scholarly journals Normal Forms for Perturbed Keplerian Systems

2002 ◽  
Vol 180 (2) ◽  
pp. 471-519 ◽  
Author(s):  
Jesús Palacián
Keyword(s):  
Normal Forms ◽  
Keplerian Systems

scholarly journals Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark

2016 ◽  
Vol 1 (2) ◽  
pp. 473-492 ◽  
Author(s):  
F. Crespo ◽  
G. Díaz-Toca ◽  
S. Ferrer ◽  
M. Lara
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Invariant Tori ◽  
Van Der Waals ◽  
Relative Equilibria ◽  
Stationary Points ◽  
Lie Transforms ◽  
Quadratic Invariants ◽  
Pros And Cons ◽  
Keplerian Systems

AbstractThis paper is devoted to studying Hamiltonian oscillators in 1:1:1:1 resonance with symmetries, which include several models of perturbed Keplerian systems. Normal forms are computed in Poisson and symplectic formalisms, by mean of invariants and Lie-transforms respectively. The first procedure relies on the quadratic invariants associated to the symmetries, and is carried out using Gröner bases. In the symplectic approach, hinging on the maximally superintegrable character of the isotropic oscillator, the normal form is computed a la Delaunay, using a generalization of those variables for 4-DOF systems. Due to the symmetries of the system, isolated as well as circles of stationary points and invariant tori should be expected. These solutions manifest themselves rather differently in both approaches, due to the constraints among the invariants versus the singularities associated to the Delaunay chart.Taking the generalized van der Waals family as a benchmark, the explicit expression of the Delaunay normalized Hamiltonian up to the second order is presented, showing that it may be extended to higher orders in a straightforward way. The search for the relative equilibria is used for comparison of their main features of both treatments. The pros and cons are given in detail for some values of the parameter and the integrals.

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems

scholarly journals CagA-PositiveHelicobacter pyloriInfection and Reduced Sperm Motility, Vitality, and Normal Morphology

2013 ◽  
Vol 35 ◽  
pp. 229-234 ◽  
Author(s):  
E. Moretti ◽  
G. Collodel ◽  
L. Mazzi ◽  
M. S. Campagna ◽  
N. Figura
Keyword(s):  
Sperm Motility ◽  
Normal Forms ◽  
Molecular Mimicry ◽  
Sperm Quality ◽  
Semen Analysis ◽  
Normal Morphology ◽  
Partial Linear ◽  
Caga Status ◽  
The Relationship ◽  
Autoimmune Phenomena

Helicobacter pylori(HP) infection, particularly when caused by strains expressing CagA, may be considered a concomitant cause of male and female reduced fertility. This study explored, in 87 HP-infected males, the relationship between infection by CagA-positive HP strains and sperm parameters. HP infection and CagA status were determined by ELISA and Western blotting; semen analysis was performed following WHO guidelines. The amino acid sequence of human enzymes involved in glycolysis and oxidative metabolism were “blasted” with peptides expressed by HP J99. Thirty-seven patients (42.5%) were seropositive for CagA. Sperm motility (18% versus 32%; ), sperm vitality (35% versus 48%; ) and the percentage of sperm with normal forms (18% versus 22%; ) in the CagA-positive group were significantly reduced versus those in the CagA-negative group. All the considered enzymes showed partial linear homology with HP peptides, but four enzymes aligned with four different segments of the samecagisland protein. We hypothesize a relationship between infection by strains expressing CagA and decreased sperm quality. Potentially increased systemic levels of inflammatory cytokines that occur in infection by CagA-positive strains and autoimmune phenomena that involve molecular mimicry could explain the pathogenetic mechanism of alterations observed.

Representation Theorems for Terms in a Certain Model for Information Systems

1982 ◽  
Vol 5 (1) ◽  
pp. 1-14
Author(s):  
Bernd Reusch ◽  
Gerd Szwillus
Keyword(s):  
Information Systems ◽  
Normal Forms ◽  
Abstract Model ◽  
Representation Theorems

We study a term-language, which is used by the “Warsaw-School” in an abstract model for information systems. Various normal forms as well as standard expansions with respect to product terms are formulated and proved correct. It is shown that the shortest sums of so-called maximal sub-products are the shortest representations of terms and algorithms for their generation are given.

scholarly journals Normal form approach in the motion planning of space robots: a case study

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

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