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

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

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 New upper bounds for noncentral chi-square cdf

2020 ◽  
pp. 70-74
Author(s):  
Valeriy A. Voloshko ◽  
Egor V. Vecherko
Keyword(s):  
Density Function ◽  
Upper Bounds ◽  
Cumulative Density Function ◽  
Coordinate Systems ◽  
Chi Square ◽  
One Dimensional ◽  
Chi Squared ◽  
Cartesian Coordinate ◽  
The One ◽  
Inverse Trigonometric Functions

Some new upper bounds for noncentral chi-square cumulative density function are derived from the basic symmetries of the multidimensional standard Gaussian distribution: unitary invariance, components independence in both polar and Cartesian coordinate systems. The proposed new bounds have analytically simple form compared to analogues available in the literature: they are based on combination of exponents, direct and inverse trigonometric functions, including hyperbolic ones, and the cdf of the one dimensional standard Gaussian law. These new bounds may be useful both in theory and in applications: for proving inequalities related to noncentral chi-square cumulative density function, and for bounding powers of Pearson’s chi-squared tests.

scholarly journals Cantor Type Basic Sets of Surface $A$-endomorphisms

2021 ◽  
Vol 17 (3) ◽  
pp. 335-345
Author(s):  
V. Z. Grines ◽  
◽  
E. V. Zhuzhoma ◽  
Keyword(s):  
Closed Surface ◽  
Orientable Surface ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Closed Orientable Surface ◽  
One Dimensional ◽  
Basic Set ◽  
Basic Sets ◽  
Nonwandering Set

The paper is devoted to an investigation of the genus of an orientable closed surface $M^{2}$ which admits $A$-endomorphisms whose nonwandering set contains a one-dimensional strictly invariant contracting repeller $\Lambda_{r}$ with a uniquely defined unstable bundle and with an admissible boundary of finite type. First, we prove that, if $M^{2}$ is a torus or a sphere, then $M^{2}$ admits such an endomorphism. We also show that, if $\Omega$ is a basic set with a uniquely defined unstable bundle of the endomorphism $f\colon M^{2}\to M^{2}$ of a closed orientable surface $M^{2}$ and $f$ is not a diffeomorphism, then $\Omega$ cannot be a Cantor type expanding attractor. At last, we prove that, if $f\colon M^{2}\to M^{2}$ is an $A$-endomorphism whose nonwandering set consists of a finite number of isolated periodic sink orbits and a one-dimensional strictly invariant contracting repeller of Cantor type $\Omega_{r}$ with a uniquely defined unstable bundle and such that the lamination consisting of stable manifolds of $\Omega_{r}$ is regular, then $M^{2}$ is a two-dimensional torus $\mathbb{T}^{2}$ or a two-dimensional sphere $\mathbb{S}^{2}$.

scholarly journals Dynamical upper bounds for one-dimensional quasicrystals

2005 ◽  
Vol 303 (1) ◽  
pp. 327-341 ◽  
Author(s):  
David Damanik
Keyword(s):  
Upper Bounds ◽  
One Dimensional

scholarly journals A Survey on Extremal Problems of Eigenvalues

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Ping Yan ◽  
Meirong Zhang
Keyword(s):  
Variational Method ◽  
Lebesgue Space ◽  
Upper Bounds ◽  
Extremal Problems ◽  
Lower And Upper Bounds ◽  
Open Problems ◽  
One Dimensional ◽  
Sturm Liouville ◽  
The One ◽  
Neumann Eigenvalues

Given an integrable potentialq∈L1([0,1],ℝ), the Dirichlet and the Neumann eigenvaluesλnD(q)andλnN(q)of the Sturm-Liouville operator with the potentialqare defined in an implicit way. In recent years, the authors and their collaborators have solved some basic extremal problems concerning these eigenvalues when theL1metric forqis given;∥q∥L1=r. Note that theL1spheres andL1balls are nonsmooth, noncompact domains of the Lebesgue space(L1([0,1],ℝ),∥·∥L1). To solve these extremal problems, we will reveal some deep results on the dependence of eigenvalues on potentials. Moreover, the variational method for the approximating extremal problems on the balls of the spacesLα([0,1],ℝ),1<α<∞will be used. Then theL1problems will be solved by passingα↓1. Corresponding extremal problems for eigenvalues of the one-dimensionalp-Laplacian with integrable potentials have also been solved. The results can yield optimal lower and upper bounds for these eigenvalues. This paper will review the most important ideas and techniques in solving these difficult and interesting extremal problems. Some open problems will also be imposed.

scholarly journals HYPERGRAPHS AND REGULARITY OF SQUARE-FREE MONOMIAL IDEALS

2013 ◽  
Vol 23 (07) ◽  
pp. 1573-1590 ◽  
Author(s):  
KUEI-NUAN LIN ◽  
JASON MCCULLOUGH
Keyword(s):  
Monomial Ideal ◽  
Upper Bounds ◽  
Monomial Ideals ◽  
Combinatorial Object ◽  
One Dimensional ◽  
Combinatorial Properties

We define a new combinatorial object, which we call a labeled hypergraph, uniquely associated to any square-free monomial ideal. We prove several upper bounds on the regularity of a square-free monomial ideal in terms of simple combinatorial properties of its labeled hypergraph. We also give specific formulas for the regularity of square-free monomial ideals with certain labeled hypergraphs. Furthermore, we prove results in the case of one-dimensional labeled hypergraphs.

Upper bounds on correlation decay for one-dimensional long-range spin-glass models

1987 ◽  
Vol 47 (5-6) ◽  
pp. 905-910 ◽  
Author(s):  
Aernout C. D. van Enter
Keyword(s):  
Spin Glass ◽  
Long Range ◽  
Upper Bounds ◽  
One Dimensional ◽  
Correlation Decay

scholarly journals One-dimensional basic sets in the three-sphere

1972 ◽  
Vol 164 ◽  
pp. 163-163 ◽  
Author(s):  
Joel C. Gibbons
Keyword(s):  
One Dimensional ◽  
Three Sphere ◽  
Basic Sets
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