• 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.

• Bulletin of the Korean Chemical Society
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• v.31 no.5
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• pp.1177-1181
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• 2010

The synthesis and characterization of gold nanoparticles coated by Gd-chelate (GdL@Au) is described, where L is a conjugate of DTPA (DTPA = diethylenetriamine-N,N,N',N",N"-pentaacetic acid) and 4-aminothiophenol. These particles are obtained by the replacement of citrate from the gold nanoparticle surfaces with gadolinium chelate (GdL). The average size of GdL@Au is 12 nm with a loading of GdL reaching up to $1.4{\times}10^3$ per particles, and they demonstrate very high r1 relaxivity (${\sim}10^4mM^{-1}s^{-1}$) and the r1 relaxivity per [Gd] is as high as $10mM^{-1}s{-1}$. Here, we also describe the use of bimodality of this contrast agent (CA) as a highly efficient CT contrast agent based on gold nanoparticles (GNPs) that overcome the limitations of iodine based contrast agent. The MTT assay performed on this CAs reveals the cytotoxicity as low as that for Omniscan$^{(R)}$ in the concentration range required to obtain intensity enhancement in the in vivo MRI study.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.731-751
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• 2023

If p(z) is a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1, then for any complex number α with |α| ≥ k, and r ≥ 1, Aziz [1] proved $$\left{{\int}_{0}^{2{\pi}}\,{\left|1+k^ne^{i{\theta}}\right|^r}\,d{\theta}\right}^{\frac{1}{r}}\;{\max\limits_{{\mid}z{\mid}=1}}\,{\mid}p^{\prime}(z){\mid}\,{\geq}\,n\,\left{{\int}_{0}^{2{\pi}}\,{\left|p(e^{i{\theta}})\right|^r\,d{\theta}\right}^{\frac{1}{r}}.$$ In this paper, we obtain an improved extension of the above inequality into polar derivative. Further, we also extend an inequality on polar derivative recently proved by Rather et al. [20] into L^r-norm. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• Fisheries and Aquatic Sciences
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• v.25 no.10
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• pp.525-536
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• 2022

Photosynthetic bacteria (PSB) attract considerable interest as useful microorganisms; nevertheless, a generalized culture technique has not been previously reported owing to difficulty in their cultivation. Therefore, a simple culture technique suitable for public use was investigated. Among the PSB tested, the strain Rhodobacter azotoformans EBN-7 was the most suitable for scale-up production because it showed the highest specific growth rate (0.20 h^-1) on basal medium. In scale-up cultivation (500 L), R. azotoformans EBN-7 showed 4.50 × 10¹⁰ colony-forming units mL^-1 (number of viable cells), dry cell weight of 26.8 g/L, and a specific growth rate of 0.15 h^-1. Cultivation using this final culture broth (as seed culture) in a 15 L simple reactor was successful, with maintenance of cell activity evident. For use as seed culture, the maximum allowable preservation period of R. azotoformans EBN-7 at 4℃ was 3 months. When R. azotoformans EBN-7 cultivated in a simple technique was applied to shrimp aquaculture water, NH₄⁺-N was reduced from 0.61 mg/L to 0.24 mg/L (by 60.7%) in 4 days in comparison with the control. Thus, this simple culture technique using R. azotoformans EBN-7 has the potential for a good removal efficiency of NH₄⁺-N, making seed culture easier and suitable for public use.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.621-635
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• 2024

An 𝑙-regular overpartition of n is an overpartition of n with no parts divisible by 𝑙. Recently, the authors introduced a partition statistic called r_𝑙-crank of 𝑙-regular overpartitions. Let M_r𝑙(m, n) denote the number of 𝑙-regular overpartitions of n with r_𝑙-crank m. In this paper, we investigate the monotonicity property and the unimodality of M_r3(m, n). We prove that M_r3(m, n) ≥ M_r3(m, n - 1) for any integers m and n ≥ 6 and the sequence {M_r3(m, n)}_|m|≤n is unimodal for all n ≥ 14.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.48 no.5
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• pp.361-368
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• 2003

The responses of five varieties and three cultivars of pea (Pisum sativum) to Rhizobium inoculation on nodulation, growth, nitrogenase activity, dry matter production and N uptake were investigated. The pea varieties were IPSA Motorshuti-l, IPSA Motorshuti-2, IPSA Motorshuti-3, BARI Motorshuti-l, BARI Motorshuti-2 and the cultivars were 063, Local small and Local white. Fifty percent seeds of each pea variety/cultivar were inoculated with a mixture of Rhizobium inoculants at rate of 15g/kg seed and the remaining fifty percent seeds were kept uninoculated. The plants inoculated with Rhizobium inoculant significantly increased nodulation, growth, nitrogenase activity, dry matter production and N uptake. Among the varieties/cultivars, BARI Motorshuti-l performed best in almost all parameters including nitrogenase activity of root nodule bacteria of the crop. There were positive correlations among the number and dry weight of nodules (r=$0.987^{**}$, $0.909^{**}$), nitrogenase activity of root nodule bacteria (r=$0.944^{**}$, $0.882^{**}$), dry weight of shoot (r=$0.787^{**}$, $0.952^{**}$), N content (r=$0.594^{**}$, $0.605^{**}$) and N uptake (r=$0.784^{**}$, $0.922^{**}$) by shoot both at flowering and pod filling stages of the crop, respectively. It was concluded that BARI Motorshuti-l in symbiotic association with Rhizobium inoculant performed best in recording nitrogenase activity, dry matter production and N uptake by pea.

• Journal of information and communication convergence engineering
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• v.14 no.1
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• pp.40-44
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• 2016

The device coupling between the stacked top/bottom field-effect transistors (FETs) in two types of monolithic 3D inverter (M3INV) with/without a metal layer in the bottom tier is investigated, and then the regime of the thickness T_ILD and dielectric constant ε_r of the inter-layer distance (ILD), the doping concentration N_d (N_a), and length L_g of the channel, and the side-wall length L_SW where the stacked FETs are coupled are studied. When N_d (N_a) < 10¹⁶ cm^-3 and L_SW < 20 nm, the threshold voltage shift of the top FET varies almost constantly by the gate voltage of the bottom FET, but when N_d (N_a) > 10¹⁶ cm^-3 or L_SW > 20 nm, the shift decreases and increases, respectively. M3INVs with T_ILD ≥ 50 nm and ε_r ≤ 3.9 can neglect the interaction between the stacked FETs, but when T_ILD or ε_r do not meet the above conditions, the interaction must be taken into consideration.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.73-84
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• 2011

Let f, g, h, k : $\mathbb{R}^n{\rightarrow}\mathbb{C}$ be locally integrable functions. We deal with the $L^{\infty}$-version of the Hyers-Ulam stability of the quadratic functional inequality and the Pexiderized quadratic functional inequality $${\parallel}f(x + y) + f(x - y) -2f(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ $${\parallel}f(x + y) + g(x - y) -2h(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ based on the concept of linear functionals on the space of smooth functions with compact support.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.