scholarly journals Topologically completely positive entropy and zero-dimensional topologically completely positive entropy

2017 ◽  
Vol 38 (5) ◽  
pp. 1894-1922
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Finite Type ◽  
Sufficient Condition ◽  
Positive Entropy ◽  
Two Dimensional ◽  
Completely Positive ◽  
Shift Of Finite Type ◽  
One Dimensional ◽  
Zero Entropy ◽  
The Difference

In a previous paper [Pavlov, A characterization of topologically completely positive entropy for shifts of finite type. Ergod. Th. & Dynam. Sys.34 (2014), 2054–2065], the author gave a characterization for when a $\mathbb{Z}^{d}$-shift of finite type has no non-trivial subshift factors with zero entropy, a property which we here call zero-dimensional topologically completely positive entropy. In this work, we study the difference between this notion and the more classical topologically completely positive entropy of Blanchard. We show that there are one-dimensional subshifts and two-dimensional shifts of finite type which have zero-dimensional topologically completely positive entropy but not topologically completely positive entropy. In addition, we show that strengthening the hypotheses of the main result of Pavlov [A characterization of topologically completely positive entropy for shifts of finite type. Ergod. Th. & Dynam. Sys.34 (2014), 2054–2065] yields a sufficient condition for a $\mathbb{Z}^{d}$-shift of finite type to have topologically completely positive entropy.

scholarly journals A characterization of topologically completely positive entropy for shifts of finite type

2013 ◽  
Vol 34 (6) ◽  
pp. 2054-2065 ◽  
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Dynamical System ◽  
Finite Type ◽  
American Mathematical Society ◽  
Equivalent Condition ◽  
Positive Entropy ◽  
Completely Positive ◽  
Shift Of Finite Type ◽  
Formula Group ◽  
Zero Entropy

AbstractA topological dynamical system was defined by Blanchard [Fully Positive Topological Entropy and Topological Mixing (Symbolic Dynamics and Applications (in honor of R. L. Adler), 135). American Mathematical Society Contemporary Mathematics, Providence, RI, 1992, pp. 95–105] to have topologically completely positive entropy (or TCPE) if its only zero entropy factor is the dynamical system consisting of a single fixed point. For ${ \mathbb{Z} }^{d} $ shifts of finite type, we give a simple condition equivalent to having TCPE. We use our characterization to derive a similar equivalent condition to TCPE for the subclass of ${ \mathbb{Z} }^{d} $ group shifts, which was proved by Lind and Schmidt in the abelian case [Homoclinic points of algebraic ${ \mathbb{Z} }^{d} $-actions. J. Amer. Math. Soc. 12(4) (1999), 953–980] and by Boyle and Schraudner in the general case [${ \mathbb{Z} }^{d} $ group shifts and Bernoulli factors. Ergod. Th. & Dynam. Sys. 28(2) (2008), 367–387]. We also give an example of a ${ \mathbb{Z} }^{2} $ shift of finite type which has TCPE but is not even topologically transitive, and prove a result about block gluing ${ \mathbb{Z} }^{d} $ SFTs motivated by our characterization of TCPE.

scholarly journals Projective subdynamics and universal shifts

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Pierre Guillon
Keyword(s):  
Large Class ◽  
Finite Type ◽  
Positive Entropy ◽  
Two Dimensional ◽  
One Dimensional ◽  
International Audience

International audience We study the projective subdynamics of two-dimensional shifts of finite type, which is the set of one-dimensional configurations that appear as columns in them. We prove that a large class of one-dimensional shifts can be obtained as such, namely the effective subshifts which contain positive-entropy sofic subshifts. The proof involves some simple notions of simulation that may be of interest for other constructions. As an example, it allows us to prove the undecidability of all non-trivial properties of projective subdynamics.

One-dimensional projective subdynamics of uniformly mixing shifts of finite type

2014 ◽  
Vol 35 (6) ◽  
pp. 1962-1999
Author(s):  
MICHAEL H. SCHRAUDNER
Keyword(s):  
Finite Type ◽  
Sufficient Condition ◽  
Mixing Conditions ◽  
One Dimensional ◽  
Strongly Irreducible ◽  
Topologically Mixing ◽  
Stark Contrast ◽  
The One

We investigate under which circumstances the projective subdynamics of multidimensional shifts of finite type can be non-sofic. In particular, we give a sufficient condition ensuring the one-dimensional projective subdynamics of such $\mathbb{Z}^{d}$ systems to be sofic and we show that this condition is already met (along certain, respectively all, sublattices) by most of the commonly used uniform mixing conditions. (Examples of the different situations are given.) Complementary to this we are able to prove a characterization of one-dimensional projective subdynamics for strongly irreducible $\mathbb{Z}^{d}$ shifts of finite type for every $d\geq 2$: in this setting the class of possible subdynamics coincides exactly with the class of mixing $\mathbb{Z}$ sofics. This stands in stark contrast to the much more diverse situation in merely topologically mixing multidimensional shifts of finite type.

Theory of ultrasonic attenuation in one and two dimensional metals

1976 ◽  
Vol 54 (14) ◽  
pp. 1454-1460 ◽  
Author(s):  
T. Tiedje ◽  
R. R. Haering
Keyword(s):  
Ultrasonic Attenuation ◽  
Three Dimensional ◽  
Electronic Systems ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
One Dimensional ◽  
The Difference

The theory of ultrasonic attenuation in metals is extended so that it applies to quasi one and two dimensional electronic systems. It is shown that the attenuation in such systems differs significantly from the well-known results for three dimensional systems. The difference is particularly marked for one dimensional systems, for which the attenuation is shown to be strongly temperature dependent.

scholarly journals CUNTZ–KRIEGER ALGEBRAS AND ONE-SIDED CONJUGACY OF SHIFTS OF FINITE TYPE AND THEIR GROUPOIDS

2019 ◽  
Vol 109 (3) ◽  
pp. 289-298
Author(s):  
KEVIN AGUYAR BRIX ◽  
TOKE MEIER CARLSEN
Keyword(s):  
Conjugacy Class ◽  
Finite Type ◽  
Negative Answer ◽  
The Other ◽  
Completely Positive Map ◽  
Completely Positive ◽  
Positive Map ◽  
Shift Of Finite Type ◽  
Abelian Subalgebra ◽  
The One

AbstractA one-sided shift of finite type $(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines on the one hand a Cuntz–Krieger algebra ${\mathcal{O}}_{A}$ with a distinguished abelian subalgebra ${\mathcal{D}}_{A}$ and a certain completely positive map $\unicode[STIX]{x1D70F}_{A}$ on ${\mathcal{O}}_{A}$. On the other hand, $(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines a groupoid ${\mathcal{G}}_{A}$ together with a certain homomorphism $\unicode[STIX]{x1D716}_{A}$ on ${\mathcal{G}}_{A}$. We show that each of these two sets of data completely characterizes the one-sided conjugacy class of $\mathsf{X}_{A}$. This strengthens a result of Cuntz and Krieger. We also exhibit an example of two irreducible shifts of finite type which are eventually conjugate but not conjugate. This provides a negative answer to a question of Matsumoto of whether eventual conjugacy implies conjugacy.

scholarly journals Determination of hard X-ray polarization from two-dimensional images

2020 ◽  
Vol 53 (6) ◽  
pp. 1559-1561
Author(s):  
Robert B. Von Dreele ◽  
Wenqian Xu
Keyword(s):  
Incident Beam ◽  
Beam Polarization ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
The Difference ◽  
Two Dimensional Images

An estimate of synchrotron hard X-ray incident beam polarization is obtained by partial two-dimensional image masking followed by integration. With the correct polarization applied to each pixel in the image, the resulting one-dimensional pattern shows no discontinuities arising from the application of the mask. Minimization of the difference between the sums of the masked and unmasked powder patterns allows estimation of the polarization to ±0.001.

scholarly journals SEM characterization of two-dimensional patterns generated in titanium by femtosecond laser interferometry

2013 ◽  
Vol 19 (S4) ◽  
pp. 143-144
Author(s):  
V. Oliveira ◽  
N.I. Polushkin ◽  
O. Conde ◽  
R. Vilar
Keyword(s):  
Laser Radiation ◽  
Femtosecond Laser ◽  
Repetition Rate ◽  
Pulse Repetition Rate ◽  
Two Dimensional ◽  
Femtosecond Laser Radiation ◽  
Scanning Velocity ◽  
One Dimensional ◽  
Scanning Electron

Laser ablation using ultrafast femtosecond lasers and holographic schemes has proven to be a powerful and versatile tool for surface and volume structuring. The principle of operation of this technique is simple: when two or more pulses overlap in time and space, an interference pattern is generated that can be used to create periodic surface structures. In addition, due to the extremely short pulse duration, a very high peak power is achieved leading to intense non-linear effects. As a result, almost any type of material can be processed without undesirable collateral thermal effects.In this paper, characterization of two-dimensional (2D) patterns generated in titanium using femtosecond laser radiation has been carried out using scanning electron microscopy (SEM). The laser source is a commercial Yb:KYW laser system providing pulses with a duration of 560 fs at a central wavelength of >= 1030 nm. The surface topography was characterized using a Hitachi S2400 scanning electron microscope operated at an electron acceleration voltage of 25.0 kV. Laser processing was performed in air on polished grade 2 titanium samples, a material typically used in low load bearing medical devices.One-dimensional (1D) gratings were created using a modified Michelson interferometer described in detail elsewhere (Oliveira et al., 2012). To create 2D gratings a double exposure method was used. First, 1D gratings were produced in linear tracks by translating the sample relatively to the stationary interfering laser beams with a fixed scanning velocity of 0.1 mm/s. As an example, Figure 1 depicts SEM pictures of horizontal and vertical 1D gratings with period of about 3.9 m, generated using a pulse energy and pulse repetition rate of 0.35 mJ and 100 Hz, respectively. The peak to valley distance of these patterns can be controlled either by changing the scanning velocity or the pulse repetition rate. By overlapping two linear tracks, different kinds of 2D structures can be created. Figure 2 depicts a square pattern obtained by overlapping two 1D gratings rotated by 90°. The dimensions of the squares depend on the one-dimensional gratings period, which in turn can be easily controlled by varying the distance between the interfering beams. Figure 3 depicts two other possibilities: i) trapezium-like patterns obtained by rotating the 1D gratings by 45°, and ii) rectangular patterns obtained using 1D gratings with different periods and rotated by 90°.The proposed optical setup offers a simple method of texturing the surface of materials and, hence, to control surface properties such as wettability. In the case of titanium, this is particularly important because surface texturing enhances its osseointegration ability. For this purpose, when compared with the columns spontaneously formed on titanium surfaces treated with femtosecond laser radiation, these 2D gratings present the major advantage of being size and shape-controllable.

One- and two-dimensional PbII compounds resulting from reaction of PbBr2 and Pb(SCN)2 with pyrimidine-2-thione

2021 ◽  
Vol 77 (7) ◽  
Author(s):  
Vânia Denise Schwade ◽  
Bárbara Tirloni
Keyword(s):  
Structural Characterization ◽  
Diffuse Reflectance ◽  
Tautomeric Form ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
One Dimensional ◽  
X Ray ◽  
Ft Ir ◽  
Compound Ii

Pyrimidine-2-thione (HSpym) reacts with lead(II) thiocyanate and lead(II) bromide in N,N-dimethylformamide (DMF) to form poly[(μ-isothiocyanato-κ2 N:S)(μ4-pyrimidine-2-thiolato-κ6 N 1,S:S:S:S,N 3)lead(II)], [Pb(C4H3N2S)(NCS)] n or [Pb(Spym)(NCS)] n , (I), and the polymeric one-dimensional (1D) compound catena-poly[[μ4-bromido-di-μ-bromido-(μ-pyrimidine-2-thiolato-κ3 N 1,S:S)(μ-pyrimidine-2-thione-κ3 N 1,S:S)dilead(II)] N,N-dimethylformamide monosolvate], {[Pb2Br3(C4H3N2S)(C4H4N2S)]·C3H7NO} n or {[Pb2Br3(Spym)(HSpym)]·DMF} n , (IIa), respectively. Poly[μ4-bromido-di-μ3-bromido-(μ-pyrimidine-2-thiolato-κ3 N 1,S:S)(μ-pyrimidine-2-thione-κ3 N 1,S:S)dilead(II)], [Pb2Br3(C4H3N2S)(C4H4N2S)] n or [Pb2Br3(Spym)(HSpym)] n , (IIb), could be obtained as a mixture with (IIa) when using a lesser amount of solvent. In the crystal structures of the pseudohalide/halide PbII stable compounds, coordination of anionic and neutral HSpym has been observed. Both Spym− (in the thiolate tautomeric form) and NCS− ligands were responsible for the two-dimensional (2D) arrangement in (I). The Br− ligands establish the 1D polymeric arrangement in (IIa). Eight-coordinated metal centres have been observed in both compounds, when considering the Pb...S and Pb...Br interactions. Both compounds were characterized by FT–IR and diffuse reflectance spectroscopies, as well as by powder X-ray diffraction. Compound (IIa) and its desolvated version (IIb) represent the first structurally characterized PbII compounds containing neutral HSpym and anionic Spym− ligands. After a prolonged time in solution, (IIa) is converted to another compound due to complete deprotonation of HSpym. The structural characterization of (I) and (II) suggests HSpym as a good candidate for the removal of PbII ions from solutions containing thiocyanate or bromide ions.

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