scholarly journals A smoothly bounded domain in a complex surface with a compact quotient

2002 ◽  
Vol 91 (1) ◽  
pp. 82 ◽  
Author(s):  
Wing Sum Cheung ◽  
Siqi Fu ◽  
Steven G. Krantz ◽  
Bun Wong
Keyword(s):  
Bounded Domain ◽  
Complex Surface ◽  
Compact Set ◽  
Bounded Domains ◽  
Complex Manifolds ◽  
Compact Sets ◽  
Compact Quotient ◽  
Hyperbolic Complex

We study the classification of smoothly bounded domains in complex manifolds that cover compact sets. We prove that a smoothly bounded domain in a hyperbolic complex surface that covers a compact set is either biholomorphic to the ball or covered by the bidisc.

scholarly journals On the construction of suitable weak solutions to the 3D Navier–Stokes equations in a bounded domain by an artificial compressibility method

2017 ◽  
Vol 20 (01) ◽  
pp. 1650064 ◽  
Author(s):  
Luigi C. Berselli ◽  
Stefano Spirito
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method

We prove that suitable weak solutions of 3D Navier–Stokes equations in bounded domains can be constructed by a particular type of artificial compressibility approximation.

A generalization of the Pompeiu mean-value theorem to compact sets

2019 ◽  
Vol 35 (2) ◽  
pp. 147-152
Author(s):  
LARISA CHEREGI ◽  
VICUTA NEAGOS ◽  
◽  
Keyword(s):  
Continuous Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Compact Set ◽  
Compact Sets

We generalize the Pompeiu mean-value theorem by replacing the graph of a continuous function with a compact set.

scholarly journals On classification of quasi-symmetric domains

1976 ◽  
Vol 62 ◽  
pp. 1-12 ◽  
Author(s):  
I. Satake
Keyword(s):  
Bounded Domain ◽  
Siegel Domain ◽  
The Third ◽  
Siegel Domains

The notion of “Siegel domains” was introduced by [8]. It was then shown that every homogeneous bounded domain is holomorphically equivalent to a Siegel domain (of the second kind) determined uniquely up to an affine isomorphism ([15], cf. also [2], [4], [9b]). In a recent note [10b], I have shown that among (homogeneous) Siegel domains the symmetric domains can be characterized by three conditions (i), (ii), (iii) on the data (U, V, Ω, F) defining the Siegel domain (see Theorem in § 2 of this paper). The class of homogeneous Siegel domains satisfying partial conditions (i), (ii), which we propose to call “quasi-symmetric”, seems to be of some interest, since for instance the fibers appearing in the expressions of symmetric domains as Siegel domains of the third kind fall in this class ([10b], [16]).

A Class of Spaces in Which Compact Sets are Finite

1981 ◽  
Vol 24 (3) ◽  
pp. 373-375 ◽  
Author(s):  
P. L. Sharma
Keyword(s):  
Hausdorff Space ◽  
Compact Set ◽  
Compact Sets

AbstractIt is shown that in a dense-in-itself Hausdorff space if every set having a dense interior is open, then every compact set is finite.

scholarly journals Spaces of Whitney Functions on Cantor-Type Sets

2002 ◽  
Vol 54 (2) ◽  
pp. 225-238 ◽  
Author(s):  
Bora Arslan ◽  
Alexander P. Goncharov ◽  
Mefharet Kocatepe
Keyword(s):  
Extension Property ◽  
Compact Set ◽  
Compact Sets ◽  
Whitney Functions ◽  
Type Sets

AbstractWe introduce the concept of logarithmic dimension of a compact set. In terms of this magnitude, the extension property and the diametral dimension of spaces Ɛ(K) can be described for Cantor-type compact sets.

ON THE TOPOLOGICAL CLASSIFICATION OF FRACTAL SQUARES

Fractals ◽  
2017 ◽  
Vol 25 (03) ◽  
pp. 1750028 ◽  
Author(s):  
FENG RAO ◽  
XIAOHUA WANG ◽  
SHENGYOU WEN
Keyword(s):  
Topological Classification ◽  
Compact Set ◽  
Nonempty Compact

A fractal square is a nonempty compact set in the plane satisfying [Formula: see text], where [Formula: see text] is an integer and [Formula: see text] is nonempty. We give the topological classification of fractal squares with [Formula: see text] and [Formula: see text].

Defect Inspection and Classification of CFRP with Complex Surface by Ultrasonic

2011 ◽  
Vol 213 ◽  
pp. 297-301
Author(s):  
Xiong Bing Li ◽  
Hong Wei Hu ◽  
Ling Li ◽  
Lin Jin Tong
Keyword(s):  
Complex Surface ◽  
Ultrasonic Measurement ◽  
Cad Model ◽  
Automatic Inspection ◽  
Ultrasonic Technique ◽  
Defect Inspection ◽  
Wave Data ◽  
Defect Position ◽  
Surface Data

In this paper, we address the problem of automatic inspection of CFRP with complex surface using an ultrasonic technique. The 3D surface data are obtained by ultrasonic measurement, and then the inspection path is planned after the CAD model has been reconstructed. Defect position and size are figured out by analyzing C-Scan image. Characters of defect type are modeling according to A-wave data. Thereafter, an algorithm based on Multi-SVM is presented to classify defect types which use the energy character of defect dynamic waveform. Finally, application experiments are conducted to verify the validity and superiority of the method proposed in this paper.

Affine compact almost-homogeneous manifolds of cohomogeneity one

2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Daniel Guan
Keyword(s):  
Einstein Metrics ◽  
Compact Manifolds ◽  
Complex Manifolds ◽  
Homogeneous Manifolds ◽  
Einstein Manifolds ◽  
Extremal Metrics ◽  
Cohomogeneity One ◽  
Fano Manifolds ◽  
Kähler Einstein Metrics

AbstractThis paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.

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