79 Results Found

Let X be a compact Riemann surface of genus $g\ge 2$ and $M\left(G_2\right)$ be the moduli space of polystable principal bundles over X, the structure group of which is the simple complex Lie group of exceptional type $G_2$. In this work, it is proved that the only aut...

The idea of monodromy groupoid we deal here is due to Pradines [1]. An application of the monodromy groupoid on principal bundles was earlier given in [2]. In this paper, a topological version of this application is given.

In this paper, the fixed points of involutions on the moduli space of principal $E_6$-bundles over a compact Riemann surface X are investigated. In particular, it is proved that the combined action of a representative $\sigma$ of the outer involution of...

This paper provides advances in the study of principal $\mathrm{SO}\left(3\right)$-bundles over smooth projective real curves, with applications to robot manipulation orientation. The work introduces a novel specific classification of these bundles, establishing a bijecti...

In this research, we establish a precise correspondence between the theory of logarithmic connections on principal G-bundles over compact Riemann surfaces and the geometric formulation of control systems on curved manifolds, providing a novel differe...

Let X be a compact Riemann surface of genus $g\ge 2$, G be a complex semisimple Lie group, and ${\mathcal{M}}_G\left(X\right)$ be the moduli space of stable principal G-bundles. This paper studies the fixed point set of involutions on ${\mathcal{M}}_G\left(X\right)$ induced by an anti-holomorphic involu...

Let X be a compact Riemann surface of genus $g\ge 2$ equipped with an anti-holomorphic involution $\tau$, and let $\mathcal{M}(G_2)$ denote the moduli space of stable principal $G_2$-bundles over X. We study the fixed-point loci $\mathcal{M}{(G_2)}^{\sigma }$ of the involutions $\sigma =$...

In this article, the special orthogonal group SO(3) is considered as a topological group. We show that SO(3) has the structure of a principal SO(2)-bundle over the sphere $S^2$. As a consequence, we prove that every orbit of an SO(3)-action on a topolog...

Let G be a connected reductive group over K with $\mathrm{char}K=p>0$. In this paper, we prove via deformation-theoretic techniques that the Frobenius pullback of a general stable G-bundle on a curve X remains stable in the moduli stack of G-bundles with fix...

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold ${\mathbb{G}}_r\left({\mathbb{R}}^k\right)$ of linear subspaces of dimension $r<k$ in ${\mathbb{R}}^k$, which avoids the use of...

We study fiber bundles where the fibers are not a group G but a free G-space with disjoint orbits. The fibers are then not torsors but disjoint unions of these; hence, we like to call them semi-torsors. Bundles of semi-torsors naturally generalize pr...

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question f...

Let X be a compact Riemann surface of genus $g\ge 2$, ${\sigma }_X\in Aut\left(X\right)$ (the group of biholomorphic self-maps of X) an involution, and $F_4\left(\mathbb{C}\right)$ (one of the five exceptional complex simple Lie groups) the fixed-point subgroup of the outer involution $\mathrm{\&si}$...

Low-temperature stress during the jointing stage severely disrupts the coordination of the source–flow–sink system in winter wheat. To elucidate the underlying mechanism, three wheat cultivars with different winter habits (Zhenmai 12, Jim...

We present the invariant structure of a Holomorphic Unified Field Theory in which gravity and gauge interactions arise from a single geometric framework. The theory is formulated using a product principal bundle, with one connection, and curvature eq...

Most datasets encountered in computer vision and medical applications present symmetries that should be taken into account in classification tasks. A typical example is the symmetry by rotation and/or scaling in object detection. A common way to buil...

This paper establishes a functorial algebraic isomorphism between the moduli space ${\mathcal{B}}_{\mathcal{C}}^{\mathrm{ps}}(\Sigma ,G)$ of polystable principal G-bundles with prescribed monodromy on a punctured Riemann surface $\Sigma$ of genus $g\ge 2$, for a complex reductive Lie group G...

We develop a matrix-theoretic framework for the natural embedding of the exceptional Lie algebra ${\mathfrak{g}}_2=\mathrm{Der}\left(\mathbb{O}\right)$ in $\mathfrak{so}\left(8\right)$, use it to make constructive a recent existence result on octonionic triality, and derive geometric applications for moduli spaces of...

In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–...

The Aharonov-Vaidman gauge additively transforms the mean energy of a quantum mechanical system into a weak valued system energy. In this paper, the equation of motion of this weak valued energy is used to provide a mathematical statement of an exten...

Hopf–Galois extensions extend the idea of principal bundles to noncommutative geometry, using Hopf algebras as symmetries. We show that the matrix embeddings in Bratteli diagrams are iterated direct sums of Hopf–Galois extensions (quantum...

The space $\Pi$ of centered m-planes is considered in projective space $P_n$ . A principal bundle is associated with the space $\Pi$ and a group connection is given on the principal bundle. The connection is not uniquely induced at the...

Let X be a compact Riemann surface of genus $g\ge 2$. An octonionic bundle over X is a fiber bundle whose fiber is the non-associative algebra of complex octonions, equivalently a principal $G_2\left(\mathbb{C}\right)$-bundle, where $G_2\left(\mathbb{C}\right)$ is the exceptional Lie group of auto...

Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”. The c...

Research article abstracts, the second most-read part of research papers after titles, generally follow disciplinary conventions, which are often manifested in their language use. This study analyzed lexical bundles or multi-word sequences in move te...

This article is a review of what could be considered the basic mathematics of Einstein–Cartan theory. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and Bianchi identities, and...

We introduce the relative tail pressure to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail pressure is conserved by the principal extension.

The relative tail pressure with subadditive potentials is introduced via open random covers for continuous bundle random transformations. A variational principle is established and the defined pressure turns out to be invariant under the principal ex...

In this paper we give a brief account of the main aspects of the theory of associated and principal super bundles. As an application, we review the Borel-Weil-Bott Theorem in the super setting, and some results on projective embeddings of homogeneous...

An understanding of the relationships among multiple ecosystem services (ES) facilitates ecosystem management and decision-making. The study of ES bundles can well explain the complex interactions between different ES in a region. Shenyang is a signi...

Differential cohomology is a topic that has been attracting considerable interest. Many interesting applications in mathematics and physics have been known, including the description of WZW terms, string structures, the study of conformal immersions,...

Ecosystem service (ES) bundles are widely used approaches to analyze ES tradeoffs in urban agglomeration. However, few ES bundle studies considered both the supply and demand sided. The objective of this study was to map ES supply–demand bundle...

Identifying ecosystem service bundles and their long-term evolutionary characteristics is essential for the overall enhancement of regional ecosystem services, as well as the division and management of functional areas, providing a basis for decision...

The survival of marginal/peripheral silver fir (Abies alba Mill.) populations in the broader region of Southeast Europe is endangered due to climate change and population decline. This study aimed to determine the level and pattern of variability for...

In-depth research on the spatial and temporal evolution of ecosystem service trade-offs and synergistic relationships, scientific identification of ecosystem service bundles, and the main factors affecting the spatial differentiation of ecosystem ser...

We give new concise Lie-theoretic proofs of basic analytic–geometric properties of connected complex Lie groups. Using Matsushima’s biholomorphic splitting $G\simeq {\mathbb{C}}^n\times \tilde{K}$ together with a refined analysis of the center via its C...

In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real...

Urban green and blue spaces (UGBS) take on critical significance in urban development. In this study, the physical characteristics and landscape-ecology-society-space (LESS) system services of 24 urban parks in 2 greenbelts surrounding Foshan City ar...

Let G be a compact connected Lie group, $(X,\omega ,\mu )$ a Hamiltonian G-manifold with moment map $\mu$, and Z a codimension-2 Hamiltonian G-submanifold of X. We study the boundedness of the differential of symplectic vortices $(A,u)$ near Z, where A is...

Expansins are cell wall (CW) proteins that mediate the CW loosening and regulate salt tolerance in a positive or negative way. However, the role of Populus trichocarpa expansin A6 (PtEXPA6) in salt tolerance and the relevance to cell wall loosening i...

Lodging is one of the major constraints in attaining high yield in crop production. Major factors associated with stalk lodging involve morphological traits and anatomical features along with the chemical composition of the stem. However, little rele...

In order to reconstruct three-dimensional (3D) structures from an image sequence captured by unmanned aerial vehicles’ camera (UAVs) and improve the processing speed, we propose a rapid 3D reconstruction method that is based on an image queue, consid...

We consider two principal bundles of embeddings with total space E m b ( M , N ) ,...

Rice cultivation faces major environmental challenges due to climate change, particularly soil salinity, which limits plant growth and productivity. Salt tolerance in rice is typically evaluated using physiological and biochemical traits, whereas lea...

This study aimed to assess the phenotypic and histological characteristics of leaves, stems, and roots of sweet potato (‘Hopungmi’ and ‘Sodammi’, Korean cultivars) under the low-temperature conditions induced by early transpla...

Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under the action of a symmetry group $\mathcal{G}$, parameter space $\mathcal{A}$ becomes a (locally) trivial principal bundle, $\mathcal{A}\&c$...

Significant instrumental systematic errors are known to exist in data captured with range cameras using lock-in pixel technology. Because they are independent of the imaged object scene structure, these errors can be rigorously estimated in a self-ca...

Major bleeding is a life-threatening condition with high morbidity and mortality. Trauma, gastrointestinal bleeding, haemoptysis, intracranial haemorrhage or other causes of bleeding represent major concerns in the Emergency Department (ED), especial...

This paper innovatively analyses the joint occurrence of cognitive biases in groups of stock exchange investors. It considers jointly a number of common fallacies: confirmation bias, loss aversion, gambler’s fallacy, availability cascade, hot-hand fa...

The Silurian marine shale in the Sichuan Basin is currently the main reservoir for shale gas reserves and production in China. This study investigates the reservoir evolution of the Silurian marine shale based on fractal dimension, quantifying the co...