct of our rationality constructions, we obtain estimates for the number of their rational points over a number field and ...
Alex Massarenti
wiley   +1 more source

Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE

, 2010
Of all real Lagrangian--Grassmannians $LG(n,2n)$, only $LG(2,4)$ admits a distinguished (Lorentzian) conformal structure and hence is identified with the indefinite M\"obius space $S^{1,2}$.
The, Dennis
core   +1 more source

PES‐trotter: A Cross‐Platform Open‐Source Application for the Analysis of Molecular Processes on 3D Potential‐Energy Landscapes

Journal of Computational Chemistry, Volume 47, Issue 14, 30 May 2026.
PES‐trotter is a cross‐platform open‐source application for the exploration and analysis of 3D potential‐energy landscapes associated to molecular systems. Along with video‐game‐like exploration, it allows plotting energy profiles from custom paths, computing critical points and minimum‐energy paths, and playing back dynamical trajectories. PES‐trotter
Erwan Privat, Ajay Mohan Singh Rawat, Bernardo Ballotta, Antonino Polimeno, Sergio Rampino   +4 more
wiley   +1 more source

Congruence classes of minimal ruled real hypersurfaces in a nonflat complex space form

Hokkaido Mathematical Journal, 2014
In this paper we study congruency of minimal ruled real hypersurfaces in a nonflat complex space form with respect to the action of its isometry group. We show that those in a complex hyperbolic space are classified into 3 classes and show that those in a complex projective space are congruent to each other hence form just one class.
ADACHI, Toshiaki, BAO, Tuya, MAEDA, Sadahiro   +2 more
openaire   +2 more sources

Fine dissipative properties of Euler solutions with measure first derivatives

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We study fine properties of bounded weak solutions to the incompressible Euler equations whose first derivatives, or only some combinations of them, are Radon measures. As consequences we obtain elementary proofs of the local energy conservation for solutions with bounded variation or deformation, without relying on the freedom in choosing the
Marco Inversi
wiley   +1 more source