• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.269-275
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• 2022

In this note, we verify that the bounded shadowing property and quasi-hyperbolicity of bounded linear operators on Hilbert spaces are preserved under Aluthge transforms.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.139-168
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• 2016

In this work, we rst introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions f(z) in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions f'(z) and $f^{\prime}_m(z)$ are determined by using the coecient estimates.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.359-376
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• 2002

We give a new interpretation of Darboux transforms in the context of orthogonal polynomials and find conditions in or-der for any Darboux transform to yield a new set of orthogonal polynomials. We also discuss connections between Darboux trans-forms and factorization of linear differential operators which have orthogonal polynomial eigenfunctions.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• Smart Structures and Systems
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• v.30 no.1
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• pp.1-15
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• 2022

This article focuses on stability analysis and fuzzy controller synthesis for large neural network (NN) systems consisting of several interconnected subsystems represented by the NN model. Advanced and fuzzy NN differential inclusion (NNDI) for stability based on the developed algorithm with H infinity can be designed based on the evolved biological design. This representation is constructed using sector linearity for NN models. Sector linearity transforms a non-linear model into a linear model based on proposed operations. New sufficient conditions are realized in the form of LMI (linear matrix inequalities) to ensure the asymptotic stability of the trans-Lyapunov function. This transforms the nonlinear model into a linear model based on multiple rules. At last, a numerical case study with simulations is derived as illustration to prove its feasibility in real nonlinear structures.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.967-990
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• 2006

In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.831-836
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• 1994

In this paper we characterize the quasiaffine transforms of quasisubscalar operators. Let H and K be separable, complex Hilbert spaces and L(H,K) denote the space of all linear, bounded operators from H to K. If H = K, we write L(H) in place of L(H,K). A linear bounded operators S on H is called scalar of order m if there is a continuous unital morphism of topological algebras $$ \Phi : C^m_0(C) \to L(H) $$ such that $\Phi(z) = S$, where as usual z stands for identity function on C, and $C^m_0(C)$ stands for the space of compactly supproted functions on C, continuously differentiable of order m, $0 \leq m \leq \infty$.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1785-1801
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• 2008

Noncommutative extensions of the Gross and Beltrami Laplacians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Fourier- Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.1
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• pp.200-220
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• 2016

Orthogonal frequency division multiplexing (OFDM) signals suffer from the problem of large peak-to-average power ratio (PAPR) which complicates the design of the analog front-end of the system. Companding is a well-known PAPR reduction technique that reduces the PAPR by transforming the signal amplitude using a deterministic function. In this paper, a novel piecewise linear companding transform is proposed. The design criteria for the proposed transform is developed by investigating the relationships between the compander and decompander's profile and parameters with the system's performance metrics. Using analysis and simulations, we relate the companding parameters with the bit error rate (BER), out-of-band interference (OBI), amount of companding noise, computational complexity and average power. Based on a set of criteria developed thereof, we formulate the design of the proposed transform. The main aim is to preserve the signal's attributes as much as possible for a predetermined amount of PAPR reduction. Simulations are carried out to evaluate and compare the proposed scheme with the existing companding transforms to demonstrate the enhancement in PAPR, BER and OBI performances.

• Journal of Korean Institute of Industrial Engineers
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• v.5 no.2
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• pp.2-7
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• 1979

The fundamental stochastic duel of Williams and Ancker is combined with the probabilistic linear, square and mixed laws of Brown and Smith when the battle time is limited and interfiring times are continuous. The Probability of a given side's winnig or a draw is derived in a recursive equation with Laplace transforms. Examples with negative exponential firing times are given. In linear law an exact closed form solution is obtained, whereas for square and mixed laws only square ($2{\times}2$) duels are considered.