• Investigative Magnetic Resonance Imaging
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• v.23 no.1
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• pp.17-25
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• 2019

We discuss recent advances in Gd-based $T_1$-weighted MR contrast agents for the mapping of cellular pH. The pH plays a critical role in various biological processes. During the past two decades, several MR contrast agents of strategic importance for pH-mapping have been developed. Some of these agents shed light on the pH fluctuation in the tumor microenvironment. A pH-responsive self-assembled contrast agent facilitates the visualization of tumor size as small as $3mm^3$. Optimization of various parameters is crucial for the development of pH-responsive contrast agents. In due course, the new contrast agents may provide significant insight into pH fluctuations in the human body.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Asian-Australasian Journal of Animal Sciences
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• v.19 no.8
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• pp.1085-1089
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• 2006

The objectives of this study were to confirm a location of the calpastatin (CAST) gene in chromosome 2 and to detect associations of genetic variations with economic traits in the porcine CAST gene as a candidate gene for growth and meat quality traits in pigs. Calpastatin is a specific endogenous inhibitor of calpains. The calpain protease system is ubiquitous, and is involved in numerous growth and metabolic processes. Three single nucleotide variations were identified within a 1.6 kb fragment of the porcine CAST gene and these polymorphisms were used for genetic linkage mapping. Linkage and QTL mapping were performed with the National Livestock Research Institute (NLRI) reference families using eight microsatellites and SNP makers in the CAST gene. The porcine CAST gene was mapped adjacent to the markers, SW395 and SW1695 on SSC2 with LOD scores of 15.32 and 8.50, respectively. According to the QTL mapping, a significant association was detected at 82 cM between SW395 and CAST-Hinf I for weight at the age of 30 weeks. In addition, an association study was performed with the $F_2$ animals of NLRI reference families for Hinf I, Msp I and Rsa I polymorphisms in the CAST gene. Two polymorphisms, CAST-Rsa I and CAST-Hinf I, showed significant correlation for growth traits at p<0.01 and p<0.05, respectively.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.785-827
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• 2023

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a P-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of H(·, ·)-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every H(·, ·)-co-accretive mapping is actually P-accretive and is not a new one. In the meanwhile, some important comments on H(·, ·)-co-accretive mappings and the results related to them appeared in the literature are pointed out.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.61-75
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• 2002

Under the cancellation property and the Lipschitz condition on kernels, we prove that the Marcinkiewicz integrals defined on a homogeneous group H are bounded from $H^1$(H) to $L^1$(H), from $L_{c}$ $^{\infty}$(H) to BMO (H), and from $L^{p}$ (H) to $L^{p}$ (H) for 1 < p < $\infty$ assuming the $L^{q}$ -boundedness for some q > 1.for some q > 1.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Molecules and Cells
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• v.39 no.6
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• pp.460-467
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• 2016

Bacteriophytochromes are phytochrome-like light-sensing photoreceptors that use biliverdin as a chromophore. To study the biochemical properties of the Deinococcus radiodurans bacteriophytochrome (DrBphP) protein, two anti-DrBphP mouse monoclonal antibodies (2B8 and 3H7) were generated. Their specific epitopes were identified in our previous report. We present here fine epitope mapping of these two antibodies by using truncation and substitution of original epitope sequences in order to identify minimized epitope peptides. The previously reported original epitope sequences for 2B8 and 3H7 were truncated from both sides. Our analysis showed that the minimal peptide sequence lengths for 2B8 and 3H7 antibodies were nine amino acids (RDPLPFFPP) and six amino acids (PGEIEE), respectively. We further characterized these peptides in order to investigate their reactivity after single deletion and single substitution of the original peptides. We found that single-substituted 2B8 epitope (RDPLPAFPP) and dual-substituted 3H7 epitope (PGEIAD) showed significantly increased reactivity. These two antibodies with high reactivity for the short modified peptide sequences are valueble for developing new peptide tags for protein research.

• Microbiology and Biotechnology Letters
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• v.15 no.6
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• pp.436-440
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• 1987

Pullulanase gene (pul) of Klebsiella pneumoniae NFB-320 which was cloned previously in Escherichia coli with plasmid pBR322. The gene was analyzed with various restriction enzymes. The cloned gene was contained within n 10 kb BamHI DNA fragment. We constructed the restriction map of the hybrid plasmid pYKL451. The optimum temperatures for pullulanases produced in E. coli (pYKL451) and K. pneumoniae NFB-320 were almost the same, 50-55 $^{\circ}C$. The optimum pHs for the reaction of the enzymes produced by E. coli (pYKL451) and K. pneumoniae NFB-320 was 6.0. Both enzyme preparations were stable under the range of pH 5.0 to 10.0 when those were kept at 40 $^{\circ}C$ for 90 min and were stable until 40 $^{\circ}C$ when allowed to stand for 1hr at various temperatures.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.59-68
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• 2011

In this paper, we first give the definition of degenerate weakly ($k_1$, $k_2$-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse H$\"{o}$lder inequality, we obtain the higher integrability result: for any $q_1$ satisfying 0 < $k_1({n \atop l})^{3/2}n^{l/2}\;{\times}\;2^{n+1}l\;{\times}\;100^{n^2}\;\[2^l(2^{n+3l}+1)\]\;(l-q_1)$ < 1 there exists an integrable exponent $p_1$ = $p_1$(n, l, $k_1$, $k_2$) > l, such that every degenerate weakly ($k_1$, $k_2$)-quasiregular mapping f ${\in}$ $W_{loc}^{1,q_1}$ (${\Omega}$, $R^n$) belongs to $W_{loc}^{1,p_1}$ (${\Omega}$, $R^m$), that is, f is a degenerate ($k_1$, $k_2$)-quasiregular mapping in the usual sense.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.