Relative Compactness | ScienceGate

Abstract In this paper we formulate a criterion for relative compactness in the space of functions regulated on a bounded and closed interval. We prove that the mentioned criterion is equivalent to a known criterion obtained earlier by D. Fraňkova, but it turns out to be very convenient in applications. Among others, it creates the basis to construct a regular measure of noncompactness in the space of regulated functions. We show the applicability of the constructed measure of noncompactness in proving the existence of solutions of a quadratic Hammerstein integral equation in the space of regulated functions.

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Experimental Study of Effects of Operation Parameters on Efficiency of Vibratory Pile Driving

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.580-583.2272 ◽

2014 ◽

Vol 580-583 ◽

pp. 2272-2276 ◽

Cited By ~ 1

Author(s):

Hui Ping Zheng ◽

Lin Chen ◽

Wei Wang ◽

Li Qiang Peng ◽

Jia Yu Zhang

Keyword(s):

Soil Samples ◽

Exciting Force ◽

Pile Driving ◽

Signal Acquisition ◽

Test Bed ◽

Relative Compactness ◽

Exciting Frequency ◽

Common Application ◽

Vibratory Pile Driving ◽

Sample Time

Vibratory pile driving is a common application method of piles foundation construction. A test bed was designed and built according to the principle of vibratory pile driving. The test bed is composed of excitation system, machinery parts and signal acquisition system. At first soil samples with different relative compactness and different saturation were made. Then tests of vibratory pile driving have been done by using the soil samples and the test bed. For each soil sample, time of pile sinking to the bottom of the container was recorded respectively under the condition of the exciting force with same amplitude. The time represents efficiency of vibratory pile driving. The former is shorter and the latter is higher. Relationships between efficiency of vibratory pile driving and exciting frequency, relative compactness of soil, saturation of soil were researched respectively by single factor method. The experimental results have guide meaning to vibratory pile driving construction.

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Relative compactness in L-fuzzy topological spaces

Fuzzy Sets and Systems ◽

10.1016/s0165-0114(98)00110-9 ◽

2000 ◽

Vol 116 (3) ◽

pp. 311-316 ◽

Cited By ~ 5

Author(s):

H. Aygün ◽

S.R.T. Kudri ◽

M.W. Warner

Keyword(s):

Topological Spaces ◽

Relative Compactness ◽

Fuzzy Topological Spaces

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On compactness results for multi-scale convergence

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500021466 ◽

1999 ◽

Vol 129 (3) ◽

pp. 467-476 ◽

Cited By ~ 1

Author(s):

Erik J. Balder

Keyword(s):

Sobolev Space ◽

Image Space ◽

Orthogonal Complement ◽

Young Measures ◽

Type Result ◽

Compactness Result ◽

Relative Compactness ◽

Multi Scale ◽

Free Fields ◽

Extension Result

Two relative compactness results for two-scale convergence in homogenization, due to G. Nguetseng, were recently extended to the multi-scale case by G. Allaire and M. Briane. Whereas their extension of Nguetseng's first result, which is in L2, is straightforward, their extension of his second result, which takes place in the Sobolev space H1, is quite complicated, even though it follows Nguetseng by using the fact that the image of H1 under the gradient mapping is the orthogonal complement of the set of divergence-free functions. Here a much simpler proof is provided by deriving the H1-type result from combining the first extension result with the fact that the above-mentioned image space is also the space of all rotation-free fields. Moreover, this approach reveals that the two results can be seen as corollaries of a fundamental relative compactness result for Young measures.

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