Article
Mathematics
Jingjun Han, Zhan Li, Lu Qi
Summary: The log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition.
AMERICAN JOURNAL OF MATHEMATICS
(2021)
Article
Multidisciplinary Sciences
Mengke Wu, Xiaoling Zhang, Lingen Sun, Lingyue Han
Summary: The paper discusses the class of warped product metrics, which are often interpreted as key space models for the general theory of relativity and theory of space-time. The PDE characterization of Finsler warped product metrics with a vanishing Riemannian curvature is obtained, and equivalent conditions for locally Minkowski Finsler warped product spaces are derived. Furthermore, the paper explicitly constructs two types of non-Riemannian examples.
Article
Mathematics, Applied
Laurian-Ioan Piscoran, Akram Ali, Barbu Catalin, Ali H. Alkhaldi
Summary: This paper aims to explore the relationship between pseudo-Riemannian geometry and Hilbert-Schmidt norms, introducing and analyzing important quantities like H-distorsion and the Hessian chi-quotient in pseudo-Riemannian geometry using the Frobenius (Hilbert-Schmidt) norm. Important examples are provided to validate the developed theory throughout the paper.
Article
Mathematics
Changliang Wang, Y. K. Wang
Summary: The study derives a general instability condition for Einstein metrics of Riemannian submersion type and investigates instability arising from Riemannian product structures on the base. Additionally, the linear stability of Einstein metrics from circle bundle constructions is examined to obtain a rigidity result for this type of metrics.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Operations Research & Management Science
Gianpaolo Oriolo, Gautier Stauffer
Summary: This paper describes the stable set polytope of quasi-line graphs and compares it with the matching polytope. In a specific subclass of quasi-line graphs, strong sufficient conditions for facet defining inequalities are obtained, leading to a refinement of the Ben Rebea Theorem.
ANNALS OF OPERATIONS RESEARCH
(2022)
Article
Mathematics, Applied
Diego Conti, Federico A. Rossi
Summary: This study investigates nice nilpotent Lie algebras with a diagonal nilsoliton metric, and classifies nice Riemannian nilsolitons of different dimensions.
JOURNAL OF GEOMETRY AND PHYSICS
(2022)
Article
Mathematics, Applied
Xiaosheng Li
Summary: In this article, we discover several new non-Riemannian Einstein-Randers metrics on homogeneous manifolds arising from generalized Wallach spaces. We first demonstrate the existence of Riemannian Einstein metrics on these manifolds, and then show that non-Riemannian Einstein-Randers metrics also exist on these manifolds.
Article
Engineering, Electrical & Electronic
Serife Yilmaz
Summary: This paper discusses stability issues of discrete-time systems, identifying nonconvexity of stable polynomials as a main obstacle in stability and stabilization problems, and emphasizes the importance of inner convex approximations of stability regions.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics
Diego Conti, Federico A. Rossi
Summary: This article discusses the relationship between nilsolitons and indefinite Einstein solvmanifolds, and highlights the flexibility in the indefinite case.
JOURNAL OF GEOMETRIC ANALYSIS
(2022)
Article
Mathematics, Applied
Zaili Yan, Shaoqiang Deng
Summary: In this paper, the authors classify Einstein basic quadruples and demonstrate the generation of new non-naturally reductive Einstein metrics in most cases. They also reveal the existence of a significant number of left invariant non-naturally reductive Einstein metrics on some compact semisimple Lie groups, uncovering a novel phenomenon not previously described in the literature.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2021)
Article
Computer Science, Software Engineering
Michele Conforti, Samuel Fiorini, Tony Huynh, Stefan Weltge
Summary: The paragraph discusses an algorithm for finding a maximum weight stable set in a graph in strongly polynomial time, as well as constructing an extended formulation for the stable set polytope.
MATHEMATICAL PROGRAMMING
(2022)
Article
Engineering, Mechanical
Zhulin Ji, Shunhua Zhang, Hanlin Dong
Summary: This paper proposes an accurate and efficient fault detection model for rotating machinery based on deep belief network (DBN). By introducing L-2, L-s-norm, and L-2, L-p-norm distance metrics regularization, the optimized feature extraction is achieved. Experimental results demonstrate the superiority of this method in terms of feature extraction ability and fault diagnosis accuracy.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Vladimir Bogachev, Alexander Shaposhnikov, Feng-Yu Wang
Summary: This paper refines and generalizes several interpolation inequalities that bound the L-p norm of a probability density with respect to the reference measure mu, using its Sobolev norm and the Kantorovich distance to mu on a smooth weighted Riemannian manifold satisfying the CD(0,infinity) condition.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2022)
Article
Mathematics, Applied
Cesar Rosales
Summary: In this study, rigidity properties of stable sets in Riemannian manifolds are deduced by using deformations constructed from parallel vector fields tangent to the boundary. The stable sets in some Riemannian cylinders with product weights are completely classified, and uniqueness results for minimizers of the weighted perimeter for fixed weighted volume are established, showing they are bounded by horizontal slices.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics
Romina M. Arroyo, Ramiro A. Lafuente
Summary: This article provides a complete description of the signatures of the Ricci curvature of left-invariant Riemannian metrics on arbitrary real nilpotent Lie groups. The main proof technique involves utilizing a connection between the kernel of the Ricci endomorphism and closed orbits in a specific representation of the general linear group, which is proven using the "real GIT" framework for the Ricci curvature of nilmanifolds.
TRANSFORMATION GROUPS
(2022)
Article
Mathematics, Applied
T. Drummond, M. Jotz Lean, C. Ortiz
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2015)
Article
Mathematics
Madeleine Jotz Lean, Mathieu Stienon, Ping Xu
MATHEMATISCHE ANNALEN
(2016)
Article
Mathematics, Applied
Madeleine Jotz Lean
JOURNAL OF GEOMETRY AND PHYSICS
(2016)
Article
Mathematics
A. Gracia-Saz, M. Jotz Lean, K. C. H. Mackenzie, R. A. Mehta
JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
(2018)
Article
Mathematics
A. Gracia-Saz, M. Jotz Lean, K. C. H. Mackenzie, R. A. Mehta
JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
(2018)
Article
Mathematics, Applied
M. Jotz Lean
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2018)
Article
Mathematics
M. Jotz Lean, C. Ortiz
INDAGATIONES MATHEMATICAE-NEW SERIES
(2014)
Article
Mathematics
M. M. Jotz, T. S. Ratiu
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2013)
Article
Mathematics, Applied
M. Jotz Lean
JOURNAL OF GEOMETRY AND PHYSICS
(2018)
Article
Mathematics
Madeleine Jotz Lean
PACIFIC JOURNAL OF MATHEMATICS
(2019)
Article
Mathematics, Applied
M. Jotz Lean
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY
(2020)
Article
Mathematics
M. Jotz, R. A. Mehta, T. Papantonis
Summary: This paper studies differential graded modules and representations up to homotopy of Lie n-algebroids, where n is a natural number. It describes the adjoint and coadjoint modules, and explains the corresponding split versions of the adjoint and coadjoint representations up to homotopy. In particular, the case of Lie 2-algebroids is analyzed in detail. It shows that the compatibility of a Poisson bracket with the homological vector field of a Lie n-algebroid is equivalent to a morphism from the coadjoint module to the adjoint module, providing an alternative characterization of the non-degeneracy of higher Poisson structures. Moreover, the Weil algebra of a Lie n-algebroid is explicitly computed in terms of splittings, and representations up to homotopy of Lie n-algebroids are used to encode decomposed VB-Lie n-algebroid structures on double vector bundles.
JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
(2023)
Article
Mathematics, Applied
Madeleine Jotz Lean, Kirill C. H. Mackenzie
Summary: This paper investigates the core diagram of a double Lie algebroid and its transitive properties, proving that a double Lie algebroid can be completely determined by its core diagram. Additionally, it introduces the concept of a comma double Lie algebroid and its relevance to transitive core diagrams.
JOURNAL OF GEOMETRIC MECHANICS
(2021)
Article
Mathematics, Applied
Malte Heuer, Madeleine Jotz Lean
THEORY AND APPLICATIONS OF CATEGORIES
(2020)
Article
Mathematics
M. Jotz Lean
JOURNAL OF SYMPLECTIC GEOMETRY
(2019)
Article
Mathematics, Applied
Pooja Rani, M. K. Vemuri
Summary: This article discusses the knot beta function for compactly supported distributions in Euclidean space and analyzes the analytic continuation of the beta function for double-layer distributions on the complex plane, as well as the relationship between residues and invariants of the second fundamental form.
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
Jacob Van Hook
Summary: This study considers complete locally irreducible conullity two Riemannian manifolds with constant scalar curvature along nullity geodesics. We find a naturally defined open dense subset where the metric can be described using several functions uniquely determined up to isometry. Additionally, we prove that the fundamental group of such manifolds is either trivial or infinite cyclic.
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2024)
Article
Mathematics, Applied
J. F. Silva Filho
Summary: In this article, we investigate quasi-Einstein manifolds admitting a closed conformal vector field, and present rigidity results for constant scalar curvature and non-parallel gradient conformal vector field.
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2024)