• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.10
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• pp.2497-2513
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• 2013

In 2010, Dijk et al. demonstrated a simple somewhat homomorphic encryption (HE) scheme over the integers of which this simplicity came at the cost of a public key size in $\tilde{O}({\lambda}^{10})$. Although in 2011 Coron et al. reduced the public key size to $\tilde{O}({\lambda}^7)$, it is still too large for practical applications, especially for the cloud computing. In this paper, we propose a new form of somewhat HE scheme to reduce further the public key size and a variation of the scheme to optimize the ciphertext size. First of all, we propose a new somewhat HE scheme which is built on the hardness of the approximate greatest common divisor (GCD) problem of two integers, where the public key size in the scheme is reduced to $\tilde{O}({\lambda}^3)$. Furthermore, we can reduce the length of the ciphertext of the new somewhat HE scheme by applying the modular reduction technique. Additionally, we give simulation results for evaluating ability of the proposed scheme.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.49-61
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• 2011

Let D be an integral domain with quotient field K, X be a nonempty set of indeterminates over D, * be a star operation on D, $N_*$={f $\in$ D[X]|c(f)$^*$= D}, $*_w$ be the star operation on D defined by $I^{*_w}$ = ID[X]${_N}_*$ $\cap$ K, and [*] be the star operation on D[X] canonically associated to * as in Theorem 2.1. Let $A^g$ (resp., $A^{[*]g}$, $A^{[*]g}$) be the global (resp.,*-global, [*]-global) transform of a ring A. We show that D is a $*_w$-Noetherian domain if and only if D[X] is a [*]-Noetherian domain. We prove that $D^{*g}$[X]${_N}_*$ = (D[X]${_N}_*$)$^g$ = (D[X])$^{[*]g}$; hence if D is a $*_w$-Noetherian domain, then each ring between D[X]${_N}_*$ and $D^{*g}$[X]${_N}_*$ is a Noetherian domain. Let $\tilde{D}$ = $\cap${$D_P$|P $\in$ $*_w$-Max(D) and htP $\geq$2}. We show that $D\;\subseteq\;\tilde{D}\;\subseteq\;D^{*g}$ and study some properties of $\tilde{D}$ and $D^{*g}$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.717-728
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• 2008

Let H be a real Hilbert space and S = {T(s) : $0\;{\leq}\;s\;<\;{\infty}$} be a nonexpansive semigroup on H such that $F(S)\;{\neq}\;{\emptyset}$ For a contraction f with coefficient 0 < $\alpha$ < 1, a strongly positive bounded linear operator A with coefficient $\bar{\gamma}$ > 0. Let 0 < $\gamma$ < $\frac{\bar{\gamma}}{\alpha}$. It is proved that the sequences {$x_t$} and {$x_n$} generated by the iterative method $$x_t\;=\;t{\gamma}f(x_t)\;+\;(I\;-\;tA){\frac{1}{{\lambda}_t}}\;{\int_0}^{{\lambda}_t}\;T(s){x_t}ds,$$ and $$x_{n+1}\;=\;{\alpha}_n{\gamma}f(x_n)\;+\;(I\;-\;{\alpha}_nA)\frac{1}{t_n}\;{\int_0}^{t_n}\;T(s){x_n}ds,$$ where {t}, {${\alpha}_n$} $\subset$ (0, 1) and {${\lambda}_t$}, {$t_n$} are positive real divergent sequences, converges strongly to a common fixed point $\tilde{x}\;{\in}\;F(S)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)\tilde{x},\;x\;-\;\tilde{x}{\rangle}\;{\leq}\;0$ for $x\;{\in}\;F(S)$.

• Proceedings of the KSRS Conference
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• v.2
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• pp.744-747
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• 2006

The sea level of the Java Sea is reproduced using HYbrid Coordinate Ocean Model (HYCOM) setting up in the horizontal grid from $100^{\circ}E$ to $125^{\circ}E$ and from $10^{\circ}S$ to $8^{\circ}N$. The model is initialized by ocean temperature and salinity profiles from Levitus 1998 and forced by the atmospheric field derived from NCEP reanalysis. In this research HYCOM is applied to explain the El $Ni{\tilde{n}}o$ Southern Oscillation (ENSO) impacts on the sea level of the Java Sea. The monthly tide gauge sea level data are produced based on hourly sea level data from 1993 to 1997. Altimeter sea level data are based on weekly merged products between TOPEX/Poseidon and ERS absolute dynamic topography (ADT). The simulated sea level both HYCOM and ADT agree well with the tide gauge sea level. The sea level of the Java Sea is high during the La $Ni{\tilde{n}}a$ period and low during the El $Ni{\tilde{n}}o$ period.

• Ocean and Polar Research
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• v.37 no.2
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• pp.149-159
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• 2015

The Southern Ocean (SO) plays a primary role in global climate by storing and transporting anthropogenic carbon dioxide through the meridional overturning circulation and the biological pumping process. In this study, we aim to investigate interannual variability of summer chlorophyll concentration in the SO and its relation with the El $Ni{\tilde{n}}o$ Southern Oscillation (ENSO), using satellite ocean color data covering 16 years from 1997 to 2012. During El $Ni{\tilde{n}}o$ periods, chlorophyll concentration tends to increase in the subtropics (north of the subantarctic front). This chlorophyll increase is likely linked to El $Ni{\tilde{n}}o$-induced surface cooling that increases nutrient supply through enhanced vertical mixing in the subtropics. On the other hand, the subpolar gyres show localized chlorophyll changes in response to the ENSO. The localized response seems to be primarily attributed to changes in sea-ice concentrations. Our findings suggest that ENSO contributes interannual variability of chlorophyll in the SO through different mechanisms depending on regions.

• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.741-758
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• 2013

In this study, inelastic displacement ratios are investigated for existing systems with known lateral strength considering soil structure interaction. For this purpose, SDOF systems for period range of 0.1-3.0 s with different hysteretic behaviors are considered for a number of 18 earthquake motions recorded on soft soil. The effect of stiffness degradation on inelastic displacement ratios is investigated. The Modified Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. Soil structure interaction analyses are conducted by means of equivalent fixed base model effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. A new equation is proposed for inelastic displacement ratio of system with SSI with elastoplastic or degrading behavior as a function of structural period ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}$/T). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.813-821
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• 2010

Let G and H be compact connected Lie groups with biinvariant Riemannian metrics g and h respectively, ${\phi}$ a group isomorphism of G onto H, and $E:={\phi}^{-1}TH$ the induced bundle by $\phi$ over the base manifold G of the tangent bundle TH of H. Let ${\nabla}$ and $^H{\nabla}$ be the Levi-Civita connections for the metrics g and h respectively, $\tilde{\nabla}$ the induced connection by the map ${\phi}$ and $^H{\nabla}$. Then, a necessary and sufficient condition for $\tilde{\nabla}$ in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) to be a Yang- Mills connection is the fact that the Levi-Civita connection ${\nabla}$ in the tangent bundle over (G, g) is a Yang- Mills connection. As an application, we get the following: Let ${\psi}$ be an automorphism of a compact connected semisimple Lie group G with the canonical metric g (the metric which is induced by the Killing form of the Lie algebra of G), ${\nabla}$ the Levi-Civita connection for g. Then, the induced connection $\tilde{\nabla}$, by ${\psi}$ and ${\nabla}$, is a Yang-Mills connection in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) over the base manifold (G, g).

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1003-1016
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• 2023

In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection ∇ is not a metric connection. Further, we prove that a totally umbilical SCR-lightlike submanifold of an indefinite Kaehler manifold ${\tilde{M}}$ does not admit any twisted product SCR-lightlike submanifold of the type M_⊥×_ϕM_T, where M_⊥ is a totally real submanifold and MT is a holomorphic submanifold of ${\tilde{M}}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product SCR-lightlike submanifolds of the type M_T×_ϕM_⊥ of an indefinite Kaehler manifold ${\tilde{M}}$, in terms of the gradient of ln ϕ, where ϕ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product SCR-lightlike submanifold in an indefinite Kaehler manifold.

• Journal of Korea Water Resources Association
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• v.38 no.12 s.161
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• pp.985-994
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• 2005

We examined problems of the principal component analysis(PCA), which is able to analyze at the low dimensionality as a methodologv to assess hydrologic time series, and introduced the theory and characteristics of independent component analysis(ICA) that can supplement problems of principal component analysis. We also applied the global sea surface temperature(SST) of the Nino region and assessed the correlation between El $\tilde{n}ino$-Southern Oscillation(ENSO) and SST. The results of examining separation-ability of principal components using mixed signals indicate that the independent component analysis is statistically superior compared to that of the principal component analysis. Finally, we assessed correlation between ENSO and global anomaly SST. The independent component analysis was applied to the $5^{\circ}{\times}5^{\circ}$(latitude and longitude) global anomaly SST in the Nino+3.4 region that is the El $\tilde{n}ino$ observation section. We assessed the correlation with the ENSO years. These results of the analysis show that only one independent component($86\%$) was able to represent the entire behavior and was consistent with the main ENSO years. Finally, we carried out independent component analysis for summer seasonal rainfalls at nine stations and could extract ICs to reflect geographical characteristics. The increasing trend has been shown at IC-1 and IC-2 since 1970s.

• Korean Journal of Agricultural and Forest Meteorology
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• v.14 no.4
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• pp.143-154
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• 2012

As demand of water resources and attentions to changes in climate (e.g., due to ENSO) increase, long/short term prediction of precipitation is getting necessary in water planning. This research evaluated the ability of MM5 to predict precipitation in the Tampa Bay region over 23 year period from 1986 to 2008. Additionally MM5 results were statistically bias-corrected using observation data at 33 stations over the study area using CDF-mapping approach and evaluated comparing to raw results for each ENSO phase (i.e., El Ni$\tilde{n}$o and La Ni$\tilde{n}$a). The bias-corrected model results accurately reproduced the monthly mean point precipitation values. Areal average daily/monthly precipitation predictions estimated using block-kriging algorithm showed fairly high accuracy with mean error of daily precipitation, 0.8 mm and mean error of monthly precipitation, 7.1 mm. The results evaluated according to ENSO phase showed that the accuracy in model output varies with the seasons and ENSO phases. Reasons for low predictions skills and alternatives for simulation improvement are discussed. A comprehensive evaluation including sensitivity to physics schemes, boundary conditions reanalysis products and updating land use maps is suggested to enhance model performance. We believe that the outcome of this research guides to a better implementation of regional climate modeling tools in water management at regional/seasonal scale.