• East Asian mathematical journal
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• 제21권1호
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• pp.77-103
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• 2005

The theory of multiple Gamma functions was studied in about 1900 and has, recently, been revived in the study of determinants of Laplacians. There is a class of mathematical constants involved naturally in the multiple Gamma functions. Here we summarize those mathematical constants associated with the Gamma and multiple Gamma functions and will show how they are involved, if possible.

• International Journal of Industrial Entomology and Biomaterials
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• 제6권2호
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• pp.139-143
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• 2003

Mathematical constants for multiplication with leaf length (I) or breadth (b) or l ${\times}$ b have been worked out for determining leaf area in promising mulberry genotypes viz., Chinese White, S-146, Chak Majra and Sujanpur Local of sub-tropical India. When pooled, the mathematical constants worked out were 8.1132, 10.1019 and 0.5992 for multiplication with leaf length, breadth and l ${\times}$ b, respectively, for genotypes bearing un-lobbed leaves and 6.9447, 8.2761 and 0.5009 for multiplication with leaf length, breadth and l ${\times}$ b, respectively for genotypes bearing lobbed leaves. Leaf area can be worked out by using any constant by multiplying either with leaf length or breadth or both (l ${\times}$ b). Estimated leaf areas worked out were found significantly and positively correlated with actual leaf area (r＝999$^{＊＊}$). The suggested present non-destructive method by using mathematical constants is very quick and alternative to electronic leaf area meter for spot leaf area determination in mulberry which is the only food source for mulberry silkworm in sericulture industry.

• 대한수학회보
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• 제56권6호
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• pp.1569-1575
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• 2019

In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness of the associated spaces. We obtain that the three constants are the same as those for $L^1$ and $L^{\infty}$ spaces.

• 충청수학회지
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• 제22권2호
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• pp.287-291
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• 2009

A comparison of constants is given to show that a better constant for the Sobolev trace inequality can be obtained from the conjectured extremal function.

• 대한수학회논문집
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• 제13권4호
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• pp.735-741
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• 1998

In this paper we will derive some new properties of q-extensions of p-adic gamma functions and p-adic Euler constants.

• East Asian mathematical journal
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• 제31권1호
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• pp.41-53
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• 2015

A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) ${\gamma}_k$ and the generalized Stieltjes constants ${\gamma}_k(a)$ have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants ${\gamma}_k(a)$ by choosing to use four known integral representations for the generalized zeta function ${\zeta}(s,a)$. As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants ${\gamma}_k$. Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.

• 대한수학회논문집
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• 제35권2호
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• pp.565-570
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• 2020

We investigate the best equivalence constants for the 𝑙_p-norms and the 𝑙_q-symmetric multilinear operator norms of vectors in ℂⁿ which are induced by symmetric n-linear forms. In this paper, we provides estimates which are either best possible or close to best possible.

• 대한수학회논문집
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• 제29권3호
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• pp.421-428
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• 2014

We explicitly calculate the polarization and unconditional constants of $\mathcal{P}(^2d_*(1,{\omega})^2)$.

• 대한수학회논문집
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• 제10권2호
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• pp.401-407
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• 1995

The best constants for two distinct weak-type inequalities for martingales and their differential subordinates with values in some spaces isomorphic to a Hilbert space are shown to be the same. This extends the result of Burkholder shown in the Hilbert space setting.

• 대한수학회보
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• 제54권5호
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• pp.1677-1697
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• 2017

The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely determine the limiting Okounkov bodies on such surfaces, and give applications to Nakayama constants and Seshadri constants. Secondly, we study how the shapes of Okounkov bodies change as we vary the divisors in the big cone.