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Arithmetic functions in algebra, geometry and analysis
J. Sandor,E. Egri 장전수학회 2007 Advanced Studies in Contemporary Mathematics Vol.14 No.2
This is a survey paper on certain classical or new arithmetic functions with connections and/or applications in Algebra, Geometry or Analysis. We want to show the importance of certain parts of Number theory (especially, of arithmetical functions) to these major elds of Mathematics. The survey is focused especially on the author's results, and in the course of presentations, many new results (with proofs) will be pointed out, too.
Applications of the Cauchy-Bouniakowsky inequality in the theory of means
J. Sandor 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.2
We oer various inequalities for means, as applications of the classical integral inequality (∫<sup>a<sub>b f(x)g(x)dx)<sup>2 ≤ ((∫<sup>a<sub>b f<sup>2(x)dx) ((∫<sup>a<sub>b g<sup>2(x)dx).
ON CERTAIN IDENTITIES FOR MEANS, III
J. Sandor,E. Egri,R. Olah-Gal 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
We offer certain in¯nite series representations of general integral means. As applications, we can reobtain in an unitary way, many known or new identities for special means, thus continuing and complementing results from parts I and II (see [9], [12]). As corollaries, many inequalities involving means are pointed out.
On (m,n)-supper-perfect numbers
J. Sandor,K. Atanassov 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.16 No.1
Some properties and examples of a modication of the perfectnumbers are discussed.
On a modification of perfect number
J. Sandor,K. Atanassov 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.17 No.2
Some properties and examples of a modi¯cation of the perfect numbers are discussed.
Meusburger, K.,Mabit, L.,Park, J.-H.,Sandor, T.,Alewell, C. Copernicus GmbH 2013 Biogeosciences Vol.10 No.8
<P><p><strong>Abstract.</strong> The aim of this study is to assess and to validate the suitability of the stable nitrogen and carbon isotope signature as soil erosion indicators in a mountain forest site in South Korea. Our approach is based on the comparison of the isotope signature of 'stable' landscape positions (reference sites), which are neither affected by erosion nor deposition, with eroding sites. For undisturbed soils we expect that the enrichment of <i>δ</i><sup>15</sup>N and <i>δ</i><sup>13</sup>C with soil depth, due to fractionation during decomposition, goes in parallel with a decrease in nitrogen and carbon content. Soil erosion processes potentially weaken this correlation. The <sup>137</sup>Cs method and the Revised Universal Soil Loss Equation (RUSLE) were applied for the soil erosion quantification. Erosion rates obtained with the <sup>137</sup>Cs method range from 0.9 t ha<sup>−1</sup> yr<sup>−1</sup> to 7 t ha<sup>−1</sup> yr<sup>−1</sup>. Considering the steep slopes of up to 40° and the erosive monsoon events (R factor of 6600 MJ mm ha<sup>−1</sup> h<sup>−1</sup> yr <sup>&ndash;1</sup>), the rates are plausible and within the magnitude of the RUSLE-modeled soil erosion rates, varying from 0.02 t ha<sup>−1</sup> yr<sup>−1</sup> to 5.1 t ha<sup>−1</sup> yr<sup>−1</sup>. The soil profiles of the reference sites showed significant (<i>p</i> < 0.0001) correlations between nitrogen and carbon content and its corresponding <i>δ</i><sup>15</sup>N and <i>δ</i><sup>13</sup>C signatures. In contrast, for the eroding sites this relationship was weaker and for the carbon not significant. These results confirm the usefulness of the stable carbon isotope signature as a qualitative indicator for soil disturbance. We could show further that the <i>δ</i><sup>15</sup>N isotope signature can be used similarly for uncultivated sites. We thus propose that the stable <i>δ</i><sup>15</sup>N and <i>δ</i><sup>13</sup>C signature of soil profiles could serve as additional indicators confirming the accurate choice of the reference site in soil erosion studies using the <sup>137</sup>Cs method.</p> </P>
Use of a Multiethnic Approach to Identify Rheumatoid- Arthritis-Susceptibility Loci, 1p36 and 17q12
CLEAR investigators,Kurreeman, Fina A.S.,Stahl, Eli A.,Okada, Y.,Liao, K.,Diogo, D.,Raychaudhuri, S.,Freudenberg, J.,Kochi, Y.,Patsopoulos, Nikolaos A.,Gupta, N.,Sandor, C.,Bang, S.Y.,Lee, H.S.,Padyuk University of Chicago Press [etc.] 2012 American journal of human genetics Vol.90 No.3
We have previously shown that rheumatoid arthritis (RA) risk alleles overlap between different ethnic groups. Here, we utilize a multiethnic approach to show that we can effectively discover RA risk alleles. Thirteen putatively associated SNPs that had not yet exceeded genome-wide significance (p < 5 x 10<SUP>-8</SUP>) in our previous RA genome-wide association study (GWAS) were analyzed in independent sample sets consisting of 4,366 cases and 17,765 controls of European, African American, and East Asian ancestry. Additionally, we conducted an overall association test across all 65,833 samples (a GWAS meta-analysis plus the replication samples). Of the 13 SNPs investigated, four were significantly below the study-wide Bonferroni corrected p value threshold (p < 0.0038) in the replication samples. Two SNPs (rs3890745 at the 1p36 locus [p = 2.3 x 10<SUP>-12</SUP>] and rs2872507 at the 17q12 locus [p = 1.7 x 10<SUP>-9</SUP>]) surpassed genome-wide significance in all 16,659 RA cases and 49,174 controls combined. We used available GWAS data to fine map these two loci in Europeans and East Asians, and we found that the same allele conferred risk in both ethnic groups. A series of bioinformatic analyses identified TNFRSF14-MMEL1 at the 1p36 locus and IKZF3-ORMDL3-GSDMB at the 17q12 locus as the genes most likely associated with RA. These findings demonstrate empirically that a multiethnic approach is an effective strategy for discovering RA risk loci, and they suggest that combining GWASs across ethnic groups represents an efficient strategy for gaining statistical power.