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Axioms, Volume 13, Issue 10

October 2024 - 74 articles

Cover Story: In this paper, we define tensor densities of arbitrary weight on a manifold in a global way. We show that they correspond to the objects which were already proposed in Einstein’s works under the name “Tensordichten” but which are only defined by means of coordinate transformation rules in most of the literature on general relativity. We construct the smooth vector bundle of tensor densities, and we show that a globally smooth tensor density field exists, as well as a globally smooth metric density in case the manifold is endowed with a pseudo-Riemannian metric. We define a natural extension of the action of an affine connection, from tensor fields to densities. We conclude the paper with an equivalent characterization for the case of a pseudo-Riemannian manifold. View this paper
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Articles (74)

  • Review
  • Open Access
1,255 Views
17 Pages

21 October 2024

This paper is dedicated to the memory of Professor Gary Gruenhage (1947–2023). This survey introduces the formation and early development of the topic of point-countable covers and sequence-covering mappings, and lists the recent progress of 38...

  • Article
  • Open Access
2 Citations
1,162 Views
22 Pages

18 October 2024

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI und...

  • Article
  • Open Access
1,504 Views
13 Pages

18 October 2024

In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of ξ-convergence, ξ-Cauchy sequence, ξ-completeness and ξ-contraction. The existence and...

  • Article
  • Open Access
2 Citations
887 Views
12 Pages

18 October 2024

The generalized theory of the double reduction of systems of partial differential equations (PDEs) based on the association of conservation laws with Lie–Bäcklund symmetries is one of the most effective algorithms for performing symmetry r...

  • Review
  • Open Access
1 Citations
6,275 Views
54 Pages

A Comprehensive Review of Golden Riemannian Manifolds

  • Bang-Yen Chen,
  • Majid Ali Choudhary and
  • Afshan Perween

18 October 2024

In differential geometry, the concept of golden structure represents a compelling area with wide-ranging applications. The exploration of golden Riemannian manifolds was initiated by C. E. Hretcanu and M. Crasmareanu in 2008, following the principles...

  • Article
  • Open Access
2 Citations
899 Views
16 Pages

18 October 2024

This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative...

  • Article
  • Open Access
789 Views
24 Pages

17 October 2024

The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are...

  • Feature Paper
  • Article
  • Open Access
959 Views
17 Pages

17 October 2024

We consider an elliptic variational–hemivariational inequality P in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution u∈K. We associate inequ...

  • Article
  • Open Access
3 Citations
863 Views
17 Pages

Notes on Modified Planar Kelvin–Stuart Models: Simulations, Applications, Probabilistic Control on the Perturbations

  • Nikolay Kyurkchiev,
  • Tsvetelin Zaevski,
  • Anton Iliev,
  • Vesselin Kyurkchiev and
  • Asen Rahnev

17 October 2024

In this paper, we propose a new modified planar Kelvin–Stuart model. We demonstrate some modules for investigating the dynamics of the proposed model. This will be included as an integral part of a planned, much more general Web-based applicati...

  • Article
  • Open Access
1,414 Views
13 Pages

17 October 2024

The existence or nonexistence of a complex structure on a differential manifold is a central problem in differential geometry. In particular, this problem on S6 was a long-standing unsolved problem, and differential geometry is an important tool. Rec...

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Axioms - ISSN 2075-1680