scholarly journals Kakutani equivalence for products of some special flows over rotations

2021 ◽  
pp. 1-28
Author(s):  
DAREN WEI
Keyword(s):  
Full Measure ◽  
Countable Family ◽  
Function Smooth ◽  
Roof Function ◽  
Kakutani Equivalence

Abstract We study Kakutani equivalence for products of some special flows over rotations with roof function smooth except a singularity at $0\in \mathbb {T}$ . We estimate the Kakutani invariant for products of these flows with different powers of singularities and rotations from a full measure set. As a corollary, we obtain a countable family of pairwise non-Kakutani equivalent products of special flows over rotations.

A canonical thickening of ℚ and the entropy ofα-continued fraction transformations

2011 ◽  
Vol 32 (4) ◽  
pp. 1249-1269 ◽  
Author(s):  
CARLO CARMINATI ◽  
GIULIO TIOZZO
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Full Measure ◽  
Countable Family

AbstractWe construct a countable family of open intervals contained in (0,1] whose endpoints are quadratic surds and such that their union is a full measure set. We then show that these intervals are precisely the monotonicity intervals of the entropy ofα-continued fractions, thus proving a conjecture of Nakada and Natsui.

scholarly journals The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

2020 ◽  
pp. 1-26
Author(s):  
SNIR BEN OVADIA
Keyword(s):  
Symbolic Dynamics ◽  
Full Measure ◽  
Probability Measures ◽  
Positive Entropy ◽  
Surface Diffeomorphisms ◽  
Srb Measures ◽  
Hyperbolic Diffeomorphisms ◽  
Set Of Points ◽  
Math Phys ◽  
Homoclinic Classes

Abstract The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

scholarly journals A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Niklas Ericsson
Keyword(s):  
Fourier Expansion ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Countable Family ◽  
Angular Variable ◽  
Two Dimensional ◽  
Sobolev Norms ◽  
Well Posed ◽  
Variational Formulations

Abstract We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.

The Reign of Mary Tudor: Historiography and Research

1989 ◽  
Vol 21 (4) ◽  
pp. 547-558 ◽  
Author(s):  
David Loades
Keyword(s):  
Full Measure ◽  
Royal Commission ◽  
English Reformation ◽  
Mary Tudor ◽  
Great Harm ◽  
Freedom Of Action

Mary made the unfortunate mistake of antagonizing her successor, without being able to impose any limitations upon her freedom of action. Writing in 1557 the Venetian ambassador, Giovanni Michieli, observed “although it is dissembled, it cannot be denied that [the queen] displays in many ways the scorn and ill will she bears her [Elizabeth]….” The younger woman reciprocated such feelings in full measure, and a few days before her accession, when there was no longer any need to be discreet, the Count of Feria reported, “She is highly indignant about what has been done to her in the queen's lifetime….” Such personal antagonism may not go far in explaining Elizabeth's decision to reverse so many of her sister's policies, but it certainly helps to account for the animus that the new queen's most trusted servants so quickly developed against their predecessors. In the last days of 1558 a royal commission was issued “to discover by what means the realm hath suffered great harm” under the previous regime, and soon came up with a long list of secular and ecclesiastical grants. Most of the latter were immediately resumed in the succeeding Parliament. It was to be another quarter of a century before Elizabeth finally emerged as the winner, and Mary as the loser, of the English reformation struggle, but those in power after 1558 did not wait to celebrate their victory.

scholarly journals Spherical Coefficients of Slice Regular Functions

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Amedeo Altavilla
Keyword(s):  
Differential Equations ◽  
Regular Function ◽  
Countable Family ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Spherical Expansion ◽  
Derivatives Of

AbstractGiven a quaternionic slice regular function f, we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtained in terms of spherical and slice derivatives of the function itself. Afterwards, we compare the coefficients of f with those of its slice derivative $$\partial _{c}f$$ ∂ c f obtaining a countable family of differential equations satisfied by any slice regular function. The results are proved in all details and are accompanied to several examples. For some of the results, we also give alternative proofs.

Emotion and Virtue

2020 ◽  
Author(s):  
Gopal Sreenivasan
Keyword(s):  
Virtue Ethics ◽  
Moral Psychology ◽  
Character Trait ◽  
Full Measure ◽  
Traditional Definition ◽  
Definition Of

What must a person be like to possess a virtue in full measure? What sort of psychological constitution does one need to be an exemplar of compassion, say, or of courage? Focusing on these two examples, this book ingeniously argues that certain emotion traits play an indispensable role in virtue. With exemplars of compassion, for instance, this role is played by a modified sympathy trait, which is central to enabling these exemplars to be reliably correct judges of the compassionate thing to do in various practical situations. Indeed, according to the book, the virtue of compassion is, in a sense, a modified sympathy trait, just as courage is a modified fear trait. While the book upholds the traditional definition of virtue as a species of character trait, it discards other traditional precepts. For example, the book rejects the unity of the virtues and raises new questions about when virtue should be taught. Unlike orthodox virtue ethics, moreover, this account does not aspire to rival consequentialism and deontology. Instead the book repudiates the ambitions of virtue imperialism, and makes significant contributions to moral psychology and the theory of virtue alike.

scholarly journals A novel hybrid method for equilibrium problem and a countable family of generalized nonexpansive-type maps with applications

2021 ◽  
Vol 22 (1) ◽  
pp. 359-376
Author(s):  
Markjoe Olunna Uba ◽  
Emmanuel Ezzaka Otubo ◽  
Maria Amarakristi Onyido
Keyword(s):  
Equilibrium Problem ◽  
Hybrid Method ◽  
Countable Family
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