• Journal of Institute of Control, Robotics and Systems
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• v.19 no.6
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• pp.489-494
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• 2013

This paper tackles the problem of designing a dynamic output-feedback control for linear discrete-time norm-bounded uncertain systems with input saturation. By employing a LPV (Linear Parameter Varying) instead of LTI (Linear Time-Invariant) control, the useful information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as a convex polytope is additionally applied in the control design procedure. By solving the addressed problem that can be recast into a convex optimization problem characterized by LMIs (Linear Matrix Inequalities) with one prescribed scalar, the vertices of convex set containing an LPV output-feedback control gain and the associated maximal invariant set of initial states are simultaneously obtained.

• Clinical and Experimental Pediatrics
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• v.53 no.2
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• pp.136-145
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• 2010

Natural killer T (NKT) cell is a special type of T lymphocytes that has both receptor of natural killer (NK) cell (NK1.1, CD161c) and T cell (TCR) and express a conserved or invariant T cell receptor called $V{\alpha}14J{\alpha}18$ in mice or Va24 in humans. Invariant NKT (iNKT) cell recognizes lipid antigen presented by CD1d molecules. Marine-sponge-derived glycolipid, ${\alpha}-galactosylceremide$ (${\alpha}-GalCer$), binds CD1d at the cell surface of antigen-presenting cells and is presented to iNKT cells. Within hours, iNKT cells become activated and start to secrete Interleukin-4 and $interferon-{\gamma}$. NKT cell prevents autoimmune diseases, such as type 1 diabetes, experimental allergic encephalomyelitis, systemic lupus erythematous, inflammatory colitis, and Graves' thyroiditis, by activation with ${\alpha}-GalCer$. In addition, NKT cell is associated with infectious diseases by mycobacteria, leshmania, and virus. Moreover NKT cell is associated with asthma, especially CD4+ iNKT cells. In this review, I will discuss the characteristics of NKT cell and the association with inflammatory diseases, especially asthma.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.1005-1018
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• 2020

A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹ⁿ(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

• The Journal of the Acoustical Society of Korea
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• v.27 no.3E
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• pp.104-111
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• 2008

Recently, a method for robust time reversal focusing has been introduced to extend the period of stable focusing in time-dependent ocean environments [S. Kim et al., J. Acoust. Soc. Am. 114, 145-157, (2003)]. In this study, concept of focal-size broadening based on waveguide invariant theory in an ocean time reversal acoustics is described. It is achieved by imposing the multiple location constraints. The signal vector used in multiple location constraints are found from the theory on waveguide invariant for frequency band corresponding the extended focal range. The broadening of foci in an ocean waveguide can play an important role in the application of time reversal processing, particularly to the underwater acoustic communication with moving vehicles. The proposed method is demonstrated in the context of the underwater acoustic communication from the transmit/receive array (TRA) to a slowly moving vehicle.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.2
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• pp.140-144
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• 2010

In the case of a linear time-varying system, it is difficult to apply the conventional stability conditions of RHC (Receding Horizon Control) to real physical systems because of computational complexity comes from time-varying system and backward Riccati equation. Therefore, in this study, a frozen time RHC for a linear discrete time-varying system is proposed. Since the proposed control law is obtained by time-invariant Riccati equation solved by forward iterations at each control time, its stability can be ensured by matrix inequality condition and the stability condition based on horizon for a time-invariant system, and they can be applied to real physical systems effectively in comparison with the conventional RHC.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.91-107
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• 2021

A bounded linear operator T on a separable infinite dimensional Banach space X is called strongly hypercyclic if $$X{\backslash}\{0\}{\subseteq}{\bigcup_{n=0}^{\infty}}T^n(U)$$ for all nonempty open sets U ⊆ X. We show that if T is strongly hypercyclic, then so are Tn and cT for every n ≥ 2 and each unimodular complex number c. These results are similar to the well known Ansari and León-Müller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem.

• The Journal of the Acoustical Society of Korea
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• v.38 no.2
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• pp.231-239
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• 2019

In sonar systems, the passive ranging of a target is an active research area. This paper analyzed the performance of passive ranging based on an array invariant method for different environmental and sonar parameters. The array invariant developed for source range estimation in shallow water. The advantages of this method are that detailed environmental information is not required, and the real-time ranging is possible since the computational burden is very small. Simulation was performed to verify the algorithm. And this method is applied to sea-going experimental data in 2013 near Jinhae port. This study shows the performance of ranging for source orientation, transmission signal length, and length of a receiver through numerical simulation experiments. Also, the results using nested array and uniform line arrays are compared.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1181-1188
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• 2010

q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.397-408
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• 1998

We often use the Hausdorff dimension as a tool of measuring how complicate the fractal is. But it is usually very difficult to calculate that value. So there have been many tries to find the dimension of the given set and most of these are related to the density theorem of invariant measure. The aims of this paper are to introduce the k-irreducible subsimilar sets as a generalization of the set defined by V.Drobot and J.Turner in ([1]) and calculate their Hausdorff dimensions by using algebraic methods.