Results 211 to 220 of about 256,760 (248)
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Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential
Journal of Mathematical Physics, 2005In this paper we study the integrability of natural Hamiltonian systems with a homogeneous polynomial potential. The strongest necessary conditions for their integrability in the Liouville sense have been obtained by a study of the differential Galois group of variational equations along straight line solutions. These particular solutions can be viewed
A. Maciejewski, M. Przybylska
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On the dynamics of mechanical systems with homogeneous polynomial potentials of degree 4
Bulletin of the Brazilian Mathematical Society, New Series, 2007In this work we study mechanical systems defined by homogeneous polynomial potentials of degree 4 on the plane, when the potential has a definite or semi-definite sign and the energy is non-negative. We get a global description of the flow for the nonnegative potential case.
M. Falconi, E. Lacomba, C. Vidal
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Weighted Poisson polynomial rings in dimension three
Journal of Noncommutative Geometry, 2023We discuss Poisson structures on a weighted polynomial algebra A:=\mathbb{k}[x, y, z] defined by a homogeneous element \Omega\in A , called a potential .
Hongdi Huang +3 more
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A family of explicit Waring decompositions of a polynomial
arXiv.org, 2023In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial $X_0^{a_0}X_1^{a_1}\cdots X_n^{a_n}$ over a field $\Bbbk$.
Kangjin Han, Hyunsuk Moon
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Journal of Partial Differential Equations, 2022
In this paper, we study the nonlinear Choquard equation \begin{eqnarray*} \Delta^{2}u-\Delta u+(1+\lambda a(x))u=(R_{\alpha}\ast|u|^{p})|u|^{p-2}u \end{eqnarray*} on a Cayley graph of a discrete group of polynomial growth with the homogeneous dimension ...
Ruo Li, Lidan Wang
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In this paper, we study the nonlinear Choquard equation \begin{eqnarray*} \Delta^{2}u-\Delta u+(1+\lambda a(x))u=(R_{\alpha}\ast|u|^{p})|u|^{p-2}u \end{eqnarray*} on a Cayley graph of a discrete group of polynomial growth with the homogeneous dimension ...
Ruo Li, Lidan Wang
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The Flow on Negative Energy of Mechanical Systems with Homogeneous Polynomial Potentials
Qualitative Theory of Dynamical Systems, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Falconi, M., Lacomba, E. A., Vidal, C.
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International Conference on VLSI Design
Implementing hardware-efficient and high-performance polynomial multiplication in finite fields is crucial for enhancing crypto-systems on silicon, which is desirable for system-on-chip (SoC) applications.
Daksh Sharma +3 more
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Implementing hardware-efficient and high-performance polynomial multiplication in finite fields is crucial for enhancing crypto-systems on silicon, which is desirable for system-on-chip (SoC) applications.
Daksh Sharma +3 more
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On the Gradient Flow Formulation of the Lohe Matrix Model with High-Order Polynomial Couplings
Journal of statistical physics, 2020We present a first-order aggregation model for a homogeneous Lohe matrix ensemble with higher order couplings via a gradient flow approach. For homogeneous free flow with the same Hamiltonian, it is well known that the Lohe matrix model with cubic ...
Seung‐Yeal Ha, Hansol Park
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IEEE transactions on industrial electronics (1982. Print)
This research focuses on gain-scheduling control for minecart active suspension systems (ASSs). Addressing practical scenarios in complex mining environments where transition probability information may be imprecisely accessible or completely unavailable,
Xingchen Shao +2 more
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This research focuses on gain-scheduling control for minecart active suspension systems (ASSs). Addressing practical scenarios in complex mining environments where transition probability information may be imprecisely accessible or completely unavailable,
Xingchen Shao +2 more
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On homogeneous polynomial solutions of the Riesz system and their harmonic potentials
Complex Variables and Elliptic Equations, 2007The spaces , of vector-valued homogeneous monogenic polynomials of degree k in are locally the building blocks of solutions to the Riesz system in . Furthermore, the Dirac operator ∂ x in determines an isomorphism between –the space of solid harmonics of degree (k + 1) in –and .
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