Results 31 to 40 of about 12,485 (261)
Equivariant decomposition of polynomial vector fields [PDF]
Communications in Contemporary Mathematics, 2020 To compute the unique formal normal form of families of vector fields with nilpotent linear part, we choose a basis of the Lie algebra consisting of orbits under the action of the nilpotent linear part. This creates a new problem: to find explicit formulas for the structure constants in this new basis. These are well known in the 2D case, and recently
Mokhtari, Fahimeh, Sanders, J.A.
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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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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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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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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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Advanced Functional Materials, EarlyView.Ferroelectric nematic liquid crystals (FNLCs) offer fast, tunable polarization and low‐voltage operation but suffer from poor polarization retention at zero field. Semiconductor‐modified FNLCs enhance polarization retention and exhibit short‐ and long‐term electro‐optical responses, while also supporting spike‐type signal integrations.
Kutay Sagdic, Weiming Yao, Danqing Liu
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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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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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