• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.697-711
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• 2017

Let X, Y be real normed vector spaces. We exhibit all the solutions $f:X{\rightarrow}Y$ of the functional equation f(rx + sy) + rsf(x - y) = rf(x) + sf(y) for all $x,y{\in}X$, where r, s are nonzero real numbers satisfying r + s = 1. In particular, if Y is a Banach space, we investigate the Hyers-Ulam stability problem of the equation. We also investigate the Hyers-Ulam stability problem on a restricted domain of the following form ${\Omega}{\cap}\{(x,y){\in}X^2:{\parallel}x{\parallel}+{\parallel}y{\parallel}{\geq}d\}$, where ${\Omega}$ is a rotation of $H{\times}H{\subset}X^2$ and $H^c$ is of the first category. As a consequence, we obtain a measure zero Hyers-Ulam stability of the above equation when $f:\mathbb{R}{\rightarrow}Y$.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.563-574
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• 2017

Let $\mathcal{A}$ be a unital real standard Jordan operator algebra acting on a Hilbert space H of dimension at least 2. We show that every bijection ${\phi}$ on $\mathcal{A}$ satisfying ${\phi}(A^2{\circ}B)={\phi}(A)^2{\circ}{\phi}(B)$ is of the form ${\phi}={\varepsilon}{\psi}$ where ${\psi}$ is an automorphism on $\mathcal{A}$ and ${\varepsilon}{\in}\{-1,1\}$. As a consequence if $\mathcal{A}$ is the real algebra of all self-adjoint operators on a Hilbert space H, then there exists a unitary or conjugate unitary operator U on H such that ${\phi}(A)={\varepsilon}UAU^*$ for all $A{\in}\mathcal{A}$.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.339-352
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• 1994

A sumbanifold M of a quaternionic Kaehlerian manifold $\tilde{M}^m$ of real dimension 4m is called a generic submanifold if the normal space N(M) of M is always mapped into the tangent space T(M) under the action of the quaternionic Kaehlerian structure tensors of the ambient manifold at the same time.The purpose of the present paper is to study generic submanifold of quaternionic Kaehlerian manifold of constant Q-sectional curvature with nonvanishing parallel mean curvature vector. In section 1, we state general formulas on generic submanifolds of a quaternionic Kaehlerian manifold of constant Q-sectional curvature. Section 2 is devoted to the study generic submanifolds with nonvanishing parallel mean curvature vector and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of those results, in section 3, we prove our main theorems. In this paper, the dimension of a manifold will always indicate its real dimension.

• Journal of Positioning, Navigation, and Timing
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• v.11 no.4
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• pp.263-268
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• 2022

Precise Point Positioning-Real Time Kinematic (PPP-RTK) is a high accuracy positioning method that combines RTK and PPP to overcome the limitations on service coverage of RTK and convergence time of PPP. PPP-RTK provides correction data in the form of State Space Representation (SSR), unlike RTK, which provides measurement-based Observation Space Representation (OSR). Due to this, PPP-RTK has an advantage that it can transmit less data than RTK. So, recently, several techniques for PPP-RTK have been proposed. However, in order to utilize PPP-RTK techniques, performance analysis of these in a real environment is essential. In this paper, we implement the local network PPP-RTK and analyze the positioning performance according to the distance within 100 km from the reference station in Korea. As results of experiment, the horizontal and vertical 95% errors of local network PPP-RTK were 6.25 cm and 5.86 cm or less, respectively.

• Korean Institute of Interior Design Journal
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• v.14 no.5 s.52
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• pp.98-105
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• 2005

Through advanced computer technology, our physical environment became a flexible and liquid space that is a multi-functional space structure, hetero-alliance, formless, interactivity. We attempt to interpretate Deleuze's Other geometry as a space designer. Hence first, the aim of this study is to define the meaning of the Other and Other geometry. Second, to extract keywords out of the Other geometry to analyze the work. Third, to analyze the work using the space formative languages(blob, blurring, distortion, folding, layering, lightness, nesting, repetition, shear, transparency, twisting, unfolding, warping, waving, and weaving). The 13 works were selected which have been issued after year 2000 with the focus on liquid space studies. The methods of this study are literature research and contents analysis. The results of the analysis were as follows. First, the source is the Other who is a hidden potentials in the surrounding environment, and this source has the capability of making it part of reality anytime. Other geometry means it is a theory that is comprised of various lines that with the kind of experiences that one has in life. Second, the key words that were extracted from the theory of Deleuze's Other geometry were of (1)hetero-alliance(reflected in a sculptured shape or a fluid abstract form), (2)dis-form(by speculating the user's movements, and combining space elements with external forces), (3)interactivity (information was exchanged real time between the user and his environment where the space took on a sensory institution). Finally, after studying the works using the space formative languages, we found that blob, warping, waving were used externally, and repetition, warping and waving for mostly used internally.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.207-213
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• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2000.11a
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• pp.135-142
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• 2000

The adjusting parameter set which enable control systems to locate on stability limit can be derived from theoretical or trial methods for an existing real system. The data from the results are much available to keep a system in the Proper stability condition even to site engineers who are inexperienced in the control system. In this paper, a general one loop control system was adopted for a model system the process of which was assumed to consist of a time-delay element and a first order-lag element in series. After obtaining the corresponding parameter set for the model system by mathematical procedures, their loci on the parameter space was taken according to frequency change. The parameter set loci of stability limit showed unique pattern, and particularity , the curves on the Kg-Ti parameter space were able to be generalized in the form of, an unique exponential formula. These properties were also compared with the results taken from experimental procedures by Nyquist response method and Ziegler & Nichols method on the time domain, and both results were confirmed to be nearly same.

• Journal of Korean Tunnelling and Underground Space Association
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• v.14 no.2
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• pp.107-116
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• 2012

The experiment was performed to analyze the intersectional ventilation efficiency by intersection structure and Jet Fan in network-form road tunnel. For this, the size of real road tunnel was reduced by 1/45. To apply traffic inertia force when driving, blower fan was used to form an airflow in model tunnel and the intersectional efficiency was also investigated by measuring the speed at local point of the tunnel. To improve the reduction of ventilation caused by the structure character, Jet Fan was installed to optimize ventilation efficiency in tunnel.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2532-2537
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• 2005

FIR(Finite Impulse Response) filter is well known to be ideal for the finite time state-space model, but it requires much computation due to its inherent non-recursive structure especially when the measurement interval grows to a large extent. And often a fixed-lag smoother based on the finite time interval is needed to monitor the soundness of the system model and the measurement model, but the computation burden of FIR-type smoother imposes much restriction of its usage for real-time application. Conventional recursive forms of FIR estimator[1]-[4] could not be used for real time applications, since they are numerically unstable in their recursive equations. To cope with this problem, we suggest a stable recursive form FIR estimator(SRFIR) and its usefulness is demonstrated for designing the real-time fixed-lag smoother on the finite time window through an example of detection of rate bias in the anti-aircraft gun fire control system.

• Proceedings of the Korean Institute of Interior Design Conference
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• 2007.05a
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• pp.227-230
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• 2007

The expansion of open education and the 7th revision of educational curriculum have brought big changes in the school facilities. In response to the integrated curriculum for the first and second grades of elementary school, various plans, such as open classroom, expanded classroom size, and the installation of multi-purpose space, have been attempted. However, such plans have appeared in the form of an open classroom--a uniform spatial composition. As a result, a plan for unit learning space to support the educational curriculum and activities for low grade levels is still insufficient. In the case of advanced countries, a lot of studies on space are being actively conducted to develop the creativity of children and to facilitate free-style learning, and such space is actually applied to a real educational environment. Therefore, this study will analyze the spatial composition of unit learning space for low grade level elementary schools in Korea. From the cases of advanced countries, a more concrete proposal will be suggested to diversify unit learning space for low grade levels.