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Periodical Solutions of Poisson-Gradient Dynamical Systems with Periodical Potential

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Constantin Udriste, Iulian Duca

Dynamical Systems · Submitted 26 Oct 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The main purpose of this paper is the study of the action that produces Poisson-gradient systems and their multiple periodical solutions.

how it is stated · asserted 0.93 read the record →

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arXiv IDmath/0510559 (version 1)
Pith IDCSVDWPUV, Pith's permanent record of this paper and its review
CitationConstantin Udriste, Iulian Duca. "Periodical Solutions of Poisson-Gradient Dynamical Systems with Periodical Potential." arXiv:math/0510559 (2005). https://pith.science/paper/CSVDWPUV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,853 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The main purpose of this paper is the study of the action that produces Poisson-gradient systems and their multiple periodical solutions. The Section 1 establishes the basic tools. The section 2 underlines conditions in which the action $\phi (u) = \displaystyle\displaystyle\int_{T_{0}}[ \displaystyle% \displaystyle{1/2}| \displaystyle\displaystyle\frac{\partial u}{% \partial t}| ^{2}+F(t,u(t)) ] dt^{1}\wedge >...\wedge dt^{p}$, that produces the Poisson-gradient systems, is continuous, and some conditions in which the general action $\phi (u) = \displaystyle\displaystyle\int_{T_{0}}L(t,u(t), \displaystyle\displaystyle\frac{\partial u}{\partial t}(t)) dt^{1}\wedge >...\wedge dt^{p}$ is continuously differentiable. The Section 3 studies the multiple periodical solutions of a Poisson-gradient system in the case when the potential function $F$ has a spatial periodicity.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The main purpose of this paper is the study of the action that produces Poisson-gradient systems and their multiple periodical solutions. contribution 0.99 0.55 0.14 asserted 0.93
s1 The Section 1 establishes the basic tools. method 0.67 0.63 0.02 asserted 0.98
s2 The section 2 underlines conditions in which the action $\phi (u) = \displaystyle\displaystyle\int_{T_{0}}[ \displaystyle% \displaystyle{1/2}| \displaystyle\displaystyle\frac{\partial u}{% \partial t}| ^{2}+F(t,u(t)) ] dt^{1}\wedge >...\wedge dt^{p}$, that produces the Poisson-gradient systems, is continuous, and some conditions in which the general action $\phi (u) = \displaystyle\displaystyle\int_{T_{0}}L(t,u(t), \displaystyle\displaystyle\frac{\partial u}{\partial t}(t)) dt^{1}\wedge >...\wedge dt^{p}$ is continuously differentiable. contribution 0.52 0.83 0.04 asserted 0.97
s3 The Section 3 studies the multiple periodical solutions of a Poisson-gradient system in the case when the potential function $F$ has a spatial periodicity. contribution 0.99 0.87 0.30 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The main purpose of this paper is the study of the action that produces Poisson-gradient systems and their multiple periodical solutions. The Section 1 establishes the basic tools. The section 2 underlines conditions in which the action $\phi (u) = \displaystyle\displaystyle\int_{T_{0}}[ \displaystyle% \displaystyle{1/2}| \displaystyle\displaystyle\frac{\partial u}{% \partial t}| ^{2}+F(t,u(t)) ] dt^{1}\wedge >...\wedge dt^{p}$, that produces the Poisson-gradient systems, is continuous, and some conditions in which the general action $\phi (u) = \displaystyle\displaystyle\int_{T_{0}}L(t,u(t), \displaystyle\displaystyle\frac{\partial u}{\partial t}(t)) dt^{1}\wedge >...\wedge dt^{p}$ is continuously differentiable. The Section 3 studies the multiple periodical solutions of a Poisson-gradient system in the case when the potential function $F$ has a spatial periodicity.

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