• Title/Summary/Keyword: Gruss

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SOME NEW RESULTS RELATED TO BESSEL AND GRUSS INEQUALITIES IN 2-INNER PRODUCT SPACES AND APPLICATIONS

  • DRAGOMIR S.S.;CHO, Y.J.;KIM, S.S.
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.591-608
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    • 2005

  • Some new reverses of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces are pointed out. Applications for some Gruss type inequalities and for determinantal integral inequalities are given as well.

  • https://doi.org/10.4134/BKMS.2005.42.3.591 인용 PDF KSCI

ON SOME INEQUALITIES FOR THE EXPECTATION AND VARIANCE

  • Cerone, P.;Dragomir, S.S.
    • Journal of applied mathematics & informatics
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    • v.8 no.2
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    • pp.449-472
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    • 2001

  • A variety bounds are obtained for the variance and expectation of a continuous random variable whose p.d.f. is defined over a finite interval. Previous results are shown to be particular cases of the current more general development.

A Study on the Indexes and Properties of Mechanical Weathering to Granite Distributed in Korea (화강암의 풍화산물에 대한 기계적 풍화지수의 특성에 관한 연구)

  • Rheem, Chong-Ho
    • Journal of the Korean Geographical Society
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    • v.28 no.2
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    • pp.99-111
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    • 1993

  • The transformation of rocks into unconsoli-dated debris is the prime geomorphic processes including weathering and soil forming process. In these processes, rocks tend to be unconsol-idated debris with small particles. Particularly, typical granite is more likely affected by weathering, since the rock consists of quartz, feldspar and mica that can be easily coarse-grained and well jointed without bedding. The purposes of this study are to clarify the index and properties of mechanical weathering that contributed to transformation of granite distributed in Korea. A total of seventy-three samples of weathering products of granite in Korea were collected during the three-year period, March 30, 1989 to February 21, 1992. The prticle analysis was performed for clay, silt and sand using Sieve and Hydrometer. The results of the analysis are as the followings: First, soil textures in the study area are included seven categories of textures as C, CL, SCL, Sil, SL, LS, and S. Among these textures, the most frequent soil texture were SL, S and SCL in order. Second, the weathering products of granite are crumbled by weathering and hydrothermal. Clay texture consisted of fine materials seems to be influenced by hydrothermal, while Sand texture composed of coarse materials, seems to be significantly influenced by weathering. Third, the index of mechanical weathering by region indicates that Hawngdeung(1) is the lowest as 2.37 and the index by soil texture shows that Clay texture is the lowest as 2.46. Forth, the regression analysis of MW showes that sand/clay variable is the most significant variable. Finally, pedochemical weathering is prevailed on the clayey gruss and geochemical weathering is on the gruss and shattering is on the weathered rock, strongly, but the fine materials in some sites were formed by argillation of hydrothermal.

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