Polynomial decay of correlations for almost Anosov diffeomorphisms

2017 ◽  
Vol 39 (3) ◽  
pp. 832-864
Author(s):  
XU ZHANG ◽  
HUYI HU
Keyword(s):  
Fixed Point ◽  
Decay Of Correlations ◽  
Polynomial Decay ◽  
Lower And Upper Bounds ◽  
Third Order ◽  
Anosov Diffeomorphisms ◽  
The Third ◽  
Srb Measures ◽  
Taylor Expansions ◽  
Almost Anosov

We investigate the polynomial lower and upper bounds for decay of correlations of a class of two-dimensional almost Anosov diffeomorphisms with respect to their Sinai–Ruelle–Bowen (SRB) measures. The degrees of the bounds are determined by the expansion and contraction rates as the orbits approach the indifferent fixed point, and are expressed by using coefficients of the third-order terms in the Taylor expansions of the diffeomorphisms at the indifferent fixed point.

scholarly journals Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yanping Guo ◽  
Fei Yang
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Third Order ◽  
Integral Boundary ◽  
First Order ◽  
The Third ◽  
Nonnegative Continuous Function

By using a fixed point theorem in a cone and the nonlocal third-order BVP's Green function, the existence of at least one positive solution for the third-order boundary-value problem with the integral boundary conditionsx′′′(t)+f(t,x(t),x′(t))=0,t∈J,x(0)=0,x′′(0)=0, andx(1)=∫01g(t)x(t)dtis considered, wherefis a nonnegative continuous function,J=[0,1], andg∈L[0,1].The emphasis here is thatfdepends on the first-order derivatives.

scholarly journals Existence of nonoscillatory solutions to third order nonlinear neutral difference equations

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4981-4991
Author(s):  
K.S. Vidhyaa ◽  
C. Dharuman ◽  
John Graef ◽  
E. Thandapani
Keyword(s):  
Fixed Point ◽  
Sufficient Conditions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Neutral Difference Equations ◽  
Positive And Negative Coefficients ◽  
The Third ◽  
Delay Difference

The authors consider the third order neutral delay difference equation with positive and negative coefficients ?(an?(bn?(xn + pxn-m)))+pnf(xn-k)- qn1(xn-l) = 0, n ? n0, and give some new sufficient conditions for the existence of nonoscillatory solutions. Banach?s fixed point theorem plays a major role in the proofs. Examples are provided to illustrate their main results.

2. On the Curves produced by Reflection from a Polished Revolving Wire

1878 ◽  
Vol 9 ◽  
pp. 302-302
Author(s):  
Edward Sang
Keyword(s):  
Fixed Point ◽  
Curved Surface ◽  
Third Order ◽  
Straight Wire ◽  
The Third ◽  
Straight Line ◽  
Plane Passing ◽  
The Subject ◽  
The Wire

When a polished thin straight wire turns on a fixed point in space, the point at which light coming from a fixed source is reflected, moves in a curved surface. In this paper the motion of the wire was supposed to be restricted to the plane passing through the eye and the source of light. The curve was shown to be of the third order, having a straight line as a symptote both ways, and to depend for its form upon a characterising angle. The interest of the subject lay chiefly in the remarkable transformations of the curve.

scholarly journals The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1274
Author(s):  
Anna Dobosz
Keyword(s):  
Convex Functions ◽  
Upper Bounds ◽  
Arithmetic Mean ◽  
Lower And Upper Bounds ◽  
Third Order ◽  
Toeplitz Determinants ◽  
The Third ◽  
Toeplitz Determinant ◽  
Symmetry Properties ◽  
Definition Of

Sharp lower and upper bounds of the second- and third-order Hermitian Toeplitz determinants for the class of α-convex functions were found. The symmetry properties of the arithmetic mean underlying the definition of α-convexity and the symmetry properties of Hermitian matrices were used.

scholarly journals Solvability of a Third-Order Singular Generalized Left Focal Problem in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-18
Author(s):  
Youwei Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Multiple Positive Solutions ◽  
Third Order ◽  
The Third ◽  
Priori Estimates

We consider the existence of positive solution for a third-order singular generalized left focal boundary value problem with full derivatives in Banach spaces. Green’s function and its properties, explicit a priori, estimates will be presented. By means of the theories of the fixed point in cones, we establish some new and general results on the existence of single and multiple positive solutions to the third-order singular generalized left focal boundary value problem. Our results are generalizations and extensions of the results of the focal boundary value problem. An example is included to illustrate the results obtained.

scholarly journals BASIC THEORY OF NONLINEAR THIRD-ORDER Q-DIFFERENCE EQUATIONS AND INCLUSIONS

2013 ◽  
Vol 18 (1) ◽  
pp. 122-135 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan Jose Nieto
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Extremal Solutions ◽  
Inclusion Problem ◽  
Third Order ◽  
The Third

We investigate the existence of solutions for boundary value problems of the third-order q-difference equations and inclusions. Our results are based on some standard fixed point theorems. In case of inclusion problem, the existence results are obtained for convex as well as nonconvex multi-valued maps. We also discuss the existence of extremal solutions for the inclusion problem.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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