• Journal of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.283-312
• /
• 2020

A sufficient condition for an Artinian complete intersection quotient S = 𝕜[x, y]/(x^m, yⁿ), where 𝕜 is an algebraically closed field of a prime characteristic, to have the strong Lefschetz property (SLP) was proved by S. B. Glasby, C. E. Praezer, and B. Xia in [3]. In contrast, we find a necessary and sufficient condition on m, n satisfying 3 ≤ m ≤ n and p > 2m-3 for S to fail to have the SLP. Moreover we find the Jordan types for S failing to have SLP for m ≤ n and m = 3, 4.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.2
• /
• pp.271-287
• /
• 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
• /
• v.61 no.2
• /
• pp.395-408
• /
• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.

• Journal of applied mathematics & informatics
• /
• v.39 no.3_4
• /
• pp.327-338
• /
• 2021

In this paper, we have introduced a new notion of recurrent structure Jacobi of real hypersurfaces in complex hyperbolic two-plane Grassmannians G^*₂(ℂ^m+2). Next, we show a non-existence property of real hypersurfaces in G^*₂(ℂ^m+2) satisfying such a curvature condition.

• Archives of Metallurgy and Materials
• /
• v.64 no.2
• /
• pp.513-518
• /
• 2019

Recently, attempts have been made to use porous metal as catalysts in a reactor for the hydrogen manufacturing process using steam methane reforming (SMR). This study manufactured Ni-Cr-Al based powder porous metal, stacked cubic form porous blocks, and investigated high temperature random stack creep property. To establish an environment similar to the actual situation, a random stack jig with a 1-inch diameter and height of 75 mm was used. The porous metal used for this study had an average pore size of ~1161 ㎛ by rolling direction. The relative density of the powder porous metal was measured as 6.72%. A compression test performed at 1073K identified that the powder porous metal had high temperature (800℃) compressive strength of 0.76 MPa. A 800℃ random stack creep test at 0.38 MPa measured a steady-state creep rate of 8.58×10^-10 s^-1, confirming outstanding high temperature creep properties. Compared to a single cubic powder porous metal with an identical stress ratio, this is a 1,000-times lower (better) steady-state creep rate. Based on the findings above, the reason of difference in creep properties between a single creep test and random stack creep test was discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1275-1283
• /
• 2010

If the Wiener-Hopf $C^*$-algebra W(G,M) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf $C^*$-algebra W(G,M) of a partially ordered group G with the positive cone M has the uniqueness property, then (G,M) is weakly unperforated. We also prove that the Wiener-Hopf $C^*$-algebra W($\mathbb{Z}$, M) of subsemigroup generating the integer group $\mathbb{Z}$ is isomorphic to the Toeplitz algebra, but W($\mathbb{Z}$, M) does not have the uniqueness property except the case M = $\mathbb{N}$.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.31 no.5
• /
• pp.875-888
• /
• 2021

In this paper, we search integral distinguishers of lightweight block cipher PIPO and propose a key recovery attack on 8-round PIPO-64/128 with the obtained 6-round distinguishers. The lightweight block cipher PIPO proposed in ICISC 2020 is designed to provide the efficient implementation of high-order masking for side-channel attack resistance. In the proposal, various attacks such as differential and linear cryptanalyses were applied to show the sufficient security strength. However, the designers leave integral attack to be conducted and only show that it is unlikely for PIPO to have integral distinguishers longer than 5-round PIPO without further analysis on Division Property. In this paper, we search integral distinguishers of PIPO using a MILP-aided Division Property search method. Our search can show that there exist 6-round integral distinguishers, which is different from what the designers insist. We also consider linear operation on input and output of distinguisher, respectively, and manage to obtain totally 136 6-round integral distinguishers. Finally, we present an 8-round PIPO-64/128 key recovery attack with time complexity 2^124.5849 and memory complexity of 2⁹³ with four 6-round integral distinguishers among the entire obtained distinguishers.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.2
• /
• pp.581-596
• /
• 2024

A new variety of non-self generalized proximal contraction, called Hardy-Rogers α⁺F-proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α⁺F-proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation.

• Korean Journal of Optics and Photonics
• /
• v.35 no.3
• /
• pp.115-120
• /
• 2024

Magneto-optical (MO) materials have attracted much attention, since they can be utilized for various optical applications, such as magnetic field sensors, optical current sensors, optical isolators, and optical circulators. In this study, alumino-borosilicate (ABS) glasses with high concentrations of Dy³⁺ ions were fabricated by a conventional melt-quenching technique, and the dependence of their thermal, optical, and magneto-optical properties on Dy³⁺ ion concentration was investigated. The MO property of the glasses was investigated by measurement of Faraday rotation at 1550 nm. The Faraday rotation angle increased linearly with the increase of Dy³⁺ ion concentration in the glasses. A very high Verdet constant of -6.86 rad/(T·m) was obtained for glass with a Dy³⁺ ion concentration of 30 mol%. In addition, the ABS-Dy glasses showed good thermal stability of greater than 128 ℃ against crystallization, and high optical transmission of 70% in the visible to near-infrared windows of 480-720, 1390-1560, and 1800-2400 nm. Due to the high Verdet constant and good thermal stability, the ABS-Dy glasses in this study could be candidate optical materials for MO device applications at 1550 nm.

• Korean Journal of Mathematics
• /
• v.30 no.3
• /
• pp.459-465
• /
• 2022

We exhibit various properties of the weighted Berezin operator T_α and its iteration T^k_α on L^p(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(𝜏) the space of radial integrable functions have performed important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T_α or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.