• Journal of applied mathematics & informatics
• /
• v.39 no.3_4
• /
• pp.437-442
• /
• 2021

In this paper, we study the characterizations of two-sided best simultaneous approximations for ℓ-tuple subset from a closed convex subset of ℝ^m with ℓ^m₁(w)-norm. Main fact is, k^* is a two-sided best simultaneous approximation to F from K if and only if there exist f₁, …, f_p in F, for any k ∈ K $${\mid}{\sum\limits_{i=1}^{m}}sgn(f_{ji}-k^*_i)k_iw_i{\mid}{\leq}\;{\sum\limits_{i{\in}Z(f_j-k^*)}}\;{\mid}k_i{\mid}w_i$$ for each j = 1, …, p and 𝐰 ∈ W.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.735-748
• /
• 2022

The global well-posedness for the fourth-order modified Zakharov equations in 1-D, which is a system of PDE in two variables describing interactions between quantum Langmuir and quantum ionacoustic waves is studied. In this paper, it is proven that the system is globally well-posed in (u, n) ∈ L² × L² by making use of Bourgain restriction norm method and L² conservation law in u, and controlling the growth of n via appropriate estimates in the local theory. In particular, this improves on the well-posedness results for this system in [9] to lower regularity.

• Korean Journal of Mathematics
• /
• v.6 no.2
• /
• pp.205-212
• /
• 1998

We investigate the behavior of $L^2$ harmonic one forms on complete manifolds and as an application, we show the space of $L^2$harmonic one forms on a complete Riemannian manifold of nonnegative Ricci curvature outside a compact set with bounded $n/2$-norm of Ricci curvature satisfying the Sobolev inequality is finite dimensional.

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1269-1283
• /
• 2018

We are concerned with elliptic equations in ${\mathbb{R}}^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to 0 in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

• Communications of the Korean Mathematical Society
• /
• v.17 no.2
• /
• pp.261-278
• /
• 2002

Let G = O(2) $\times$ O(2) $\times$O(2) and let M$^4$be closed G-invariant minimal hypersurface with constant scalar curvature in S$^{5}$ . If M$^4$has 2 distinct principal curvatures at some point, then S = 4. Moreover, if S > 4, then M$^4$does not have simple principal curvatures everywhere.

• Kyungpook Mathematical Journal
• /
• v.46 no.1
• /
• pp.31-48
• /
• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.487-494
• /
• 2019

We classify all the extreme and exposed bilinear forms of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ which leads to a complete formula of ${\parallel}f{\parallel}$ for every $f{\in}{\mathcal{L}}(^2l^3_{\infty})^*$. It follows from this formula that every extreme bilinear form of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ is exposed.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.815-828
• /
• 2021

Under some mild conditions for the weight function K, the boundedness, compactness and essential norm of integral operators T_g and I_g from Morrey type spaces H^p_K to weighted BMOA spaces $BMOAK_{K,{\frac{2}{p}}}$ investigated in this paper.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.5_6
• /
• pp.269-286
• /
• 2022

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝ^N , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

• Journal of Radiation Protection and Research
• /
• v.41 no.4
• /
• pp.359-367
• /
• 2016

Background: As new legislation has come into force implementing radiation safety management for the use of naturally occurring radioactive materials (NORM), it is necessary to establish a rapid and accurate measurement technique. Measurement of $^{238}U$ and $^{232}Th$ using conventional methods encounter the most significant difficulties for pretreatment (e.g., purification, speciation, and dilution/enrichment) or require time-consuming processes. Therefore, in this study, the applicability of ED-XRF as a non-destructive and rapid screening method was validated for raw materials and by-product samples. Materials and Methods: A series of experiments was conducted to test the applicability for rapid screening of XRF measurement to determine activity of $^{238}U$ and $^{232}Th$ based on certified reference materials (e.g., soil, rock, phosphorus rock, bauxite, zircon, and coal ash) and NORM samples commercially used in Korea. Statistical methods were used to compare the analytical results of ED-XRF to those of certified values of certified reference materials (CRM) and inductively coupled plasma mass spectrometry (ICP-MS). Results and Discussion: Results of the XRF measurement for $^{238}U$ and $^{232}Th$ showed under 20% relative error and standard deviation. The results of the U-test were statistically significant except for the case of U in coal fly ash samples. In addition, analytical results of $^{238}U$ and $^{232}Th$ in the raw material and by-product samples using XRF and the analytical results of those using ICP-MS ($R^2{\geq}0.95$) were consistent with each other. Thus, the analytical results rapidly derived using ED-XRF were fairly reliable. Conclusion: Based on the validation results, it can be concluded that the ED-XRF analysis may be applied to rapid screening of radioactivities ($^{238}U$ and $^{232}Th$) in NORM samples.