scholarly journals On 2-Diffeomorphisms with One-Dimensional Basic Sets and a Finite Number of Moduli

2016 ◽  
Vol 16 (4) ◽  
pp. 727-749
Author(s):  
V. Z. Grines ◽  
Z. Grines ◽  
S. Van Strien
Keyword(s):  
Finite Number ◽  
One Dimensional ◽  
Basic Sets

Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Trung Thành
Keyword(s):  
Finite Number ◽  
Scattering Problem ◽  
One Dimensional ◽  
Globally Convergent ◽  
Convergent Method ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Objective Functional

AbstractWe investigate a globally convergent method for solving a one-dimensional inverse medium scattering problem using backscattering data at a finite number of frequencies. The proposed method is based on the minimization of a discrete Carleman weighted objective functional. The global convexity of this objective functional is proved.

A one dimensional random space-filling problem

1968 ◽  
Vol 5 (02) ◽  
pp. 427-435 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Asymptotic Behavior ◽  
Finite Number ◽  
Real Line ◽  
Random Variables ◽  
Random Interval ◽  
Space Filling ◽  
One Dimensional ◽  
The Real ◽  
Fixed Constant ◽  
Filling Problem

Consider an interval of the real line (0, x), x > 0; and place in it a random subinterval S(x) defined by the random variables Xx and Yx , the position of the center of S(x) and the length of S(x). The set (0, x)– S(x) consists of two intervals of length δ and η. Let a > 0 be a fixed constant. If δ ≦ a, then a random interval S(δ) defined by Xδ, Yδ is placed in the interval of length δ. If δ < a, the placement of the second interval is not made. The same is done for the interval of length η. Continue to place non-intersecting random subintervals in (0, x), and require that the lengths of all the random subintervals be ≦ a. The process terminates after a finite number of steps when all the segments of (0, x) uncovered by random subintervals are of length < a. At this stage, we say that (0, x) is saturated. Define N(a, x) as the number of random subintervals that have been placed when the process terminates. We are interested in the asymptotic behavior of the moments of N(a, x), for large x.

Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets

2020 ◽  
Vol 84 (5) ◽  
pp. 862-909
Author(s):  
V. Z. Grines ◽  
E. D. Kurenkov
Keyword(s):  
One Dimensional ◽  
Basic Sets

scholarly journals Lyapunov optimization for non-generic one-dimensional expanding Markov maps

2019 ◽  
Vol 40 (9) ◽  
pp. 2571-2592 ◽  
Author(s):  
MAO SHINODA ◽  
HIROKI TAKAHASI
Keyword(s):  
Periodic Orbit ◽  
Finite Number ◽  
Dense Subset ◽  
Equilibrium States ◽  
Positive Entropy ◽  
Hölder Continuous ◽  
Perturbation Theorem ◽  
One Dimensional ◽  
Lyapunov Optimization ◽  
Shift Map

For a non-generic, yet dense subset of$C^{1}$expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are equilibrium states for some Hölder continuous potentials. We also prove the existence of another non-generic dense subset for which the optimizing measure is unique and supported on a periodic orbit. A key ingredient is a new$C^{1}$perturbation theorem which allows us to interpolate between expanding Markov maps and the shift map on a finite number of symbols.

Exact upper bounds for the number of one-dimensional basic sets of surfaceA-diffeomorphisms

1997 ◽  
Vol 3 (1) ◽  
pp. 1-18 ◽  
Author(s):  
S. Kh. Aranson ◽  
R. V. Plykin ◽  
A. Yu. Zhirov ◽  
E. V. Zhuzhoma
Keyword(s):  
Upper Bounds ◽  
One Dimensional ◽  
Basic Sets

A Set of Plane Measure Zero Containing all Finite Polygonal Arcs

1970 ◽  
Vol 22 (4) ◽  
pp. 815-821 ◽  
Author(s):  
D. J. Ward
Keyword(s):  
Finite Number ◽  
Measure Zero ◽  
One Dimensional ◽  
The One ◽  
The Given ◽  
Plane Measure

We say a (plane) set A contains all sets of some type if, for each B of type , there is a subset of A that is congruent to B. Recently, Besicovitch and Rado [3] and independently, Kinney [5] have constructed sets of plane measure zero containing all circles. In these papers it is pointed out that the set of all similar rectangles, some sets of confocal conies and other such classes of sets can be contained in sets of plane measure zero, but all these generalizations rely in some way on the symmetry, or similarity of the sets within the given type.In this paper we construct a set of plane measure zero containing all finite polygonal arcs (i.e., the one-dimensional boundaries of all polygons with a finite number of sides) with slightly stronger results if we restrict our attention to k-gons for some fixed k.

XX. On the classification of Loci

1878 ◽  
Vol 169 ◽  
pp. 663-681 ◽  
Keyword(s):  
Finite Number ◽  
Linear Transformation ◽  
Infinite System ◽  
Flat Space ◽  
One Dimensional

By a curve we mean a continuous one-dimensional aggregate of any sort of elements, and therefore not merely a curve in the ordinary geometrical sense, but also a singly infinite system of curves, surfaces, complexes, &c., such that one condition is sufficient to determine a finite number of them. The elements may be regarded as determined by k coordinates; and then, if these be connected by k —1 equations of any order, the curve is either the whole aggregate of common solutions of these equations, or, when this breaks up into algebraically distinct parts, the curve is one of these parts. It is thus convenient to employ still further the language of geometry, and to speak of such a curve as the complete or partial intersection of k —1 loci in flat space of k dimensions, or, as we shall sometimes say, in a k -flat. If a certain number, say h , of the equations are linear, it is evidently possible by a linear transformation to make these equations equate h of the coordinates to zero ; it is then convenient to leave these coordinates out of consideration altogether, and only to regard the remaining k — h —1 equations between k — h coordinates. In this case the curve will, therefore, be regarded as a curve in flat space of k — h dimensions. And, in general, when we speak of a curve as in flat space of k dimensions, we mean that it cannot exist in flat space of k —1 dimensions.

A Darboux-type theorem for germs of holomorphic one-dimensional foliations

2014 ◽  
Vol 35 (8) ◽  
pp. 2458-2473
Author(s):  
CÉSAR CAMACHO ◽  
BRUNO SCÁRDUA
Keyword(s):  
Finite Number ◽  
Type Theorem ◽  
First Integral ◽  
One Dimensional ◽  
Integrating Factor

We show that a germ of a holomorphic one-dimensional foliation at a singularity in a space of dimension two admits a holomorphic first integral if and only if there are infinitely many closed leaves and a finite number of separatrices, with each separatrix having linearizable holonomy. Indeed, if there are infinitely many closed leaves and the set of separatrices is finite, then the foliation admits either a holomorphic first integral or a formal simple integrating factor of Darboux type.

scholarly journals Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model

Systems ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 71
Author(s):  
Petro Feketa ◽  
Alexander Schaum ◽  
Thomas Meurer
Keyword(s):  
Finite Number ◽  
Exponential Convergence ◽  
Reaction Diffusion ◽  
Distributed Parameter ◽  
System State ◽  
State Information ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
Complete State ◽  
The One

A constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locations are derived that ensure the exponential convergence of the estimated state to the original one. The designed observer is capable of tracking a variety of complex spatiotemporal behaviors and self-replicating patterns. The theoretical findings are illustrated in particular numerical case studies. The results of the paper can be used for the synchronization analysis of the master–slave configuration of two identical Gray–Scott models coupled via a finite number of spatial points and can also be exploited for the purposes of feedback control applications in which the complete state information is required.

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