Explicit solutions of normal form of driven oscillatory systems

1987 ◽  
Vol 87 (11) ◽  
pp. 6538-6543 ◽  
Author(s):  
George E. Tsarouhas ◽  
John Ross
Keyword(s):  
Normal Form ◽  
Explicit Solutions ◽  
Oscillatory Systems

Explicit solutions of normal form of driven oscillatory systems in entrainment bands

1988 ◽  
Vol 89 (9) ◽  
pp. 5715-5720 ◽  
Author(s):  
George E. Tsarouhas ◽  
John Ross
Keyword(s):  
Normal Form ◽  
Explicit Solutions ◽  
Oscillatory Systems

NORMAL FORM PERTURBATION ANALYSIS OF NON-AUTONOMOUS OSCILLATORY SYSTEMS

1995 ◽  
pp. 359-374
Author(s):  
PETER B. KAHN ◽  
YAIR ZARMI
Keyword(s):  
Normal Form ◽  
Perturbation Analysis ◽  
Oscillatory Systems

The normal form of perturbations of non-linear oscillatory systems

2002 ◽  
Vol 66 (6) ◽  
pp. 881-887 ◽  
Author(s):  
V.F. Zhuravlev
Keyword(s):  
Normal Form ◽  
Oscillatory Systems ◽  
Non Linear

Study of the algebra of smooth integro-differential operators with applications

2019 ◽  
Vol 18 (01) ◽  
pp. 1950009
Author(s):  
A. Haghany ◽  
Adel Kassaian
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Integral Equations ◽  
Differential Operators ◽  
Unit Group ◽  
Volterra Integral Equations ◽  
Explicit Solutions ◽  
Smooth Kernels ◽  
Smooth Coefficients

We study the algebra of integro-differential operators with smooth coefficients and kernels on a subspace of [Formula: see text]. We find a normal form for elements of this algebra and determine its unit group. The formulation of inverses gives explicit solutions of inhomogeneous linear Volterra integro-differential equations and Volterra integral equations of first kind with smooth kernels.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

A 3D Field Expression in Multilayered Structures using Jordan Normal Form

2012 ◽  
Vol 132 (8) ◽  
pp. 698-699 ◽  
Author(s):  
Hideaki Wakabayashi ◽  
Jiro Yamakita
Keyword(s):  
Normal Form ◽  
Jordan Normal Form ◽  
Multilayered Structures

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.

Analysis of a 2DOF Nonlinear Mechanical System Using the Normal Form Method

2019 ◽  
Author(s):  
David Julian Gonzalez Maldonado ◽  
Peter Hagedorn ◽  
Thiago Ritto ◽  
Rubens Sampaio ◽  
Artem Karev
Keyword(s):  
Normal Form ◽  
Mechanical System ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Normal Form Method

Normal form method in search for periodic solutions of ordinary differential equations. Case of the fourth order

2018 ◽  
pp. 24-34
Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Computational Time ◽  
Resonant Normal Form ◽  
Normal Form Method

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.

Explicit Solutions for a Class of Nonlinear PDE that Arise in Allocation Problems

2006 ◽  
Author(s):  
Paul Dupuis ◽  
Jim X. Zhang
Keyword(s):  
Nonlinear Pde ◽  
Explicit Solutions ◽  
Allocation Problems
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