Asymptotic Behaviour of the Conformal Representation of a Jordan Domain with a Small Hole in Schauder Spaces

2003 ◽  
Vol 2 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Massimo Lanza de Cristoforis
Keyword(s):  
Asymptotic Behaviour ◽  
Jordan Domain ◽  
Small Hole ◽  
Conformal Representation

scholarly journals Escape rates for Gibbs measures

2011 ◽  
Vol 32 (3) ◽  
pp. 961-988 ◽  
Author(s):  
ANDREW FERGUSON ◽  
MARK POLLICOTT
Keyword(s):  
Hausdorff Dimension ◽  
Asymptotic Behaviour ◽  
Gibbs Measure ◽  
Gibbs Measures ◽  
Small Hole ◽  
Escape Rate ◽  
Conformal Repeller

AbstractIn this paper we study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of the Hausdorff dimension of the survivor set.

Advanced TEM sample preparation techniques for submicron Si devices

1995 ◽  
Vol 53 ◽  
pp. 516-517 ◽  
Author(s):  
P. B. Basham ◽  
H. L. Tsai
Keyword(s):  
Sample Preparation ◽  
Process Development ◽  
Light Transmission ◽  
Specific Area ◽  
Turnaround Time ◽  
Small Hole ◽  
Area Of Interest ◽  
Transmission Electron ◽  
Polished Side ◽  
Preparation Techniques

The use of transmission electron microscopy (TEM) to support process development of advanced microelectronic devices is often challenged by a large amount of samples submitted from wafer fabrication areas and specific-spot analysis. Improving the TEM sample preparation techniques for a fast turnaround time is critical in order to provide a timely support for customers and improve the utilization of TEM. For the specific-area sample preparation, a technique which can be easily prepared with the least amount of effort is preferred. For these reasons, we have developed several techniques which have greatly facilitated the TEM sample preparation.For specific-area analysis, the use of a copper grid with a small hole is found to be very useful. With this small-hole grid technique, TEM sample preparation can be proceeded by well-established conventional methods. The sample is first polished to the area of interest, which is then carefully positioned inside the hole. This polished side is placed against the grid by epoxy Fig. 1 is an optical image of a TEM cross-section after dimpling to light transmission.

Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 545-556 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Probabilistic Interpretation ◽  
Stationary Markov Chain

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

scholarly journals Asymptotic behaviour of ground state solutions for the fractional Hénon equation

2021 ◽  
pp. 125456
Author(s):  
Haixia Chen ◽  
Xiaolin Xu ◽  
Xiaolong Yang
Keyword(s):  
Asymptotic Behaviour ◽  
Ground State ◽  
Ground State Solutions ◽  
Hénon Equation

scholarly journals Analysis of Multi-Physics Coupling of Small Holes in GH4169 Alloy by Electrolytic Processing of Tube Electrodes

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 828
Author(s):  
Zhaolong Li ◽  
Ye Dai
Keyword(s):  
Oxide Layer ◽  
Small Hole ◽  
Machining Accuracy ◽  
Tool Electrode ◽  
Metallic Oxide ◽  
Power Sources ◽  
Processing Stability ◽  
Hole Structure ◽  
Gh4169 Alloy ◽  
Small Holes

This paper presents a simulation and experimental study of the structure of small holes in GH4169 alloy electrolytic ally processed by tube electrodes with different characteristic power sources. It analyzes the multi-physical field coupling relationship of flow, temperature, and electric fields within the interstitial space. The results indicate that the tube electrode electrolytic processing of the GH4169 alloy small hole structure with a pulsed power supply has more uniform temperature and current density distribution within the gap, which is beneficial to the processing accuracy and smoothness of the small hole structure. Meanwhile, SEM was used to analyze the microscopic morphology of the electrode end surface during short-circuiting, and it was concluded that as the processing continued, the electrode end surface gradually produced a non-metallic oxide layer, which destroyed the electric field of the gap and affected the processing stability. The use of high-frequency positive and negative pulse power can effectively avoid the generation of a non-metallic oxide layer. Through the combination of simulation analysis and experimental verification, it is concluded that increasing electrolyte pressure in stages can effectively improve machining accuracy and stability. The interstitial current increases as the feed rate of the tool electrode increases, and the diameter of the machined small hole decreases as it increases.

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

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