• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.35 no.1A
• /
• pp.54-61
• /
• 2010

We propose a subspace interference alignment by orthogonalization of reference vectors. The proposed method improves the sum-rate capacity degradation due to the channel decomposition error and channel estimation error in the real environment. Using the proposed method, each cell uses the reference vector that is orthogonal to the adjacent cells. Then the residual interference produced by the channel decomposition error and the channel estimation error is decreased. The simulation results demonstrate that the proposed method achieves the enhanced sum-rate capacity.

• 유체기계공업학회:학술대회논문집
• /
• 2003.12a
• /
• pp.397-403
• /
• 2003

In an attempt to solve multiobjective optimization problems, weighted sum method is most widely used for the advantage that a designer can consider the relative significance of each object functions by weight values but it can be highly sensitive to weight vector and occasionally yield a deviated optimum from the relative weighting values designer designated because the multiobjective function has the form of simple sum of the product of the weighting values and the object functions in traditional approach. To search the design solution well agree to the designer's weighting values, we proposed new multiobjective function which is the functional of each normalized objective functions and considered to find the design solution comparing the distance between the characteristic line and the ideal optimum. In this study, proposed multiobjective function was applied to design high efficiency and low noise axial flow fan and the result shows this approach will be effective for the case that the qualify of the design can be highly affected by the designer's subjectiveness represented as weighting values in multiobjective design optimization process.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.99-107
• /
• 1993

A vector space K with scalar product <.,.> is called a Krein space if it can be decomposed as a northogonal sum of a Hilbert space and an anti-space of a Hilbert space. The space K induces a Hilbert space $K_{J}$ in the inner product <.,.> $K_{J}$=<.,.>K, where $J^{2}$=I. the eigenspaces of J are denoted by $K^{+}$$_{J}$, which is a Hilbert space and $K^{-}$$_{J}$, which is an anti-space of a Hilbert space. Then the Krein space K is the orthogonal sum of $K^{+}$$_{J}$ and $K^{-}$$_{J}$. Such a decomposition of K is called a fundamental decomposition. In general, fundamental decompositions are not unique. The norm of the Hilbert space depends on the choice of a fundamental decomposion, but such norms are equivalent. The topology generated by these norms is called the strong or Mackey topology of K. It is used to define all topological notions on the Krein space K with respect to this topology. The Pontryagin index of a Krein space is the dimension of the antispace of a Hilbert space in any such decomposition. the dimension does not depend on the choice of orthogonal decomposition. A Krein space is called a Pontryagin space if it has finite Pontryagin index.dex.yagin index.dex.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.287-301
• /
• 2011

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$(\ddag)\hspace{50}dk\;f\left(\frac{\sum_{j=1}^{dk}x_j}{dk}\right)=\displaystyle\sum_{j=1}^{dk}f(x_j)$$ if and only if the mapping $f$ : X ${\rightarrow}$ Y is Cauchy additive, and prove the Cauchy-Rassias stability of the functional equation ($\ddag$) in Banach modules over a unital $C^{\ast}$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^{\ast}$-algebras. As an application, we show that every almost homomorphism $h\;:\;\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h((k-1)^nuy)=h((k-1)^nu)h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and $n$ = 0,1,2,$\cdots$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^{\ast}$-algebras.

• Korean Journal of Mathematics
• /
• v.22 no.1
• /
• pp.91-121
• /
• 2014

Let X and Y be vector spaces. It is shown that a mapping $f:X{\rightarrow}Y$ satisfies the functional equation ${\ddag}$ $$2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^jx_j}{2d})-2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^{j+1}x_j}{2d})=2\sum_{j=2}^{2d}(-1)^jf(x_j)$$ if and only if the mapping $f:X{\rightarrow}Y$ is additive, and prove the Cauchy-Rassias stability of the functional equation (${\ddag}$) in Banach modules over a unital $C^*$-algebra, and in Poisson Banach modules over a unital Poisson $C^*$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras. As an application, we show that every almost homomorphism $h:\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h(d^nuy)=h(d^nu)h(y)$ or $h(d^nu{\circ}y)=h(d^nu){\circ}h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and n = 0, 1, 2, ${\cdots}$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras, and of Lie $JC^*$-algebra derivations in Lie $JC^*$-algebras.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.41 no.6
• /
• pp.209-220
• /
• 2004

The main feature of H.264 standard against conventional video standards is the high coding efficiency and the network friendliness. In spite of these outstanding features, it is not easy to implement H.264 codec as a real-time system due to its high requirement of memory bandwidth and intensive computation. Although the variable block size motion compensation using multiple reference frames is one of the key coding tools to bring about its main performance gain, it demands substantial computational complexity due to SAD (Sum of Absolute Difference) calculation among all possible combinations of coding modes to find the best motion vector. For speedup of motion estimation process, therefore, this paper proposes fast algorithms for both integer-pel and fractional-pel motion search. Since many conventional fast integer-pel motion estimation algorithms are not suitable for H.264 having variable motion block sizes, we propose the motion field adaptive search using the hierarchical block structure based on the diamond search applicable to variable motion block sizes. Besides, we also propose fast fractional-pel motion search using small diamond search centered by predictive motion vector based on statistical characteristic of motion vector.

• The Bulletin of The Korean Astronomical Society
• /
• v.42 no.2
• /
• pp.59.5-60
• /
• 2017

We present the relationship between vector magnetic field parameters and solar major flare occurrence rate. Based on this, we are developing a forecast model of major flare (M and X-class) occurrence rate within a day using hourly vector magnetic field data of Space-weather HMI Active Region Patch (SHARP) from May 2010 to April 2017. In order to reduce the projection effect, we use SHARP data whose longitudes are within ${\pm}60$ degrees. We consider six SHARP magnetic parameters (the total unsigned current helicity, the total photospheric magnetic free energy density, the total unsigned vertical current, the absolute value of the net current helicity, the sum of the net current emanating from each polarity, and the total unsigned magnetic flux) with high F-scores as useful predictors of flaring activity from Bobra and Couvidat (2015). We have considered two cases. In case 1, we have divided the data into two sets separated in chronological order. 75% of the data before a given day are used for setting up a flare model and 25% of the data after that day are used for test. In case 2, the data are divided into two sets every year in order to reduce the solar cycle (SC) phase effect. All magnetic parameters are divided into 100 groups to estimate the corresponding flare occurrence rates. The flare identification is determined by using LMSAL flare locations, giving more numbers of flares than the NGDC flare list. Major results are as follows. First, major flare occurrence rates are well correlated with six magnetic parameters. Second, the occurrence rate ranges from 0.001 to 1 for M and X-class flares. Third, the logarithmic values of flaring rates are well approximated by two linear equations with different slopes: steeper one at lower values and lower one at higher values. Fourth, the sum of the net current emanating from each polarity gives the minimum RMS error between observed flare rates and predicted ones. Fifth, the RMS error for case 2, which is taken to reduce SC phase effect, are smaller than those for case 1.

• East Asian mathematical journal
• /
• v.33 no.5
• /
• pp.571-585
• /
• 2017

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigen vectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we showed that a 2-type surface M in $E^3$ satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle},{\rangle}$ is the usual inner product in $E^3$, then M is an open part of a circular cylinder. Also we showed that if a quadric hypersurface M in a Euclidean space satisfies ${\langle}{\Delta}x,x{\rangle}=c$ for a constant c, then it is one of a minimal quadric hypersurface, a genaralized cone, a hypersphere, and a spherical cylinder.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.1
• /
• pp.31-39
• /
• 2015

This paper deals with a method for estimating variance components on the basis of projections under the assumption of random effects model. It discusses how to use projections for getting sums of squares to estimate variance components. The use of projections makes the vector subspace generated by the model matrix to be decomposed into subspaces that are orthogonal each other. To partition the vector space by the model matrix stepwise procedure is used. It is shown that the suggested method is useful for obtaining Type I sum of squares requisite for the ANOVA method.

• Proceedings of the KIEE Conference
• /
• 1995.11a
• /
• pp.502-504
• /
• 1995

In video image compression, it is important to extract the exact notion information from image sequence in order to perform the data compression, the field rate conversion, and the motion compensated interpolation effectively. It is well known that the location of the smallest sum of absolute difference(SAD) does not always give the true motion vector(MV) since the MV obtained via full block search is often corrupted by noise. In this paper, we first classifies the input blocks into 3 categories : the background, the shade-motion, and the edge-motion. According to the characteristics of the classified blocks, multiple locations of relatively small SAD are searched with an adaptive search window by using the proposed method. The proposed method picks MVs among those candidates by using temporal correlation. Since temporal correlation reveals the noise level in a particular region of the video image sequence, we are able to reduce the search are very effectively.