arXiv research

Researchers found 5 local fields to uniquely describe 3D director fields, related through 6 differential relations.

New methods reveal compatible liquid crystal phases in 3D.

We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in $\mathbb{R}^3$ equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such type of energies for example arise…

Discretizes Helfrich-type energies on surfaces using triangular complexes.

Visualizes board connections for socially responsible investing insights.

Traded corporations are required by law to have a majority of outside directors on their board. This requirement allows the existence of directors who sit on the board of two or more corporations at the same time, generating what is commonly known as interlocking directorates. While research has shown that networks of …

Theory models nonlinear soft tissue elasticity and remodeling using extended Finsler geometry.

Director learns hierarchical behaviors from pixels, outperforming exploration methods.

Study proposes new framework for Board-CEO relationship.

We study the optimal execution of market and limit orders with permanent and temporary price impacts as well as uncertainty in the filling of limit orders. Our continuous-time model incorporates a trade speed limiter and a trader director to provide better control on the trading rates. We formulate a stochastic control…

In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow between two blades in impeller and circulation flow through aircrafts with comp…

In this study, we have obtained the distribution parameter of a ruled surface generated by a straight line in Frenet trihedron moving along a timelike curve and also along another curve with the same parameter. At this time, the Frenet frames of these timelike curves are not the same. We have moved the director vector …

In this work, we consider Corporate Governance (CG) ties among companies from a multiple network perspective. Such a structure naturally arises from the close interrelation between the Shareholding Network (SH) and the Board of Directors network (BD). In order to capture the simultaneous effects of both networks on CG,…

China Vanke Co. faced a hostile takeover by Baoneng Group, sparking controversy.

We describe and document three mechanisms by which corporations can influence or even control stock prices. (i) Parent and holding companies wield control over other publicly traded companies. (ii) Through clever management of treasury stock based on buyback programs and stock issuance, stock price fluctuations can be …

Improved ranking method for scarce data with feature info.

New method allows sheets to morph into multiple shapes via spatially varying stimuli.

Study detects unlawful insider trading using SHAP and CF, identifying key features.

To provide more accurate, diverse, and explainable recommendation, it is compulsory to go beyond modeling user-item interactions and take side information into account. Traditional methods like factorization machine (FM) cast it as a supervised learning problem, which assumes each interaction as an independent instance…

Television is an ever-evolving multi billion dollar industry. The success of a television show in an increasingly technological society is a vast multi-variable formula. The art of success is not just something that happens, but is studied, replicated, and applied. Hollywood can be unpredictable regarding success, as m…

This paper maps the insurability of AI risks across various insurance products.

Generates music with video emotion using deep neural networks.

Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field's topology -- the entanglement of its field lines -- is non-trivial,…

Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.

The paper explores how fields in higher dimensions are quantized.

Paper transforms torse-forming vector fields into simpler forms.

Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.

Conformal vector fields on LCP manifolds are orthogonal and Killing.

Paper describes holomorphic polyvector fields on toric varieties.

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we obtain a global extension result for every local field of the sheaf. This generalizes…

The paper establishes a connection between force-free fields and conformally geodesic fields.

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…

Vector fields invariant under Lie group action are finitely generated by polynomial fields.

Quantum field theory uses Lorentzian bordisms to describe time evolution.

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …

Study on vector fields on Lie groups reveals surprising algebraic coincidences.

This work discovers latent field effects governing interacting dynamical systems.

Study proves conformal vector fields on certain Finsler manifolds are Killing fields.

For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…

Study magnetic field evolution in inhomogeneous axion stars.

In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the action principle to define the conservation law for such general fields. By con…

A Ricci soliton $(M,g,v,λ)$ on a Riemannian manifold $(M,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in \cite{CD2}. The most important concurrent vector field is …

Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.

New field invariant refines real spectrum and relates to absolute Galois group.

Study biharmonic vector fields and unit vector fields on Riemannian manifolds.

Classifies vector fields in the kernel of a 1-form, up to equivalence.