• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.839-865
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• 2013

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.

• Nuclear Engineering and Technology
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• v.53 no.6
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• pp.2000-2010
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• 2021

Mechanical moduli, such as Young's modulus (E), Bulks modulus (B), Shear modulus (S), longitudinal modulus (L), Poisson's ratio (σ) and micro Hardness (H) were theoretically calculated for (100-x)TeO₂+x MgO glasses, where x = 10, 20, 30, 40 and 45 mol%, based on the Makishima-Mackenzie model. The estimated results showed that the mechanical moduli and the microhardness of the glasses were improved with the increase of the MgO contents in the TM glasses, while Poisson's ratio decreased with the increase in MgO content. Moreover, the radiation shielding capacity was evaluated for the studied TM glasses. Thus, the linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), transmission factor (TF) and half-value thickness (𝚫_0.5) were simulated for gamma photon energies between 0.344 and 1.406 MeV. The simulated results showed that glass TM10 with 10 mol % MgO possess the highest LAC and varied in the range between 0.259 and 0.711 cm^-1, while TM45 glass with 45 mol % MgO possess the lowest LAC and vary in the range between 0.223 and 0.587 cm^-1 at gamma photon energies between 0.344 and 1.406 MeV. Furthermore, the BXCOM program was applied to calculate the effective atomic number (Z_eff), equivalent atomic number (Z_eq) and buildup factors (EBF and EABF) of the glasses. The effective removal cross-section for the fast neutrons (ERCSFN, ∑_R) was also calculated theoretically. The received data depicts that the lowest ∑_R was achieved for TM10 glasses, where ∑_R = 0.0193 cm² g^-1, while TM45 possesses the highest ERCSFN where ∑_R = 0.0215 cm² g^-1.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.235-240
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• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Journal of Preventive Medicine and Public Health
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• v.28 no.1 s.49
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• pp.73-84
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• 1995

This study was conducted to measure the lead level in the blood, scalp hair and toenail of the elementary schoolchildren and assess the relationship among those samples. Lead concentration of the blood, scalp hair and toenail was measured for 100(male 50, female 50) fourth grade elementary schoolchildren in Taegu city. The mean lead level in the blood, scalp hair and toenail was $6.00{\pm}2.44{\mu}g/dl,\;6.68{\pm}3.54{\mu}g/g,\;and\;7.33{\pm}3.18{\mu}g/g. The mean lead level in the blood of schoolboys was $6.43{\pm}2.77{\mu}g/dl$, and that of schoolgirls was $5.59{\pm}2.01{\mu}g/dl$. The mean lead level in the scalp hair of schoolboys was $7.66{\pm}2.97{\mu}g/g$ and that of schoolgirls was $6.88{\pm}3.54{\mu}g/g$. The mean lead level in the toenail of schoolboys was $8.19{\pm}3.5{\mu}g/g$ and that of schoolgirls was $6.47{\pm}2.52{\mu}g/g$ and their difference was statistically significant. In schoolboys, the correlation coefficient between the lead level in the blood and scalp hair was 0.4909, and the data were fitted best by the regression equation Y = 0.5255X+4. 2810, where Y and X are scalp hair and blood concentration. In schoolgirls the correlation coefficient between the lead level in the blood and scalp hair was 0.3778, and the data were fitted best by the regression equation Y = 0.6655X+2.9632, where Y and X are scalp hair and blood concentration. In schoolboys, the correlation coefficient between the lead level in the blood and in the toenail was 0.5533, and the data were fitted best by the regression equation Y = 0.7076X+3. 6472, where Y and X are toenail and blood concentration. In schoolgirls the correlation coefficient between the lead level in the blood and in the toenail was 0.2738, and the data were fitted best by the regression equation Y = 0.3431X+4.5570, where Y and X are toenail and blood concentration In schoolboys, the correlation coefficient between the lead level in the scalp hair and in the toenail, in the schoolboys was 0.4148, and the data were fitted best by the regression equation Y = 0.4956X+4.3986, where Y and X are toenail and scalp hair concentration. In schoolgirls, the correlation coefficient between the lead level in the scalp hair and in the toenail was 0.1159, and the data were fitted best by the regression equation Y = 0.0825X+5. 9214, where Y and X are toenail and scalp hair concentration. Correlation among lead concentration in the blood, scalp hair and toenail of schoolchildren were statistically significant except between scalp hair and toenail in schoolgirls. These finding suggest that blood, scalp hair and toenail can be used as substitutive samples between each others.

• Asian-Australasian Journal of Animal Sciences
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• v.16 no.10
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• pp.1438-1442
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• 2003

A method for the determination of nitrogen in ruminant feedstuffs, products and excreta (e.g. milk and urine) using a spectrophotometer is developed, where samples processed for P determination are also used to determine N. Samples are digested with sulphuric acid and subsequently with hydrogen peroxide in Kjeldahl tubes. Digested solutions along with phenol and buffered alkaline hypochlorite reagents are incubated in a water bath at $37^{\circ}C$ for 30 min and presented in the spectrophotometer. The spectrophotometer set at 625 nm measures the concentration of N of each sample. Nitrogen in 261 of the samples was also determined by the classical Kjeldahl method in order to develop a relationship between N determined by the Kjeldahl method (Y) and the colorimetric method (X). The mean value of Y was as high as that of X (0.92 vs. 0.96; p>0.05). The colorimetric method predicted Kjeldahl N highly significantly (Y=0.985X-0.024, $R^2=0.993$, p<0.001; or more simply Y=0.974X, $R^2=0.993$, p<0.001). An analysis of regression found no difference (p>0.05; both t-test and F-test) between colorimetric (0.96% N) and adjusted (0.96% N) N. In comparison with the Kjeldahl method, the analytical capacity of N by colorimetric method increases greatly, where 200-300 determinations of N are possible in a working day. In addition, the system provides an opportunity to use not only the same digested solution for both N and P determination of a particular sample, but also uses the same spectrophotometer to assay both N and P. Therefore, the system may be attractive in situations where both elements of a sample are to be determined. In conclusion, the speed of N determination, low cost, efficient use of labour, time and reagents, fewer items of equipment, and the reduction of environmental pollution by reducing effluent and toxic elements are the advantages of this method of N determination.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• Research in Plant Disease
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• v.13 no.3
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• pp.152-156
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• 2007

Incidences of leaf blight of lily cultivars Raizan and Casa Blanca in the open field cultivation were 50% and 45.4%, respectively, while those in the green house cultivation were significantly reduced to 1.5% and 1.9%, respectively, In the green house, the incidences of the disease in sprinkler watering cultivation were $14.5{\sim}16.5%$, while those in drip watering cultivation were only $1.5{\sim}2%$. Incidence of the disease was severe in the field where the lily was cultivated successively for 2 to 3 years. Isolation frequencies of B. elliptica from overwintered plant debrises such as leaves, stems, capsules, and bulbs were 43.3%, 46.7%, 60% and 0%, respectively, while those of B. cinerea were 10.3%, 0%, 3.3% and 0%, respectively, Incidence of leaf blight in the field where diseased plant debris was cleaned was 7.3%, while that in the field where diseased plant debris was not cleaned was 56.5%. Incidences of the disease in the field where coverages of soil surface with black vinyl, bark or rice straw were used were 6.6%, 8.2% and 11.3%, respectively, while that in the field where the coverage was not used was 21.3%.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.179-200
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $X_n:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ by $Xn(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t$ is a partition of $[0,t]$. In the present paper, using a simple formula for the conditional expectation given the conditioning function $X_n$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions which have the form $$f((v_1,x),{\cdots},(v_r,x))\;for\;x{\in}C[0,t]$$, where {$v_1,{\cdots},v_r$} is an orthonormal subset of $L_2[0,t]$ and $f{\in}L_p(\mathbb{R}^r)$. We then investigate several relationships between the conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions.

• 한국해양학회지
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• v.5 no.1
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• pp.6-13
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• 1970

Ten days and monthly mean temperatures were analysed daily data observed during July, 1916 to March, 1970 statistically. Periodic characters were calculated by Δn, new method of approximate solution of Schuster Method. According to ten days mean temperatures, annual variation function is F($\theta_d$)=16.29-5.27 cos $\theta_d$+0.75 cos2 $\theta_d$-3.14 sin $\theta_d$+1.16 sin2 $\theta_d$-0.63 sin $\3{theta}_d$, where $\theta_d$=$-\frac{\pi}{18}$(d-3), d is the order of ten days period, 1 to 36. Annual mean water temperature is 16.3$^{\circ}C$, minimum in the last ten days of February 10.9$^{\circ}C$, maximum in the last ten days of August 24.5$^{\circ}C$. Periodic character of secular variation shows 11 year and its curve is F($\theta_y$)=16.29+0.53 cos $\theta_y$ -0.16cos $2{\theta}_y$+0.10 cos$3{\theta}_y$-0.10 sin $\theta_y$, where $\theta_y$=2$-\frac{2\pi}{11}$(y-1920), y is calendar year. And the relation between air temperature x and water temprature y is following. y=9.67 1.035$\^x$