• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.257-262
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• 2010

Let f be a $C^2$-diffeomorphism on a closed surface which satisfies the Axiom A. Then f is in the $C^2$-interior of the set of all diffeomorphisms having the inverse shadowing property with respect to the class of the continuous methods if and only if f satisfies the strong transversality condition.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.395-408
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• 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 the Korean Mathematical Society
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• v.61 no.2
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• pp.309-339
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• 2024

Let M be a real hypersurface in the complex hyperbolic quadric Q^m*, m ≥ 3. The Riemannian curvature tensor field R of M allows us to define a symmetric Jacobi operator with respect to the Reeb vector field ξ, which is called the structure Jacobi operator R_ξ = R( · , ξ)ξ ∈ End(TM). On the other hand, in [20], Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator R_ξ for a real hypersurface M in the complex hyperbolic quadric Q^m*. Furthermore, we give a complete classification of Hopf real hypersurfaces in Q^m* with such a property.

• Communications of the Korean Mathematical Society
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• v.8 no.3
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• pp.383-387
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• 1993

• Bulletin of the Korean Chemical Society
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• v.28 no.10
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• pp.1860-1862
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• 2007

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.147-154
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• 2022

In this article, we prove that an absolutely summing operator on 𝓛^λ₁ spaces has a lifting under the conditions that a target Banach space is a quotient of reflexive Banach subspaces.

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

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

• Journal of the Korean Society for Heat Treatment
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• v.33 no.4
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• pp.161-172
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• 2020

The tensile property of A5082 and A6060 aluminium wrought alloys was investigated, in terms of the strain rate sensitivity on alloy conditions by heat treatment and bake hardenability on pre-strain prior to strain ageing. The tensile test was carried out in a range of strain rate of 4.17 × 10^-5 s^-1 ~ 4.17 × 10^-5 s^-1 in room temperature and the nominal range of pre-strain was 3.0 ~ 10.5%. The tensile deformation of A5082 alloys is characterized as typical case of dynamic strain ageing with negative strain rate sensitivity for all conditions, and the tensile strength indicates a similar level regardless of alloy conditions, except only in full annealed condition. The stress-relief annealing on A6060 alloys can induce practical decrease in strength level of over approximately 100 MPa without any ductility loss, compared to as-rolled condition, while a full annealed and aged condition leads remarkable strengthening effect with the decrease of tensile elongation. Additionally, the bake hardenability of A5082 alloy by strain ageing indicates a negative dependence upon the increase of pre-strain, while A6060 alloy exhibits a positive sign even in low level relatively compared with conventional SPCC.

• Earthquakes and Structures
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• v.22 no.5
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• pp.487-502
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• 2022

China is prone to earthquake disasters, and the higher seismic performance is required by many existing civil buildings. And seismic evaluation and retrofit are effective measures to mitigate seismic hazards. With the development of performance-based seismic design and diverse retrofit technology for buildings, advanced evaluation methods and retrofit strategies are in need. In this paper, we introduced the evolution of seismic performance objectives in China combined with performance-based seismic design. Accordingly, multi-phase evaluation methods and comprehensive seismic capacity assessment are introduced. For buildings with seismic deficiency or higher performance requirements, the retrofit technologies are categorized into three types: component strengthening, system optimization, and passive control. Both engineering property and social property for the retrofit methods are discussed. The traditional seismic retrofit methods usually are costly and disturbing, and for example in Beijing, seismic strengthening costs approx. 1000 RMB/m² (for 160 USD/m²), for hospital building even more expensive as 5000 RMB/m²(for 790 USD/m²). So cost-efficient and little disturbance methods are promising techniques. In the end, some opinions about the retrofit strategy and schemes category are shared and wish to discuss the situation and future of seismic retrofit in China.