• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.31-39
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• 2011

Stone's theorem states that "A bounded linear operator A is infinitesimal generator of a $C_0$-group of unitary operators on a Hilbert space H if and only if iA is self adjoint". In this paper we establish a generalization of Stone's theorem in the framework of Hilbert $C^*$-modules.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.126-129
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• 2002

An intelligent digital redesign technique (IDR) for the observer-based output feedback Takagi-Sugeno (T-5) fuzzy control system with fuzzy outputs is developed. The considered IDR condition is cubically parameterized as convex minimization problems of the norm distances between linear operators to be matched.'rho stability condition is easily embedded and the separations principle is explicitly shown.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2628-2630
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• 2001

This paper developed a 3D inspection system. The system consists of two parts : one includes hardwares such as actuators, linear scales and a probe, etc. the other involves softwares for management and control of the system. Compared with existing 3D measurement systems, this system achieved automatically the inspection. This automatic inspection makes the system have some advantages to reduce a measurement time and to be easily used by operators.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.7
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• pp.1556-1562
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• 2003

In this paper, a new representations of extended threshold Boolean filter(ETBF), called SA filter, is introduced. The structure of this representations is a one of multistage filters. The first stage is subfilters of nonlinear filters such as maximum, minimum, or exclusive-OR operators. The second stage is linear combination of Int stage outputs. Although the structure of this representations is very similar to SAM filters, SA filters encampass all ETBF not subset of ETBF.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.3070-3072
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• 1999

We developed an automatic 3D inspection system. The system consists of two parts : one includes hardwares such as actuators, linear scales and a probe, etc. the other involves softwares for management and control of the system. Compared with existing 3D measurement systems, this system achieved automatically the inspection. This automatic inspection makes the system have some advantages to reduce a measurement time and to be easily used by operators.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.109-115
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• 1993

In 1940 Eidelheit showed that every homomorphism of a Banach algebra onto the Banach algebra B(X) of all bounded linear operators on a Banach space X is continuous. At about the same time, Gelfand proved that every homomorphism of a commutative Banach algebra into a commutative semi-simple Banach algebra is continuous. In [7] Johnson proved that every homomorphism of a Banach algebra onto non-commutative semi-simple Banach algebra is continuous, and this is still the most important result of this type. In this paper we are concerned with continuity of derivations on commutative Banach algebras and of homomorphisms into commutative Banach algebras. Throughout this paper we suppose that A is a commutative Banach algebra. R will denote the redical of A.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.117-123
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• 2009

This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ${\ell}^2$; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that $MM^*=M^*PM$ for some positive operator P on ${\ell}^2$; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint $M^*$ to be posinormal, and it is observed that, unless M is essentially trivial, $M^*$ cannot be hyponormal. A few examples are considered that exhibit special behavior.

• Journal of Information Processing Systems
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• v.10 no.2
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• pp.223-239
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• 2014

New IIR digital differintegrators (differentiator and integrator) with very minor absolute relative errors are presented in this paper. The digital integrator is designed by interpolating some of the existing integrators. The optimum value of the interpolation ratio is obtained through linear programming optimization. Subsequently, by modifying the transfer function of the proposed integrator appropriately, new digital differentiator is obtained. Simulation results demonstrate that the proposed differintegrator are a more accurate approximation of ideal ones, than the existing differintegrators. Furthermore, the proposed differentiator has been tested in an image processing application. Edges characterize boundaries and are, therefore, a problem of fundamental importance in image processing. For comparison purpose Prewitt, Sobel, Roberts, Canny, Laplacian of Gaussian (LOG), Zerocross operators were used and their results are displayed. The results of edge detection by some of the existing differentiators are also provided. The simulation results have shown the superiority of the proposed approach over existing ones.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.301-314
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• 2019

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.