• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2095-2105
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• 2015

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.99-113
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• 2011

In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, $f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5{\sum\limits_{i=1}^4}f(x_i)$. Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.595-601
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• 1997

Let $C_d$ be the rational curve of degree d in $P_k ^3$ given parametrically by $x_0 = u^d, X_1 = u^{d - 1}t, X_2 = ut^{d - 1}, X_3 = t^d (d \geq 4)$. Then the defining ideal of $C_d$ can be minimally generated by d polynomials $F_1, F_2, \ldots, F_d$ such that $degF_1 = 2, degF_2 = \cdots = degF_d = d - 1$ and $C_d$ is a set-theoretically complete intersection on $F_2 = X_1^{d-1} - X_2X_0^{d-2}$ for every field k of characteristic p > 0. For the proofs we will use the notion of Grobner basis.

• The Journal of Natural Sciences
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• v.11 no.1
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• pp.15-17
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• 1999

Let {f(n)} be an increasing sequence such that f(n)>0 for each n and f(n)$\rightarrow$$\infty$. Let {X$_n$,n$\geq1$} be a sequence of pairwise independent random variables. In this paper we give sufficient conditions on {X$_n$,n$\geq1$} such that $sum_{i=1}^n$(X$_i$-EX$_i$)/f(n) converges to zero almost surely.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.889-906
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• 2020

In this article, we consider the uniqueness problem of the shift polynomials $f^n(z)(f^m(z)-1){\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$ and $f^n(z)(f(z)-1)^m{\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$, where f(z) is a transcendental entire function of finite order, cj (j = 1, 2, …, s) are distinct finite complex numbers and n(≥ 1), m(≥ 1), s and µj (j = 1, 2, …, s) are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238].

• Development and Reproduction
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• v.25 no.3
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• pp.193-197
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• 2021

In previous reports, bisphenol A (BPA) exposure affects reproductive function in Drosophila melanogaster females. To test the maternal effect of BPA exposure on fly reproductive function, F0 mothers were exposed to 0, 0.1, 1, and 10 mg/L of BPA and the fecundity in F1 and F2 generations were checked. In this experiment, 1 and 10 mg/L BPA significantly decreased the fecundity of F1 females. Moreover, 0.1 and 1 mg/L BPA substantially reduced egg production in the F2 generation. These results suggested that maternal exposure to BPA at enviromentally relavant concnetrations reduces reproductive function in Drosophila melanogaster females and that this effect is transgenerational.

• Korean Journal Plant Pathology
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• v.10 no.2
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• pp.129-135
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• 1994

Ninety-two isolates of Fusarium species were obtained from Chinese corn samples. The predominant Fusarium species isolated from corn seeds were F. moniliforme, F. proliferatum, F. oxysporum and F. subglutinans, and all 13 species were identified. Each isolate was grown on autoclaved wheat grains and wheat cultures were fed by twenty-one-day-old female rats for the toxicity test. Twenty-six out of 92 isolates caused the death accompanying feed refusal, severe weight loss, liver damage, and hemorrhages in the stomach and intestines. Of the toxigenic isolates, 17 isolates of F. moniliforme, 4 of F. oxysporum, 3 of F. proliferatum, and one of each F. sporotrichioides and unknown species were lethal to rats. The analyses of fumonisin B1 production of the 26 toxigenic Fusarium isolates were carried out by thin layer chromatography and high-performance liquid chromatography, and fumonisin B1 was confirmed by mass spectrometry. Fumonisin B1 was produced in wheat culture at levels ranging from 280 $\mu\textrm{g}$/g to 3,952 $\mu\textrm{g}$/g by all of toxigenic F. moniliforme and F. proliferatum, but by none of the other toxigenic Fusarium species. The present results suggest the high possibility of natural occurrence of fumonisin B1 in corn samples imported from China.

• BMB Reports
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• v.31 no.1
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• pp.44-47
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• 1998

Asymmetry amongst nucleotide binding sites of Escherichia coli $F_1$-ATPase was examined using $^{19}F$ NMR signal from fluorinated analogs of adenine nucleotides bound to nucleotide binding sites. ADP-$CF_2-{PO_3}^{2-}$ showed no inhibitory effect to $F_1$-ATPase. But ADP-CHF-${PO_3}^{2-}$ (racemic mixture) showed competitive inhibition of $F_1$-ATPase with $K_i$ of $60\;{\mu}m$. ADP-CHF-${PO_3}^{2-}$ shows only negligible binding to $EF_1$ in the absence of $Mg^2+$. With the addition of $Mg^2+$ to the medium, the $^{19}F$ resonance of free ADP-CHF-${PO_3}^{2-}$ disappeared and the new broad resonances appeared. Appearance of more than two new asymmetric resonances following the binding of ADP-CHF-${PO_3}^{2-}$ to $EF_1$ may indicate that at least one of the isomers showed split resonances. This may suggest that the region between ${\alpha}$-and ${\beta}$-phosphate of ADP-CHF-${PO_3}^{2-}$ which is bound to catalytic sites is experiencing a different environment at different sites.

• Bulletin of the Korean Chemical Society
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• v.8 no.4
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• pp.318-324
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• 1987

Experimental results for viscous flow of poly (${\gamma}$ -methyl L-glutamate) solutions have been published elsewhere. The data of $[{\eta}]^f / [{\eta}]^0$ are expressed by the following equation, $\frac{[{\eta}^f]}{[{\eta}^{\circ}]}=1-\frac{A}{\eta^\circ}{1-\frac{sin^{-1}[{\beta}_2(f/{\eta}_0)\;{e}xp\;(-c_2f^2/{\eta}_0^2kT)]}{{\beta}_2f/{\eta}_0}$ (A1) where $[{\eta}]^f\; and\; [{\eta} ]^0$ are the intrinsic viscosity at shear stress f and zero, respectively, $ A{\equiv}lim\limits_{C{\rightarrow}0}[(1/C)(X_2/{\alpha}_2)({\beta}_2/{\eta}_0)],{\eta}_0$ viscosity of the solvent, ${\beta}_2$ is the relaxation time of flow unit 2, $c_2$ is a constant related to the elasticity of flow unit 2. The theoretical derivation of Eq.(A1) is given in the text. The experimental curves of $[{\eta}]^f / [{\eta}]^0$ vs. log f are compared with the theoretical curves calculated from Eq.(A1) with good results. Eq.(A1) is also applied to non-biopolymeric solutions, and it was found that in the latter case $c_2 = 0.$ The reason for this is explained in the text. The problems related to non-Newtonian flows are discussed.