• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.413-420
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal 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 rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. 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 double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. 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 ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) 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 reciprocal 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1007-1025
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• 2015

Let $\mathbb{N}_0$ be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., $P(n,l)=\{(x_1,x_2,{\cdots},x_l){\in}\mathbb{N}^l_0\;:\;x_1+x_2+{\cdots}+x_l=n\}$. For any element $u=(u_1,u_2,{\cdots},u_l){\in}P(n,l)$, denote its ith-coordinate by u(i), i.e., $u(i)=u_i$. A family $A{\subseteq}P(n,l)$ is said to be t-intersecting if ${\mid}\{i:u(i)=v(i)\}{\mid}{\geq}t$ for all $u,v{\epsilon}A$. A family $A{\subseteq}P(n,l)$ is said to be trivially t-intersecting if there is a t-set T of $[l]=\{1,2,{\cdots},l\}$ and elements $y_s{\in}\mathbb{N}_0(s{\in}T)$ such that $A=\{u{\in}P(n,l):u(j)=yj\;for\;all\;j{\in}T\}$. We prove that given any positive integers l, t with $l{\geq}2t+3$, there exists a constant $n_0(l,t)$ depending only on l and t, such that for all $n{\geq}n_0(l,t)$, if $A{\subseteq}P(n,l)$ is non-trivially t-intersecting, then $${\mid}A{\mid}{\leq}(^{n+l-t-l}_{l-t-1})-(^{n-1}_{l-t-1})+t$$. Moreover, equality holds if and only if there is a t-set T of [l] such that $$A=\bigcup_{s{\in}[l]{\backslash}T}\;A_s{\cup}\{q_i:i{\in}T\}$$, where $$A_s=\{u{\in}P(n,l):u(j)=0\;for\;all\;j{\in}T\;and\;u(s)=0\}$$ and $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.415-423
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• 2004

In allelic model X = ($x_1,\;x_2,...x_{d}$), $M_f(t)$= f(p(t)) - ${{\int}^{t}}_0$Lf(p(t))ds is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show uniqueness of martingale problem associated with mean vector and obtain a complete description of ergodic property by using of the semigroup method.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.369-378
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• 2005

In this paper we will consider the weighted composition operator $W=uC_{\varphi}$ between two different $L^p(X,\;\Sigma,\;\mu)$ spaces, generated by measurable and non-singular transformations $\varphi$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\varphi$ that induce weighted composition operators between $L^p-spaces$ by using some properties of conditional expectation operator, pair $(u,\;\varphi)$ and the measure space $(X,\;\Sigma,\;\mu)$. Also, Fredholmness of these type operators will be investigated.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.191-202
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• 2007

By using the weighted averaging techniques, we establish oscillation criteria for the second order damped quasilinear elliptic differential equation $$\sum_{i,j=1}^{N}D_i(a_{ij}(x){\parallel}Dy{\parallel}^{p-2}D_jy)+{\langle}b(x),\;{\parallel}Dy{\parallel}^{p-2}Dy{\rangle}+c(x)f(y)=0,\;p>1$$. The obtained theorems include and improve some existing ones for the undamped halflinear partial differential equation and the semilinear elliptic equation.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.419-421
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• 1994

Recently Hong and Oh [5] provided a fairly general weak law for arrays in the following form: Let {(X/sub ni/, l ≤ i ≤ k/sub n/), n ≥ l}, k/sub n/ → ∞ as n → ∞, be an array of random variables on (Ω, F, P) and set F/sub nj/ = σ{X/sub ni/, 1 ≤ i ≤ j}, 1 ≤ j ≤ k/sub n/, n ≥ 1, and F/sub n0/ = {ø, Ω}, n ≥ 1. Suppose that (equation omitted) aP { X/sub ni/ /sup p/ ＞ a} → 0 as a → ∞ uniformly in n for some 0 < p < 2. Then S/sub n//(equation omitted) → 0 in probability as n → ∞ where S/sub n/ = (equation omitted)(X/sub ni/ - E(X/sib ni/I( X/sub ni/ /sub p/ ≤ k/sub n/) F/sub n,i-l/)). In this note, we will prove the following result under the same domination condition of Hong and Oh [5].(omitted)

• Journal of Korean Public Health Nursing
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• v.18 no.2
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• pp.330-341
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• 2004

Parental smoking status and smoking environment do not only affect children's health through exposure to nicotine, but are also related to children's smoking attitude, intention and knowledge of smoking. Since this study was conducted to examine a relationship between family members smoking and smoking attitude, intention and knowledge of their children, little is known about psychosocial factors influencing smoking among Korean preschool children. This study aimed to determine the psychosocial factors (sociodemographic factors, education for smoking cigarette, knowledge about smoke cigarette) influencing smoking attitude and smoking intention, with a purpose of providing directions for future education programs for Korean preschool children. A cross sectional sample of 840 children, ages 4-7 years, living in a rural district were interviewed during August 6 - November 14, 2003. Among them, 834 children whose missing data were less than $10\%$ were included the analysis. The independent variables included sociodemographic characteristics and education for smoking cigarette, while the dependent variables were knowledge about smoking, the children's smoking attitude and their intention of smoking. The data on sociodemographic characteristics were analyzed using descriptive statistics including frequency, percentage, mean, and standard deviation. The correlations between the independent variables and attitude and intention of smoking were analyzed using chi-square test, t-test, and logistic regression. The results of this study were s follows. The factors that were found to be significantly correlated to smoking attitude include mother's smoking $(x^2=4.86,\;p=.03)$, grandmother's smoking $(x^2=5.56,\;p=.02)$, and knowledge of smoking cigarette $(x^2=-5.13 p<.01)$. The factors that were significantly correlated to the intention of smoking include gender $(x^2=.08,\; p=.02)$, education for smoking$(x^2=17.65,\;p<.01)$, mother's smoking $(x^2=19.05,\; p<.01)$, grandmother's smoking $(x^2=17.67,\; p<.01)$, and knowledge$(x^2=-2.17,\;p=.03)$. The children who had non smoking mother were more likely to have negative attitude (OR=2.29). The children who had a higher knowledge about smoking were more likely to have negative attitude (OR=1.58). The findings suggest that a smoking prevention program specific for preschool children is necessary to prevent early onset of smoking. The findings also suggest that the program should involve children's family members who influence their smoking attitude and intention.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1659-1666
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• 2018

Let $P_r$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer N, the equation $$N=x^2+p_1^2+p_2^3+p_3^3+p_4^4+p_5^4$$ is solvable with x being an almost-prime $P_4$ and the other variables primes. This result constitutes an improvement upon that of $L{\ddot{u}}$ [7].

• Journal of the Korean Vacuum Society
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• v.13 no.2
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• pp.86-91
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• 2004

Transiton-metal gallides attract wide interest as a candidate for high-temperature structural materials. In a wide composition range, in which it was known that Co-Ga alloy have CsCl (B2) crystallographic structure, a systematic study on the correlation between physical properties and electronic structures of Co-gallides was performed. $Co_{l-x}Ga$ $_{x}$ alloys ($0.35\leq$x$\leq0.55$) were prepared by arc-melting method and were annealed at $1000 ^{\circ}C$ for 48hour to increase the homogeneity. In this composition range all the prepared alloys have the CsCl (B2) structure. The chemical states and the electronic structure were studied by using x-ray photoemission spectroscopy (XPS), and x-ray absorption near-edge structure (XANES), and exhibit different physical properties depending on the composition. During the annealing, a significant oxidation has happened and all the oxygen atoms are incorporated with the Ga atoms to form a $Ga_2O_3$ phase. In a view point of electronic structure, the $Co_{l-x}Ga$ $_{x}$ alloys were formed by the Ga(p) - Co(d) hybridization.

• Korean Journal of Agricultural Science
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• v.36 no.2
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• pp.135-145
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• 2009

This research was conducted to investigate the effect of various phosphorus concentrations in fertilizer solution on growth of and nutrient uptake by 'Chugyang' egg plant (Solanum melongena L.). Tissue and soil analyses were also conducted to set the threshold levels of phosphorus in plants when disorders develop for phosphorus deficiency or excess. Brown and purple areas developed on the margin of mature leaves and it enlarged rapidly in P deficient plants. The fruits in P deficient plants were small and dull purple in color. When P were excess in fertigation solution, the margins of lower leaves became scorched and it enlarged to inner part of the leaves. The fruits of P excess plants became small and had the curl shape. The tissue $PO_4$-P contents in the most recently fully expanded leaves and dry weight of full above ground plant tissue at 35 days after transplanting showed quadratic response ($y=0.7887+0.2394x-0.0197x^2$) and cubic response ($y=10.43+14.47x-4.7642x^2+0.3977x^3$) to elevated $PO_4$-P concentrations, respectively. When 10% reduction in dry weight set to threshold levels, optimum tissue $PO_4$-P contents are between 0.98 to 1.35%. The yield determined at 150 days after transplanting also showed cubic response to elevated phosphorus concentrations in fertigation solution ($y=1194.6+1502.2x-454.5x^2+35.64x^3$). When the 10% reduction in yield is set to threshold levels, the tissue $PO_4$-P contents for maximum yield should be around 1.53% to 2.25% in most recently fully expanded leaves at 150 days after transplanting.