• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.293-298
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• 1994

It is well known that the approximation property and the compact approximation property are not hereditary properties; that is, a closed subspace M of a Banach space X with the (compact) approximation property need not have the (compact) approximation property. In 1973, A. Davie [2] proved that for each 2 < p < $\infty$, there is a closed subspace $Y_{p}$ of $\ell_{p}$ which does not have the approximation property. In fact, the space Davie constructed even fails to have a weaker property, the compact approximation property. In 1991, A. Lima [12] proved that if X is a Banach space with the approximation property and a closed subspace M of X is locally $\lambda$-complemented in X for some $1\leq\lambda < $\infty$, then M has the approximation property.(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.251-260
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• 2019

It has been little known when an Artinian (point) quotient has the strong Lefschetz property. In this paper, we find the Artinian complete intersection quotient having the SLP. More precisely, we prove that if ${\mathbb{X}}$ is a complete intersection in ${\mathbb{P}}^2$ of type (2, 2) and ${\mathbb{Y}}$ is a finite set of points in ${\mathbb{P}}^2$ such that ${\mathbb{X}}{\cup}{\mathbb{Y}}$ is a basic configuration of type (2, a) with $a{\geq}3$ or (3, a) with a = 3, 4, 5, 6, then $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP. We also show that if ${\mathbb{X}}$ is a complete intersection in ${\mathbb{P}}^2$ of type (3, 2) and ${\mathbb{Y}}$ is a finite set of points in ${\mathbb{P}}^2$ such that ${\mathbb{X}}{\cup}{\mathbb{Y}}$ is a basic configuration of type (3, 3) or (3, 4), then $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.689-701
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• 2019

We study the recovery results of ${\ell}_p$-constrained compressive sensing (CS) with $p{\geq}1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon from ${\ell}_2$-constrained CS to ${\ell}_p$-constrained case with $p{\geq}1$ and complements the recovery analysis for robust CS with ${\ell}_p$ loss function.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.1-6
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• 2008

Duggal-Jeon-Kubrusly([2]) introduced Hilbert space operator T satisfying property ${\mid}T{\mid}^2{\leq}{\mid}T^2{\mid}$, where ${\mid}T{\mid}=(T^*T)^{1/2}$. In this paper we extend this property to general version, namely property B(n). In addition, we construct examples which distinguish the classes of operators with property B(n) for each $n{\in}\mathbb{N}$.

• Environmental Analysis Health and Toxicology
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• v.6 no.1_2
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• pp.1-6
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• 1991

The quality of water in Kyungan stream was analyzed in three different areas between season of irrigation on May and of nonirrigation on august in 1990. The results of Water quality from this study were summarized as follows: 1. The quality of water is season of irrigation containing metal ions, such as Cu and Zn as well as TN was exceeded standard levels of quality of agricultural water However, in season of nonirrigation, the quality of water in Kyungan stream was not suitable for using agricultural water due to over standard levels of containing ions of Cu and Zn or DO, COD and TN. 2. The correlation of water quality exception of pH was shown a reliance when p values were greater than 0.01 for containing ions such as Cu and Zn with the DO, COD and TN. 3. The comparison of water qualities for pH between season of irrigation and season of nonirrigation in Kyungan stream was a considerable significance property when p values were less than 0.05. The water quality containing ions of Cu and Zn with DO, COD, TN and SS also indicated a significant property when p values were less than 0.01. 4. The average water qualities of a year in three different areas for pH have shown a significant property when p values are less than 0.01. The average water qualities of a year containing DO have also shown a significant property having p values of less than 0.05. But other constituents have shown no significant property in the above three different areas.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9C
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• pp.835-842
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• 2003

For an odd prime p and integer n, m and k such that n=(2m＋1)ㆍk, a new family of p-ary sequences of period p$^{n}$ -1 with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation, where the size of the sequence family is p$^{n}$ . That is, the maximum nontrivial correlation value R$_{max}$ of all pairs of distinct sequences in the family does not exceed p$^{n}$ 2/ ＋1, which means the optimal correlation property in terms of Welch's lower bound. It is also derived that the linear span of the sequences in the family is (m＋2)ㆍn except for the m-sequence in the family.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.271-287
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• 2022

In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d^*) satisfying the following ξ-weakly expansive condition: d^*(𝒫c, 𝒫d) ≥ d^* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.645-667
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• 2019

It has been little known when an Artinian point quotient has the strong Lefschetz property. In this paper, we find the Artinian point star configuration quotient having the strong Lefschetz property. We prove that if ${\mathbb{X}}$ is a star configuration in ${\mathbb{P}}^2$ of type s defined by forms (a-quadratic forms and (s - a)-linear forms) and ${\mathbb{Y}}$ is a star configuration in ${\mathbb{P}}^2$ of type t defined by forms (b-quadratic forms and (t - b)-linear forms) for $b=deg({\mathbb{X}})$ or $deg({\mathbb{X}})-1$, then the Artinian ring $R/(I{\mathbb_{X}}+I{\mathbb_{Y}})$ has the strong Lefschetz property. We also show that if ${\mathbb{X}}$ is a set of (n+ 1)-general points in ${\mathbb{P}}^n$, then the Artinian quotient A of a coordinate ring of ${\mathbb{X}}$ has the strong Lefschetz property.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.9
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• pp.2147-2154
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• 2014

JXTA does not need to be managed by the central server, and has the property that can communicate with any device that is connected to the network. Thus, JXTA can be applied to the communication between heterogeneous P2P systems. This paper deals with the design of a data exchange system utilizing the JXTA's foregoing property, which is able to connect P2P systems with different protocols and APIs.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.929-934
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• 2001

This study aimed to examine the cause of latent hydraulic property manifestation of ground granulated blast-furnace slag(GGBFS) using different alkali activators in pH, type and quantity. According to the experimental result, the higher pH value accelerated lastly latent hydraulic property and the early stage strength of GCBFS was ranked as activators with the higher pH, in an order of NaOH, $Ca(OH)_{2}$ and $Na_{2}$$Co_{3}$. Also, NaOH had accelerated latent hydraulic property of GGBFS, which had 40~50% of the 3 and 7 days compressive strength of base mortar in case of using 10% of powder-weight. In the case of 30% of GGBFS substitution with annexing 2.5% $Ca(OH)_{2}$, the compressive strength on the 3 and 7 days of the early-age, was increased to 5~10% than that of the same admixture with no activator. With annexing 5.0% $Ca(OH)_{2}$, the strength was increased to 10~20%. Although activator NaOH was effective on the manifestation of latent hydraulic property, it caused cement mortar compressive strength decrease by enlarging pore diameter.