Offsetting and blending with perturbation functions

2019 ◽  
Author(s):  
Piotr Popiel ◽  
Sergey Vyatkin ◽  
Olexander Romanyuk ◽  
Arman Abenovd ◽  
Kalamkas Begaliyeva ◽  
...  
Keyword(s):  
Perturbation Functions

3D Shape Modeling Using Perturbation Functions

2021 ◽  
Author(s):  
Pavlo Mykhaylov ◽  
Sergey Vyatkin ◽  
Roman Chekhmestruk ◽  
Ivan Perun ◽  
Tetiana Korobeinikova
Keyword(s):  
Shape Modeling ◽  
3D Shape ◽  
Perturbation Functions

Variational Principles

2012 ◽  
Author(s):  
Joram Lindenstrauss ◽  
David Preiss ◽  
Tiˇser Jaroslav
Keyword(s):  
Variational Principle ◽  
Lower Semicontinuity ◽  
Variational Principles ◽  
Perfect Information ◽  
Perturbation Functions ◽  
Abstract Version ◽  
Recursive Constructions ◽  
Natural Description

This chapter describes smooth variational principles (of Ekeland type) as infinite two-player games. These variational principles are based on a simple but careful recursive choice of points where certain functions that change during the process have values close to their infima. Like many other recursive constructions, the choice has a natural description using the language of infinite two-player games with perfect information. The chapter first considers the perturbation game used in Theorem 7.2.1 to formulate an abstract version of the variational principle before showing how to specialize it to more standard formulations. It then examines the bimetric variant of the smooth variational principle, along with the perturbation functions that are relatively simple. It concludes with an assessment of cases when completeness and lower semicontinuity hold only in a bimetric sense.

scholarly journals Real-Time Deformations of Function-Based Surfaces using Perturbation Functions

2018 ◽  
Vol 1015 ◽  
pp. 032115 ◽  
Author(s):  
S I Vyatkin ◽  
A N Romanyuk ◽  
L A Savytska ◽  
T I Troianovska ◽  
N V Dobrovolska
Keyword(s):  
Real Time ◽  
Perturbation Functions

scholarly journals On Gravothermal Instability of Anisotropic Self-Gravitating Gas Spheres: Singular Equilibrium Solution

1993 ◽  
Vol 132 ◽  
pp. 241-253
Author(s):  
R. Spurzem
Keyword(s):  
Equilibrium Solution ◽  
Stellar System ◽  
Hydrostatic Equilibrium ◽  
Linear Perturbation ◽  
Total Entropy ◽  
Boltzmann Entropy ◽  
First Order ◽  
Perturbation Functions ◽  
The Common ◽  
Linear Perturbation Theory

AbstractA reinvestigation of the linear perturbation theory is presented, which examines the hydrostatic readjustment of an isolated self-gravitating gas sphere to a redistribution of energy. The here presented model describes a stellar system by the common equations of gas in hydrostatic equilibrium but with the effect of the anisotropic velocity distribution on the pressure gradient. We take as equilibrium models the singular isothermal solution with and without anisotropy. The total variation of the Boltzmann entropy resulting from a perturbation of the system caused by a redistribution of heat (i.e. r.m.s. kinetic energy of the stars) is calculated for anisotropic solutions to first order as well as to second order for the isotropic equilibrium. The extremized eigenfunctions which represent the entropy and anisotropy perturbation functions, are determined analytically. They exhibit gravothermal behaviour in the central region where heat is removed. It is also found that the anisotropy readjusts non-thermally in the sense that the system departs from isotropy although the total entropy increases.

Method for Compressing Volume Data Using Perturbation Functions

2021 ◽  
Author(s):  
Pavlo Mykhaylov ◽  
Sergey Vyatkin ◽  
Roman Chekhmestruk ◽  
Ivan Perun ◽  
Tetiana Korobeinikova ◽  
...  
Keyword(s):  
Volume Data ◽  
Perturbation Functions
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