• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.745-762
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• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.1
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• pp.188-198
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• 2005

The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Asian-Australasian Journal of Animal Sciences
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• v.29 no.4
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• pp.487-499
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• 2016

The aim of the present study was to examine the effects of testosterone (T) and estradiol-$17{\beta}$ ($E_2$) on the production of progesterone ($P_4$) by granulosa cells, and of the $E_2$ on the production of $P_4$ and T by theca internal cells. In the first experiment, granulosa cells isolated from the largest ($F_1$) and third largest ($F_3$) preovulatory follicle were incubated for 4 h in short-term culture system, $P_4$ production by granulosa cells of both $F_1$ and $F_3$ was increased in a dose-dependent manner by ovine luteinizing hormone (oLH), but not T or $E_2$. In the second experiment, $F_1$ and $F_3$ granulosa cells cultured for 48 h in the developed monolayer culture system were recultured for an additional 48 h with increasing doses of various physiological active substances existing in the ovary, including T and $E_2$. Basal $P_4$ production for 48 h during 48 to 96 h of the cultured was about nine fold greater by $F_1$ granulosa cells than by $F_3$ granulosa cells. In substances examined oLH, chicken vasoactive intestinal polypeptide (cVIP) and T, but not $E_2$, stimulated in a dose-dependent manner $P_4$ production in both $F_1$ and $F_3$ granulosa cells. In addition, when the time course of $P_4$ production by $F_1$ granulosa cells in response to oLH, cVIP, T and $E_2$ was examined for 48 h during 48 to 96 h of culture, although $E_2$ had no effect on $P_4$ production by granulosa cells of $F_1$ during the period from 48 to 96 h of culture, $P_4$ production with oLH was found to be increased at 4 h of the culture, with a maximal 9.14 fold level at 6 h. By contrast, $P_4$ production with cVIP and T increased significantly (p<0.05) from 8 and 12 h of the culture, respectively, with maximal 6.50 fold response at 12 h and 6, 48 fold responses at 36 h. Furthermore, when $F_1$ granulosa cells were precultured with $E_2$ for various times before 4 h culture with oLH at 96 h of culture, the increase in $P_4$ production in response to oLH with a dose-related manner was only found at a pretreatment time of more than 12 h. In the third experiment, theca internal cells of $F_1$, $F_2$ and the largest third to fifth preovulatory follicles ($F_{3-5}$) were incubated for 4 h in short-term culture system with increasing doses of $E_2$. The production of $P_4$ and T by theca internal cells were increased with the addition of $E_2$ of $10^{-6}M$. These increases were greater in smaller follicles. These results indicate that, in granulosa cells of the hen, T may have a direct stimulatory action in the long term on $P_4$ production, and on $E_2$ in long-term action which may enhance the sensitivity to LH for $P_4$ production, and thus, in theca internal cells, $E_2$ in short term action may stimulate the production of $P_4$ and T.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.473-481
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• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Animal cells and systems
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• v.5 no.1
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• pp.59-64
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• 2001

To understand the late gut development and differentiation, identification and characterization of target genes of homeotic genes involved in gut development are required. We have previously reported that homeodomain proteins can regulate expression of the cell proliferation-related genes. We investigated here the expression of the Drosophila proliferating cell nuclear antigen(PCNA) and E2F(dE2F) genes in larval and adult guts using transgenic flies bearing lacz reporter genes. Both PCNA and dE2F genes were expressed strongly in whole regions of the larval and adult guts including the esophagus, proventriculus, midgut and hindgut, showing higher expression in foregut and hindgut imaginal rings of larva. Nitric Oxide(NO) has been known to be involved in cell proliferation and tumor growth and also to have an antiproliferative activity. Therefore, we also investigated effects of NO on the expression of PCNA and dE2F genes in gut through analyses of lacz reporter expression level in the SNP (NO donor)-treated larval guts. Expressions of both PCNA and dE2F were greatly declined by SNP. The inhibitory effect of NO was shown in whole regions of the gut, especially in hindgut, while the internal region of proventriculus, esophagus, foregut imaginal ring and hindgut imaginal ring was resistant. Our results suggest that this inhibitory effect may be related with the antiproliferative activity of NO.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.87-97
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• 2024

For any fixed integers k, l with kl(l - 1) ≠ 0, we establish the generalized Hyers-Ulam stability of an Euler-Lagrange quadratic functional equation f(kx + ly) + f(kx - ly) + 2(l - 1)[k²f(x) - lf(y)] = l[f(kx + y) + f(kx - y)] in normed spaces and in non-Archimedean spaces, respectively.

• Proceedings of the Korean Magnestics Society Conference
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• 2000.09a
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• pp.251-265
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• 2000

S $m_{2}$F $e_{17}$ $N_{x}$ film magnets using a S $m_{2}$F $e_{17}$ target were prepared at $N_{2}$ gas atmosphere using a Nd-YAG laser ablation technique. The effect of nitrogen pressure, deposition temperature, pulsation time and film thickness on the structure and magnetic properties of S $m_{2}$F $e_{17}$ $N_{x}$ film were studied. Increasing the nitrogen pressure up to 5 atm. was confirmed to lead the formation of complete S $m_{2}$F $e_{17}$ $N_{x}$ compound. Optimized magnetic properties with the nitrogenation temperature ranging over 500-53$0^{\circ}C$ could be obtained by extending the nitrogenation time up to 4 hours. Relatively low coercivities of 400~600 Oe were exhibited from the S $m_{2}$F $e_{17}$ $N_{x}$ films having the thickness of 50~100 nm while 4$\pi$ $M_{s}$ of 10~12 kG could be achieved. In-plane anisotropic characteristic, which was the basic goal in this study, was achieved by controlling the nitrogenation parameters.ameters.ers.ameters.

• Journal of Life Science
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• v.7 no.4
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• pp.358-360
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• 1997

Soybean [Glycine max (L.) Merr.] seed size is a important yield component and is a primary consideration in the development of cultivars for specialty markets. Our objective was to examine the consistency of QTLs for seed size across generations. A 68-plant F$_{2} segregation population derived from a mating between Marcury (small seed) and PI 467.468 (large seed) was evaluated with RAPD markers. In the F$_{2} plant generation (i.e. F$_{3} seed), three markers, OPL09a, OPM)7a, and OPAC12 were significantly (P<0.01) associated with seed size QTLs. In the F$_{2} ; F$_{3} generation (i.e., F$_{4} seed), four markers, OPA092, OPG19, OPL09b, and OPP11 were significantly (P<0.01) associated with seed size QTLs. Just two markers, OPL09a, and OPL09b were significantly (P<0.05) associated with seed size QTLs in both generations. The consistency of QTLs across generations indicates that marker-assisted selection for seed size is possible in a soybean breeding program.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.379-389
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• 2004

Given operators X and Y acting on a Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for $i=1,2,{\cdots},n$. In this article, we obtained the following : Let ${\mathcal{H}}$ be a Hilbert space and let ${\mathcal{L}}$ be a commutative subspace lattice on ${\mathcal{H}}$. Let X and Y be operators acting on ${\mathcal{H}}$. Then the following statements are equivalent. (1) There exists an operator A in $Alg{\mathcal{L}}$ such that AX = Y, A is positive and every E in ${\mathcal{L}}$ reduces A. (2) sup ${\frac{{\parallel}{\sum}^n_{i=1}\;E_iY\;f_i{\parallel}}{{\parallel}{\sum}^n_{i=1}\;E_iX\;f_i{\parallel}}}:n{\in}{\mathbb{N}},\;E_i{\in}{\mathcal{L}}$ and $f_i{\in}{\mathcal{H}}<{\infty}$ and <${\sum}^n_{i=1}\;E_iY\;f_i$, ${\sum}^n_{i=1}\;E_iX\;f_i>\;{\geq}0$, $n{\in}{\mathbb{N}}$, $E_i{\in}{\mathcal{L}}$ and $f_i{\in}H$.