If a finite extension of a Bernoulli shift has no finite rotation factors, it is Bernoulli

1978 ◽  
Vol 30 (3) ◽  
pp. 193-206 ◽  
Author(s):  
Daniel J. Rudolph
Keyword(s):  
Bernoulli Shift ◽  
Finite Extension ◽  
Finite Rotation

On Finite Coding Factors of a Class of Random Markov Chains

1994 ◽  
Vol 37 (3) ◽  
pp. 399-407 ◽  
Author(s):  
M. Rahe
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Direct Product ◽  
Finite Length ◽  
Bernoulli Shift ◽  
Finite Rotation ◽  
Step Size ◽  
Zero Entropy

AbstractFor k-step Markov chains, factors generated by finite length codes split off with Bernoulli complement when maximal in entropy. Those not maximal are relatively finite in another factor which generates or splits off.These results extend to random Markov chains with finite expected step size, implying that random Markov chains with finite expected step size can have only finitely many ergodic components, each of which is isomorphic to a finite rotation, a Bernoulli shift, or a direct product of a Bernoulli shift with a finite rotation. This result limits the type of zero entropy factors which occur in random Markov chains with finite expected step size, providing a counterpoint to the work of Kalikow, Katznelson, and Weiss, who have shown that each zero entropy process can be embedded in some random Markov chain.Extending Rudolph and Schwarz, random Markov chains with finite expected step size are limits in of their canonical Markov approximants. The -closure of the class is the Bernoulli cross Generalized Von Neuman processes.Finitary isomorphism of aperiodic ergodic random Markov chains with finite expected step size is considered.Applications are made to a class of generalized baker's transformations.

scholarly journals DIOPHANTINE SETS OF POLYNOMIALS OVER ALGEBRAIC EXTENSIONS OF THE RATIONALS

2014 ◽  
Vol 79 (3) ◽  
pp. 733-747
Author(s):  
CLAUDIA DEGROOTE ◽  
JEROEN DEMEYER
Keyword(s):  
Minimal Polynomial ◽  
Finite Extension ◽  
Algebraic Extension ◽  
Recursively Enumerable

AbstractLet L be a recursive algebraic extension of ℚ. Assume that, given α ∈ L, we can compute the roots in L of its minimal polynomial over ℚ and we can determine which roots are Aut(L)-conjugate to α. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of α, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in ℝ, or in a finite extension of ℚp (with p an odd prime). Then we show that subsets of L[X]k that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X].

scholarly journals Probing bacterial cell wall growth by tracing wall-anchored protein complexes

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yi-Jen Sun ◽  
Fan Bai ◽  
An-Chi Luo ◽  
Xiang-Yu Zhuang ◽  
Tsai-Shun Lin ◽  
...  
Keyword(s):  
Cell Wall ◽  
Cell Shape ◽  
Bernoulli Shift ◽  
Protein Complexes ◽  
Axial Direction ◽  
Cell Wall Growth ◽  
Flagellar Motors ◽  
Shift Map ◽  
Dynamic Assembly ◽  
Wall Growth

AbstractThe dynamic assembly of the cell wall is key to the maintenance of cell shape during bacterial growth. Here, we present a method for the analysis of Escherichia coli cell wall growth at high spatial and temporal resolution, which is achieved by tracing the movement of fluorescently labeled cell wall-anchored flagellar motors. Using this method, we clearly identify the active and inert zones of cell wall growth during bacterial elongation. Within the active zone, the insertion of newly synthesized peptidoglycan occurs homogeneously in the axial direction without twisting of the cell body. Based on the measured parameters, we formulate a Bernoulli shift map model to predict the partitioning of cell wall-anchored proteins following cell division.

scholarly journals FAMILIES OF AFFINE RULED SURFACES: EXISTENCE OF CYLINDERS

2016 ◽  
Vol 223 (1) ◽  
pp. 1-20 ◽  
Author(s):  
ADRIEN DUBOULOZ ◽  
TAKASHI KISHIMOTO
Keyword(s):  
Minimal Model ◽  
Finite Extension ◽  
Smooth Curve ◽  
Ruled Surfaces ◽  
Model Program ◽  
Minimal Model Program ◽  
Generic Fiber ◽  
Projective Model ◽  
The Family

We show that the generic fiber of a family $f:X\rightarrow S$ of smooth $\mathbb{A}^{1}$-ruled affine surfaces always carries an $\mathbb{A}^{1}$-fibration, possibly after a finite extension of the base $S$. In the particular case where the general fibers of the family are irrational surfaces, we establish that up to shrinking $S$, such a family actually factors through an $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ over a certain $S$-scheme $Y\rightarrow S$ induced by the MRC-fibration of a relative smooth projective model of $X$ over $S$. For affine threefolds $X$ equipped with a fibration $f:X\rightarrow B$ by irrational $\mathbb{A}^{1}$-ruled surfaces over a smooth curve $B$, the induced $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ can also be recovered from a relative minimal model program applied to a smooth projective model of $X$ over $B$.

A Study of Belleville Spring and Diaphragm Spring in Engineering

1990 ◽  
Vol 57 (4) ◽  
pp. 1026-1031 ◽  
Author(s):  
Ye Zhiming ◽  
Yeh Kaiyuan
Keyword(s):  
Integral Equation ◽  
Experimental Method ◽  
Conical Shell ◽  
Large Deflection ◽  
Integral Equation Method ◽  
Mechanical Analysis ◽  
Static Response ◽  
Finite Rotation ◽  
Calculating Method ◽  
Distribution Rules

This paper deals with the static response of a Belleville spring and a diaphragm spring by using the finite rotation and large deflection theories of a beam and conical shell, and an experimental method as well. The authors propose new mechanical analysis mathematical models. The exact solution of a variable width cantilever beam is obtained. By using the integral equation method and the iterative method to solve the simplified equations and Reissner’s equations of finite rotation and large deflection of a conical shell, this paper has calculated a great number of numerical results. The properties of loads, strains, stresses and displacements, and the distribution rules of strains and stresses of diaphragm springs are investigated in detail by means of the experimental method. The unreasonableness of several assumptions in traditional theories and calculating method is pointed out.

scholarly journals Fields of Definition for Representations of Associative Algebras

2018 ◽  
Vol 62 (1) ◽  
pp. 291-304
Author(s):  
Dave Benson ◽  
Zinovy Reichstein
Keyword(s):  
Finite Extension ◽  
Representation Type ◽  
Essential Dimension ◽  
Extension Field ◽  
Associative Algebras ◽  
Separable Extension ◽  
Finite Representation ◽  
Field Of Definition ◽  
Finite Dimensional ◽  
A Finite Group

AbstractWe examine situations, where representations of a finite-dimensionalF-algebraAdefined over a separable extension fieldK/F, have a unique minimal field of definition. Here the base fieldFis assumed to be a field of dimension ≼1. In particular,Fcould be a finite field ork(t) ork((t)), wherekis algebraically closed. We show that a unique minimal field of definition exists if (a)K/Fis an algebraic extension or (b)Ais of finite representation type. Moreover, in these situations the minimal field of definition is a finite extension ofF. This is not the case ifAis of infinite representation type orFfails to be of dimension ≼1. As a consequence, we compute the essential dimension of the functor of representations of a finite group, generalizing a theorem of Karpenko, Pevtsova and the second author.

Classical, Covariant Finite-size Model of the Radiating Electron

1974 ◽  
Vol 29 (11) ◽  
pp. 1671-1684 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Finite Size ◽  
Finite Extension ◽  
Equation Of Motion ◽  
Mass Renormalization ◽  
Classical Electron ◽  
Size Model

The finite extension of the classical electron is defined in a new, covariant manner. This new definition enables one to calculate exactly the bound and emitted four-momentum and to find an equation of motion different from the Lorentz-Dirac equation and from other equations proposed in the literature. Neither mass renormalization nor use of advanced quantities nor asymptotic conditions are necessary. Runaway solutions and pre-acceleration do not occur in the framework of the model presented here.

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