Conditions for a limit set to be a singleton

1985 ◽  
pp. 35-41 ◽  
Author(s):  
Bernd Aulbach
Keyword(s):  
Limit Set

Compositional Analysis of III-V Interface Lattice Images

1980 ◽  
Vol 38 ◽  
pp. 318-319
Author(s):  
A. Olsen ◽  
J.C.H. Spence ◽  
P. Petroff
Keyword(s):  
Crystal Structure ◽  
Image Matching ◽  
Compositional Analysis ◽  
Depth Of Field ◽  
Limit Set ◽  
High Contrast ◽  
Resolution Limit ◽  
Fourier Image ◽  
Lattice Images ◽  
True Structure

Since the point resolution of the JEOL 200CX electron microscope is up = 2.6Å it is not possible to obtain a true structure image of any of the III-V or elemental semiconductors with this machine. Since the information resolution limit set by electronic instability (1) u0 = (2/πλΔ)½ = 1.4Å for Δ = 50Å, it is however possible to obtain, by choice of focus and thickness, clear lattice images both resembling (see figure 2(b)), and not resembling, the true crystal structure (see (2) for an example of a Fourier image which is structurally incorrect). The crucial difficulty in using the information between Up and u0 is the fractional accuracy with which Af and Cs must be determined, and these accuracies Δff/4Δf = (2λu2Δf)-1 and ΔCS/CS = (λ3u4Cs)-1 (for a π/4 phase change, Δff the Fourier image period) are strongly dependent on spatial frequency u. Note that ΔCs(up)/Cs ≈ 10%, independent of CS and λ. Note also that the number n of identical high contrast spurious Fourier images within the depth of field Δz = (αu)-1 (α beam divergence) decreases with increasing high voltage, since n = 2Δz/Δff = θ/α = λu/α (θ the scattering angle). Thus image matching becomes easier in semiconductors at higher voltage because there are fewer high contrast identical images in any focal series.

Influence of Applied Phytosanitary Treatments and Climatic Crop Year on Zinc Content in Wines from Tohani Vineyard

2017 ◽  
Vol 68 (9) ◽  
pp. 2092-2097
Author(s):  
Catalina Calin ◽  
Gina Vasile Scaeteanu ◽  
Roxana Maria Madjar ◽  
Otilia Cangea
Keyword(s):  
Zinc Content ◽  
Soil Samples ◽  
Limit Set ◽  
Red Wines ◽  
Metallic Ions ◽  
Sauvignon Blanc ◽  
Before And After ◽  
Haze Formation ◽  
Zinc Levels ◽  
Concentration Levels

Metallic ions present a great importance in oenological practice and usually are present in wines in levels that are not hazardous. Among all metallic ions, zinc presents a great interest because may cause the persistence of the wine sour taste and by the side of Al, Cu, Fe and Ni, contribute to the haze formation and the change of color. The present study was focused on measuring the concentration levels of mobile zinc from vineyard soil before and after phytosanitary treatments and zinc content from white (Feteasca Alba - FA, Riesling Italian - RI, Sauvignon Blanc - SB, Tamaioasa Rom�neasca - TR), rose (Busuioaca de Bohotin - BB) and red (Feteasca Neagra - FN) wines within the wine-growing Tohani area, Romania. Other objective was to investigate of the influence of crop year and variety on zinc levels found in wine samples. Mobile zinc content for all analyzed soil samples is low ([1.5 mg/kg). Analyses indicated that zinc content found in wines was below 5 mg/L, limit set by Organisation Internationale of Vine and Wine (OIV). Also, it was found that red wines contain zinc in higher concentrations than white ones.

Limit set trichotomy and dichotomy for skew-product semiflows with applications

2009 ◽  
Vol 71 (7-8) ◽  
pp. 2834-2839
Author(s):  
Bin-Guo Wang ◽  
Wan-Tong Li
Keyword(s):  
Limit Set ◽  
Skew Product ◽  
Limit Set Trichotomy

scholarly journals A non-Borel special alpha-limit set in the square

2021 ◽  
pp. 1-11
Author(s):  
STEPHEN JACKSON ◽  
BILL MANCE ◽  
SAMUEL ROTH
Keyword(s):  
Dynamical Systems ◽  
Limit Set ◽  
Limit Sets ◽  
Unit Square

Abstract We consider the complexity of special $\alpha $ -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necessarily Borel, even in the case of a surjective map on the unit square. This answers a question posed by Kolyada, Misiurewicz, and Snoha.

scholarly journals Graph directed Markov systems on Hilbert spaces

2009 ◽  
Vol 147 (2) ◽  
pp. 455-488 ◽  
Author(s):  
R. D. MAULDIN ◽  
T. SZAREK ◽  
M. URBAŃSKI
Keyword(s):  
Hausdorff Measure ◽  
Iterated Function System ◽  
Sufficient Conditions ◽  
Topological Pressure ◽  
Limit Set ◽  
Covering Theorem ◽  
Limit Sets ◽  
Markov Systems ◽  
Polish Spaces ◽  
Iterated Function

AbstractWe deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient conditions are provided for the closure of limit sets to be compact, connected, or locally connected. Conformal measures, topological pressure, and Bowen's formula (determining the Hausdorff dimension of limit sets in dynamical terms) are introduced and established. We show that, unlike the Euclidean case, the Hausdorff measure of the limit set of a finite iterated function system may vanish. Investigating this issue in greater detail, we introduce the concept of geometrically perfect measures and provide sufficient conditions for geometric perfectness. Geometrical perfectness guarantees the Hausdorff measure of the limit set to be positive. As a by–product of the mainstream of our investigations we prove a 4r–covering theorem for all metric spaces. It enables us to establish appropriate co–Frostman type theorems.

scholarly journals Non-Homogeneous Markov Set Systems

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 471
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Asymptotic Behavior ◽  
Population Structure ◽  
Confidence Intervals ◽  
Limit Set ◽  
Stroke Patients ◽  
Relative Population ◽  
Set Systems ◽  
Population Structures ◽  
Basic Parameters ◽  
Initial Distributions

A more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (NHMS) processes for which the required basic parameters are in intervals. We call such processes Non-Homogeneous Markov Set Systems (NHMSS). First we study the set of the relative expected population structure of memberships and we prove that under certain conditions of convexity of the intervals of the parameters the set is compact and convex. Next, we establish that if the NHMSS starts with two different initial distributions sets and allocation probability sets under certain conditions, asymptotically the two expected relative population structures coincide geometrically fast. We continue proving a series of theorems on the asymptotic behavior of the expected relative population structure of a NHMSS and the properties of their limit set. Finally, we present an application for geriatric and stroke patients in a hospital and through it we solve problems that surface in an application.

scholarly journals Free vs. locally free Kleinian groups

2019 ◽  
Vol 2019 (746) ◽  
pp. 149-170
Author(s):  
Pekka Pankka ◽  
Juan Souto
Keyword(s):  
Hausdorff Dimension ◽  
Kleinian Group ◽  
Cantor Set ◽  
Cantor Sets ◽  
Kleinian Groups ◽  
The Other ◽  
Limit Set ◽  
Limit Sets ◽  
Other Hand

Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < 1 are free. On the other hand we construct for any ε > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < 1 + ε.

scholarly journals Equilibrium measures for the Hénon map at the first bifurcation: uniqueness and geometric/statistical properties

2014 ◽  
Vol 36 (1) ◽  
pp. 215-255 ◽  
Author(s):  
SAMUEL SENTI ◽  
HIROKI TAKAHASI
Keyword(s):  
Existence And Uniqueness ◽  
Thermodynamic Formalism ◽  
Invariant Probability Measure ◽  
Statistical Properties ◽  
Limit Set ◽  
Bifurcation Parameter ◽  
Large Interval ◽  
Equilibrium Measures ◽  
Uniform Hyperbolicity ◽  
Unstable Direction

For strongly dissipative Hénon maps at the first bifurcation parameter where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we establish a thermodynamic formalism, i.e. we prove the existence and uniqueness of an invariant probability measure that minimizes the free energy associated with a non-continuous geometric potential$-t\log J^{u}$, where$t\in \mathbb{R}$is in a certain large interval and$J^{u}$denotes the Jacobian in the unstable direction. We obtain geometric and statistical properties of these measures.

On the Limit Set in the Law of the Iterated Logarithm for U-statistics of Order Two

2004 ◽  
pp. 111-126
Author(s):  
Stanislaw Kwapień ◽  
Rafał Latała ◽  
Krzysztof Oleszkiewicz ◽  
Joel Zinn
Keyword(s):  
Limit Set ◽  
U Statistics ◽  
Iterated Logarithm ◽  
The Law

scholarly journals INVESTIGATION ON THE ENVIROMENTAL EFFECT OF LOCAL PRODUCTION METHOD OF ALUMINIUM UTENSIL IN KANO

2020 ◽  
Vol 4 (3) ◽  
pp. 256-262
Author(s):  
Y. I. Yakubu ◽  
I. A. Yola
Keyword(s):  
Heavy Metals ◽  
Water Samples ◽  
Production Method ◽  
Soil Samples ◽  
Permissible Limit ◽  
Limit Set ◽  
Local Production ◽  
Two Samples ◽  
S Model ◽  
Concentration Levels

This research investigated the environmental effect of local production methods of aluminium utensils in Bachirawa, Ungogo local government Kano. Three soil samples and two samples of water were collected from sites A, B,C, D and E. The samples were then taken to faculty of agriculture for analysis. Atomic absorption spectrophotometer (A A S model No 240 FSAA) was used to determine the concentration levels of heavy metals in the samples. The results show that, the concentration levels of  heavy metals in the soil samples A, B and C are:  Zn ranges between  (1158.13 - 11,117.80)  mg/kg; Mn  between  (285.719 – 1809.672) mg/kg; Cd between (0.026 – 0.540) mg/kg; Cr (0.498 – 0.832) mg/kg and Pb between (42.54 - 285.53) mg/kg. The observed concentration levels in water samples for Zn ranges between (0.2411 – 0.4435)mg/l; Cd between (0.091 – 0.123) mg/l; Cr between (0.015 – 0.022) mg/l; Mn between (0.284 – 0.728) mg/l and Pb between (0.00-0.08) mg/l. Zinc and Manganese have higher concentration levels than the recommended  permissible limit set by European Union (EU) and  United Kingdom(UK)  while Cd, Cr and  Pb have lower concentration levels than the recommended permissible limit set by EU and UK in soil samples  A, B and C. The concentration levels of Mn, Cd and Pb in water samples were higher than the permissible limit set by World Healh Organization (WHO) whereas Zn and Cr have concentrations lower than the recommended permissible limit set by 

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