Results 31 to 40 of about 12,964 (262)
Projections of Polynomial Vector Fields and the Poincaré Sphere
Journal of Differential Equations, 1997 Let \(p:\mathbb{R}^n\to\mathbb{R}^n\) be a homogeneous polynomial vector function, and let \(\rho:\mathbb{R}^n \to\mathbb{R}\) be a homogeneous polynomial of positive degree \(d\). The authors introduce the projection of \(p\) with respect to \(\rho\) by the formula \[ p^{\rho}(x)=- {\textstyle\frac{1}{d}} L_p(\rho)(x)x+\rho(x)p(x), \] where \(L_p(\rho)
Röhrl, Helmut, Walcher, Sebastian
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Symbolic Computations of First Integrals for Polynomial Vector Fields [PDF]
Foundations of Computational Mathematics, 2019 In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing, if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a polynomial planar vector field.
Chèze, Guillaume, Combot, Thierry
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Physical Review Research, 2021 With a view toward a fracton theory in condensed matter, we introduce a higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector global symmetry for p=0 and p=1 respectively).
Juven Wang, Kai Xu, Shing-Tung Yau
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Topological enumeration of complex polynomial vector fields [PDF]
Ergodic Theory and Dynamical Systems, 2014 AbstractThe enumeration of combinatorial classes of the complex polynomial vector fields in$ \mathbb{C} $presented by K. Dias [Enumerating combinatorial classes of the complex polynomial vector fields in$ \mathbb{C} $.Ergod. Th. & Dynam. Sys. 33(2013), 416–440] is extended here to a closed form enumeration of combinatorial classes for degree$d ...
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Advanced Engineering Materials, EarlyView.We develop a data‐driven method to derive the mathematical expressions of the Flory–Huggins interaction parameter χ for the swelling behavior of temperature–responsive hydrogels. Starting from initial assumptions of χ, our workflow combines Bayesian optimization, Flory–Rehner theory, and symbolic regression to generate candidate χ expressions.
Yawen Wang +2 more
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Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields
Comptes Rendus. MathématiqueEvery Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in velocities integral of the geodesic ...
Matveev, Vladimir S., Nikolayevsky, Yuri
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An Exponential Formula for Polynomial Vector Fields
Advances in Mathematics, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Advanced Engineering Materials, EarlyView.A novel workflow for investigating hydride vapor phase epitaxy for GaN bulk crystal growth is proposed. It combines Design of experiments (DoE) with physical simulations of mass transport and crystal growth kinetics, serving as an intermediate step between DoE and experiments.
J. Tomkovič +7 more
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Computation of focus quantities of three-dimensional polynomial systems
上海师范大学学报. 自然科学版, 2014 Fix a collection of polynomial vector fields on R3 with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue.Some such systems admit a local analytic first integral,which then
Valery G. Romanovski, Douglas S. Shafer
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Advanced Functional Materials, EarlyView.ABSTRACT Chitosan, a polysaccharide upcycled from biowaste, has long promised sustainable, biocompatible, and antimicrobial films and devices, an appeal reinforced by its recent regulatory recognition, with several chitosan‐based antibacterial dressings gaining clearance through the Food and Drug Administration's 510(k) pathway.
Jacopo Nicoletti +16 more
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