scholarly journals Physical measures of discretizations of generic diffeomorphisms

2016 ◽  
Vol 38 (4) ◽  
pp. 1422-1458 ◽  
Author(s):  
PIERRE-ANTOINE GUIHÉNEUF
Keyword(s):  
Numerical Experiments ◽  
Invariant Measures ◽  
The Other ◽  
Spatial Discretization ◽  
Generic Point ◽  
Physical Measures ◽  
Generic Points ◽  
Ergodic Behaviour

What is the ergodic behaviour of numerically computed segments of orbits of a diffeomorphism? In this paper, we try to answer this question for a generic conservative $C^{1}$-diffeomorphism and segments of orbits of Baire-generic points. The numerical truncation is modelled by a spatial discretization. Our main result states that the uniform measures on the computed segments of orbits, starting from a generic point, accumulate on the whole set of measures that are invariant under the diffeomorphism. In particular, unlike what could be expected naively, such numerical experiments do not see the physical measures (or, more precisely, cannot distinguish physical measures from the other invariant measures).

scholarly journals On density of ergodic measures and generic points

2016 ◽  
Vol 38 (5) ◽  
pp. 1745-1767 ◽  
Author(s):  
KATRIN GELFERT ◽  
DOMINIK KWIETNIAK
Keyword(s):  
Invariant Measures ◽  
Metric Spaces ◽  
Probability Measures ◽  
Geodesic Flows ◽  
Generic Point ◽  
Negatively Curved ◽  
Ergodic Measures ◽  
Compact Case ◽  
Coded Systems ◽  
Generic Points

We introduce two properties of dynamical systems on Polish metric spaces: closeability and linkability. We show that they imply density of ergodic measures in the space of invariant probability measures and the existence of a generic point for every invariant measure. In the compact case, it follows from our conditions that the set of invariant measures is either a singleton of a measure concentrated on a periodic orbit or the Poulsen simplex. We provide examples showing that closability and linkability are independent properties. Our theory applies to systems with the periodic specification property, irreducible Markov chains over a countable alphabet, certain coded systems including $\unicode[STIX]{x1D6FD}$-shifts and $S$-gap shifts, $C^{1}$-generic diffeomorphisms of a compact manifold $M$ and certain geodesic flows of a complete connected negatively curved manifold.

Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

2021 ◽  
pp. 2150002
Author(s):  
Guimin Yang ◽  
Yuanguo Zhu
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Numerical Experiments ◽  
Critical Value ◽  
The Other ◽  
Options Pricing ◽  
Underlying Asset ◽  
Pricing Problems ◽  
Fractional Differential ◽  
The One

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

Multidimensional regular C-fraction with independent variables corresponding to formal multiple power series

2019 ◽  
Vol 150 (4) ◽  
pp. 1853-1870 ◽  
Author(s):  
R. I. Dmytryshyn
Keyword(s):  
Power Series ◽  
Continued Fractions ◽  
Numerical Experiments ◽  
The Other ◽  
Independent Variables ◽  
Classical Algorithm ◽  
Multiple Power ◽  
The One ◽  
The Given ◽  
Multiple Power Series

AbstractIn the paper the correspondence between a formal multiple power series and a special type of branched continued fractions, the so-called ‘multidimensional regular C-fractions with independent variables’ is analysed providing with an algorithm based upon the classical algorithm and that enables us to compute from the coefficients of the given formal multiple power series, the coefficients of the corresponding multidimensional regular C-fraction with independent variables. A few numerical experiments show, on the one hand, the efficiency of the proposed algorithm and, on the other, the power and feasibility of the method in order to numerically approximate certain multivariable functions from their formal multiple power series.

Numerical and Experimental Analysis of the Nonlinear Dynamics due to Impacts of a Continuous Overhung Rotor

1997 ◽  
Author(s):  
Mohammed F. Abdul Azeez ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
The Other ◽  
Experimental Setup ◽  
Partial Differential ◽  
Qualitative Comparison ◽  
Set Up ◽  
Theory And Experiments

Abstract This work is aimed at obtaining the transient response of an overhung rotor when there are impacts occurring in the system. An overhung rotor clamped on one end, with a flywheel on the other and impacts occurring in between, due to a bearing with clearance, is considered. The system is modeled as a continuous rotor system and the governing partial differential equations are set up and solved. The method of assumed modes is used to discretize the system in order to solve the partial differential equations. Using this method numerical experiments are run and a few of the results are presented. The different numerical issues involved are also discussed. An experimental setup was built to run experiments and validate the results. Preliminary experimental observations are presented to show qualitative comparison of theory and experiments.

Further Study on Reverse 1-Center Problem on Trees

2020 ◽  
Vol 37 (06) ◽  
pp. 2050034
Author(s):  
Ali Reza Sepasian ◽  
Javad Tayyebi
Keyword(s):  
Dynamic Programming ◽  
Time Complexity ◽  
Numerical Experiments ◽  
Linear Time ◽  
Minimum Cost ◽  
Fixed Number ◽  
The Other ◽  
Center Problem ◽  
Objective Value ◽  
Linear Cost

This paper studies two types of reverse 1-center problems under uniform linear cost function where edge lengths are allowed to reduce. In the first type, the aim is that the objective value is bounded by a prescribed fixed value [Formula: see text] at minimum cost. The aim of the other is to improve the objective value as much as possible within a given budget. An algorithm based on dynamic programming is proposed to solve the first problem in linear time. Then, this algorithm is applied as a subroutine to design an algorithm to solve the second type of the problem in [Formula: see text] time in which [Formula: see text] is a fixed number dependent on the problem parameters. Under the similarity assumption, this algorithm has a better complexity than the Nguyen algorithm (2013) with quadratic-time complexity. Some numerical experiments are conducted to validate this fact in practice.

scholarly journals Shape Preserving Data Interpolation Using Rational Cubic Ball Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ayser Nasir Hassan Tahat ◽  
Abd Rahni Mt Piah ◽  
Zainor Ridzuan Yahya
Keyword(s):  
Numerical Experiments ◽  
Smooth Curve ◽  
The Other ◽  
Data Interpolation ◽  
Shape Parameters ◽  
Interpolation Scheme ◽  
Shape Preserving ◽  
Curve Interpolation ◽  
Two Parameters

A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness isC1. The outputs from a number of numerical experiments are presented.

FiniteElement Vibration Characteristics of Composite Hypar Shallow Shells with Various Edge Supports

2005 ◽  
Vol 11 (10) ◽  
pp. 1291-1309 ◽  
Author(s):  
S. Sahoo ◽  
D. Chakravorty
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Laminated Composite ◽  
Shell Element ◽  
Vibration Characteristics ◽  
The Other ◽  
Mode Shapes ◽  
Review Of The Literature ◽  
Shallow Shells ◽  
Fundamental Frequencies

A review of the literature reveals that information regarding fundamental frequencies and mode shapes of shallow laminated composite hypar shells with practical civil engineering boundary conditions is not available. The present investigation aims to fill this gap by applying an eight-noded isoparametric shell element as the tool. Numerical experiments are carried out for different parametric variations including boundary conditions and stacking orders to obtain the fundamental frequencies and mode shapes. Some of the results are used for validating the correctness of the present approach by comparing with the existing benchmark, while the other results are studied meticulously to extract a set of meaningful conclusions regarding the free vibration characteristics of composite shallow hypar shells.

scholarly journals Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems

2016 ◽  
Vol 19 (5) ◽  
pp. 1435-1460 ◽  
Author(s):  
Binjie Li ◽  
Xiaoping Xie ◽  
Shiquan Zhang
Keyword(s):  
Convergence Rate ◽  
Numerical Experiments ◽  
Sharp Estimate ◽  
Model Problem ◽  
The Other ◽  
Extended Version ◽  
Weak Galerkin ◽  
Hybridizable Discontinuous Galerkin ◽  
Theoretical Results ◽  
Diffusion Problems

AbstractThis paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate of the algorithm, and show that the theoretical results also are applied to weak Galerkin (WG) methods. The main features of our analysis are twofold: one is that we only need the minimal regularity of the model problem; the other is that we do not require the triangulations to be quasi-uniform. Numerical experiments are provided to confirm the theoretical results.

scholarly journals A Study on Many-Objective Optimization Using the Kriging-Surrogate-Based Evolutionary Algorithm Maximizing Expected Hypervolume Improvement

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Chang Luo ◽  
Koji Shimoyama ◽  
Shigeru Obayashi
Keyword(s):  
Monte Carlo ◽  
Evolutionary Algorithm ◽  
Numerical Experiments ◽  
Test Problem ◽  
Kriging Model ◽  
Monte Carlo Sampling ◽  
The Other ◽  
Expected Improvement ◽  
Design Variables ◽  
The Many

The many-objective optimization performance of the Kriging-surrogate-based evolutionary algorithm (EA), which maximizes expected hypervolume improvement (EHVI) for updating the Kriging model, is investigated and compared with those using expected improvement (EI) and estimation (EST) updating criteria in this paper. Numerical experiments are conducted in 3- to 15-objective DTLZ1-7 problems. In the experiments, an exact hypervolume calculating algorithm is used for the problems with less than six objectives. On the other hand, an approximate hypervolume calculating algorithm based on Monte Carlo sampling is adopted for the problems with more objectives. The results indicate that, in the nonconstrained case, EHVI is a highly competitive updating criterion for the Kriging model and EA based many-objective optimization, especially when the test problem is complex and the number of objectives or design variables is large.

Determination of a Constitutive Relation for Passive Myocardium: I. A New Functional Form

1990 ◽  
Vol 112 (3) ◽  
pp. 333-339 ◽  
Author(s):  
J. D. Humphrey ◽  
R. K. Strumpf ◽  
F. C. P. Yin
Keyword(s):  
Constitutive Relation ◽  
Invariant Measures ◽  
Functional Form ◽  
Transversely Isotropic ◽  
The Other ◽  
Material Symmetry ◽  
Material Parameters ◽  
Experimental Protocols ◽  
Theory And Experiment

The specific aim of this study is to determine a constitutive relation for non-contracting myocardium in terms of a pseudostrain-energy function W whose form is guided by both theory and experiment. We assume that the material symmetry of myocardium is initially and locally transversely-isotropic, and seek a W which depends upon only two coordinate invariant measures of the finite deformation. The specific functional form of such a W is inferred directly from experimental protocols in which one invariant is held constant while the other is varied, and vice versa. On the basis of data from families of these “constant invariant” tests on thin slabs of myocardium taken from the mid-walls of six canine left ventricles, we propose a new polynomial form of W containing only five material parameters.

Sign in / Sign up

Export Citation Format

Share Document