• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.163-180
• /
• 2016

We study the structure of an arbitrary graded Lie triple system $\mathfrak{T}$ with restrictions neither on the dimension nor the base field. We show that $\mathfrak{T}$ is of the form $\mathfrak{T}=U+\sum_{j}I_j$ with U a linear subspace of the 1-homogeneous component $\mathfrak{T}_1$ and any $I_j$ a well described graded ideal of $\mathfrak{T}$, satisfying $[I_j,\mathfrak{T},I_k]=0$ if $j{\neq}k$. Under mild conditions, the simplicity of $\mathfrak{T}$ is characterized and it is shown that an arbitrary graded Lie triple system $\mathfrak{T}$ is the direct sum of the family of its minimal graded ideals, each one being a simple graded Lie triple system.

• Korean Journal of Mathematics
• /
• v.28 no.3
• /
• pp.613-621
• /
• 2020

In this paper, we investigate the general solution and the Hyers-Ulam stability of n-variable additive functional equation of the form $${\Im}\(\sum\limits_{i=1}^{n}(-1)^{i+1}x_i\)=\sum\limits_{i=1}^{n}(-1)^{i+1}{\Im}(x_i)$$, where n is a positive integer with n ≥ 2, in Banach spaces by using the direct method.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.293-300
• /
• 1995

Let $R = k[y_1,\cdots,y_n] \otimes E[x_1, \cdots, x_n]$ with characteristic $k = p > 2$ (odd prime), where $$\mid$y_i$\mid$ = 2, $\mid$x_i$\mid$ = 1$ and $y_i = \betax_i, \beta$ is the Bockstein homomorphism. Topologically, $R = H^*(B(Z/p)^n,k)$. For a symmetric group $\sum_n, R^{\sum_n} = k[\sigma_1,\cdots,\sigma_n] \otimes E[d\sigma_1, \cdots, d\sigma_n]$ where d is the derivation satisfying $d(y_i) = x_i$ and $d(x_iy_i) = x_iy_i + x_jy_i, 1 \leq i, j \leq n$. We give a direct proof of this theorem by using induction.

• Communications for Statistical Applications and Methods
• /
• v.26 no.2
• /
• pp.175-189
• /
• 2019

The problem of the estimation of quantitative sensitive variable using the item sum technique (IST) on successive occasions has been discussed. IST difference, IST regression, and IST general class of estimators have been proposed to estimate quantitative sensitive variable at the current occasion in two occasion successive sampling. The proposed new estimators have been elaborated under Trappmann et al. (Journal of Survey Statistics and Methodology, 2, 58-77, 2014) as well as Perri et al. (Biometrical Journal, 60, 155-173, 2018) allocation designs to allocate long list and short list samples of IST. The properties of all proposed estimators have been derived including optimum replacement policy. The proposed estimators have been mutually compared under the above mentioned allocation designs. The comparison has also been conducted with a direct method. Numerical applications through empirical as well as simplistic simulation has been used to show how the illustrated IST on successive occasions may venture in practical situations.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.1-13
• /
• 2022

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.19 no.12
• /
• pp.2800-2804
• /
• 2015

Recently, device-to-device (D2D) direct communication is attracting much interest and many researches have been conducted. In this paper, we investigated an algorithm to support the D2D direct communication in cellular mobile communication networks. We investigated the optimal D2D scheduling algorithm which can achieve the maximal sum-rate in cellular uplink frequency. We also proposed a simple scheduling algorithm which can considerably reduce the computational complexity, compared to the optimal scheme. Finally, we analyzed the performance of the proposed scheme based on computer simulations.

• The Journal of the Acoustical Society of Korea
• /
• v.36 no.4
• /
• pp.279-284
• /
• 2017

The localization of sources has a numerous number of applications. To estimate the position of sources, the relative time delay between two or more received signals for the direct signal must be determined. Although the GCC (Generalized Cross-Correlation) method is the most popular technique, an approach based on CCA (Canonical Correlation Analysis) was also proposed for the TDE (Time Delay Estimation). In this paper, we propose a new adaptive algorithm based on CCA in order to utilized the sparsity in the eigenvector of CCA based time delay estimator. The proposed algorithm uses the eigenvector corresponding to the maximum eigenvalue with log-sum regularization in order to utilize the sparsity in the eigenvector. We have performed simulations for several SNR(signal to noise ratio)s, showing that the new CCA based algorithm can estimate the time delays more accurately than the conventional CCA and GCC based TDE algorithms.

• Communications of the Korean Mathematical Society
• /
• v.10 no.1
• /
• pp.109-113
• /
• 1995

For a Hilbert space H, let L(H) denote the algebra of all bounded operators on H. For an $n \in N$, it is well known that any element $T \in L(\oplus^n H)$ is expressed as an $n \times n$ matrix each of whose entries lies in L(H) so that T is written as $$ (1) T = (T_{ij}), i, j = 1, 2, ..., n, T_{ij} \in L(H), $$ where $\oplus^n H$ is the direct sum Hilbert space of n copies of H.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.241-246
• /
• 2007

For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.

• Journal of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.475-491
• /
• 2009

In [2], we identified the group of units of finite local rings $\mathbb{Z}_4[X]$/($X^k+2X^a$, $2X^r$) with certain restrictions on a. In this paper we find direct sum decomposition of the group of units of such rings without restrictions on a into cyclic subgroups by finding their generators. And further generalization is considered.