On the complexity of the lattices of subvarieties and congruences

2020 ◽  
Vol 30 (08) ◽  
pp. 1609-1624 ◽  
Author(s):  
A. V. Kravchenko ◽  
A. M. Nurakunov ◽  
M. V. Schwidefsky
Keyword(s):  
Finite Type ◽  
Finite Lattice ◽  
Sufficient Conditions ◽  
Structure Formula

We find sufficient conditions guaranteeing that for a quasivariety [Formula: see text] of structures of finite type containing a [Formula: see text]-class with respect to [Formula: see text], there exists a subquasivariety [Formula: see text] and a structure [Formula: see text] such that the problems whether a finite lattice embeds into the lattice [Formula: see text] of [Formula: see text]-varieties and into the lattice [Formula: see text] are undecidable.

Recurrence in pairs

2008 ◽  
Vol 28 (4) ◽  
pp. 1135-1143 ◽  
Author(s):  
KAMEL HADDAD ◽  
WILLIAM OTT
Keyword(s):  
Finite Number ◽  
Finite Type ◽  
Sufficient Conditions ◽  
Dense Orbit ◽  
Subshift Of Finite Type

AbstractWe introduce and study the notion of weak product recurrence. Two sufficient conditions for this type of recurrence are established. We deduce that any point with a dense orbit in either the full one-sided shift on a finite number of symbols or a mixing subshift of finite type is weakly product recurrent. This observation implies that distality does not follow from weak product recurrence. We have therefore answered, in the negative, a question posed by Auslander and Furstenberg.

Prevalence of rapid mixing in hyperbolic flows

1998 ◽  
Vol 18 (5) ◽  
pp. 1097-1114 ◽  
Author(s):  
DMITRY DOLGOPYAT
Keyword(s):  
Finite Type ◽  
Periodic Orbits ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Suspension Flow ◽  
Subshift Of Finite Type ◽  
Rapid Mixing ◽  
Hyperbolic Flows ◽  
Necessary And Sufficient

We provide necessary and sufficient conditions for a suspension flow, over a subshift of finite type, to mix faster than any power of time. Then we show that these conditions are satisfied if the flow has two periodic orbits such that the ratio of the periods cannot be well approximated by rationals.

On The Critical Lattices of Arbitrary Point Sets

1949 ◽  
Vol 1 (1) ◽  
pp. 78-87 ◽  
Author(s):  
K. Mahler
Keyword(s):  
Finite Type ◽  
Sufficient Conditions ◽  
Arbitrary Point ◽  
Necessary And Sufficient Conditions ◽  
Star Body ◽  
Point Sets ◽  
Point Set ◽  
Critical Lattice ◽  
Necessary And Sufficient

In this note, I shall establish necessary and sufficient conditions for the existence of critical lattices of an arbitrary point set, and I shall construct a non-trivial example of a point set without any critical lattice. In a previous paper, I proved that every star body of the finite type possesses at least one critical lattice.

Discrete Lyapunov exponents and Hausdorff dimension

2000 ◽  
Vol 20 (1) ◽  
pp. 145-172 ◽  
Author(s):  
SHMUEL FRIEDLAND
Keyword(s):  
Hausdorff Dimension ◽  
Finite Type ◽  
Lyapunov Exponents ◽  
Thermodynamic Formalism ◽  
Sufficient Conditions ◽  
Kleinian Groups ◽  
Limit Sets ◽  
Geometrically Finite ◽  
Subshifts Of Finite Type ◽  
Discrete Analogs

We study certain metrics on subshifts of finite type for which we define the discrete analogs of Lyapunov exponents. We prove Young's formula for $\mu$-Hausdorff dimension. We give sufficient conditions on the above metrics for which the Hausdorff dimension is given by thermodynamic formalism. We apply these results to the Hausdorff dimension of the limit sets of geometrically finite, purely loxodromic, Kleinian groups.

The subalgebra lattice of a finite algebra

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Konrad Pióro
Keyword(s):  
Finite Algebra ◽  
Finite Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Algebras ◽  
Subalgebra Lattice ◽  
Partial Algebras ◽  
Necessary And Sufficient

AbstractThe aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.

scholarly journals Approximation of entire functions over Carathéodory domains

1982 ◽  
Vol 25 (2) ◽  
pp. 221-229 ◽  
Author(s):  
G.P. Kapoor ◽  
A. Nautiyal
Keyword(s):  
Entire Function ◽  
Analytic Continuation ◽  
Finite Type ◽  
Finite Order ◽  
Jordan Curve ◽  
Entire Functions ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Image Position ◽  
Necessary And Sufficient

Let D be a domain bounded by a Jordan curve. For 1 ≤ p ≤ ∞, let Lp(D) be the class of all functions f holomorphic in D such that where A is the area of D. For f ∈Lp(D), setπn consists of all polynomials of degree at most n. Recently, Andre Giroux (J. Approx. Theory 28 (1980), 45–53) has obtained necessary and sufficient conditions, in terms of the rate of decrease of the approximation error , such that has an analytic continuation as an entire function having finite order and finite type. In the present paper we have considered the approximation error (*) on a Carathéodory domain and have extended the results of Giroux for the case 1 ≤ p < 2.

scholarly journals Efficient Auctions and Interdependent Types

2012 ◽  
Vol 102 (3) ◽  
pp. 319-324 ◽  
Author(s):  
Dirk Bergemann ◽  
Stephen Morris ◽  
Satoru Takahashi
Keyword(s):  
Finite Type ◽  
Sufficient Conditions ◽  
General Setting ◽  
Efficient Allocation ◽  
Type Space ◽  
Interdependent Preferences ◽  
Interdependent Values ◽  
Partial Implementation

We consider the efficient allocation of a single good with interdependent values in a quasilinear environment. We present an approach to modeling interdependent preferences distinguishing between “payoff types” and “belief types” and report a characterization of when the efficient allocation can be partially Bayesian implemented on a finite type space. The characterization can be used to unify a number of sufficient conditions for efficient partial implementation in this classical auction setting. We report how a canonical language for discussing interdependent types - developed in a more general setting by Bergemann, Morris and Takahashi (2011) - applies in this setting and note by example that this canonical language will not allow us to distinguish some types in the payoff type - belief type language.

scholarly journals Matrix characterization of multidimensional subshifts of finite type

2019 ◽  
Vol 20 (2) ◽  
pp. 407
Author(s):  
Puneet Sharma ◽  
Dileep Kumar
Keyword(s):  
Finite Type ◽  
Sufficient Conditions ◽  
Periodic Points ◽  
Alternative View ◽  
Subshift Of Finite Type ◽  
Shift Space ◽  
The Matrix ◽  
Subshifts Of Finite Type ◽  
Necessary And Sufficient

<p>Let X ⊂ A<sup>Zd </sup>be a 2-dimensional subshift of finite type. We prove that any 2-dimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general d-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space X to exhibit periodic points.</p>

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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