• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1215-1235
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• 2022

In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.473-482
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• 2015

Let Qf be the maximal derivative of f with respect to the Bergman metric $b_B$. In this paper, we will find conditions such that $(1-{\parallel}z{\parallel})^s(Qf)^p(z)$ is bounded on B. We will also find conditions such that Bergman projection type operator $P_r$ is bounded operator from $L^p(B,d{\mu}_r)$ to the holomorphic Besov p-space Bs $B^s_p(B)$ with weight s.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.65-74
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• 2006

In this paper, we will define the Bergman projection type operator Pr and find conditions on which the operator Pr is bound-ed on $L^p$(B, dv). By using the properties of the Bergman projection type operator Pr, we will show that if $f{\in}L_a^p$(B, dv), then $(1-{\parallel}{\omega}{\parallel}^2){\nabla}f(\omega){\cdot}z{\in}L^p(B,dv)$. We will also show that if $(1-{\parallel}{\omega}{\parallel}^2)\; \frac{{\nabla}f(\omega){\cdot}z}{},\;{\in}L^p{B,\;dv),\;then\;f{\in}L_a^p(B,\;dv)$.

• Journal of Power System Engineering
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• v.21 no.4
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• pp.42-50
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• 2017

A velocity controller using a modified model reference adaptive controller (M-MRAC) and a projection operator for a fish sorting belt conveyor system with uncertainty parameters, input saturation and bounded disturbances is proposed in this paper. To improve the tracking performance and robustness of the proposed controller in the presence of bounded disturbances, the followings are done. Firstly, the reference model for the conventional model reference adaptive controller (CMRAC) is replaced by a modified reference model for a M-MRAC to reduce unexpected high frequency oscillation in control input signal when the adaptation rate is increased. Secondly, estimated parameters in an adaptive law are varied smoothly under bounded external disturbances and a projection operator is utilized in an adaptive law for the proposed M-MRAC controller to be robust. Thirdly, an auxiliary error vector is introduced for compensating the error dynamics of the system when the saturation input occurs. Finally, the experimental results are shown to verify the better effectiveness and performance of the proposed controller under the bounded disturbance and saturated input than that of a CMRAC.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.241-246
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• 2013

Choi [1] identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. In this note, we define the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. We show the martingale property on this operator and measure. Also we conclude that the martingale problem for diffusion operator of projection is well-posed.

• Journal of the Korean Chemical Society
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• v.21 no.5
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• pp.362-371
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• 1977

In this paper application of the projection operator technique to the study of NMR absorption line shape and free induction decay curve is explored. It is found that the projection operator technique can provide a convenient means for deriving a set of hierarchy equations which may serve as a good starting point for theoretical calculation of the absorption line and free induction decay function by successive approximation or by an appropriate decoupling approximation. A brief review of linear response theory of NMR line shape and the relation between the absorption line shape and free induction decay function are also described.

• Nuclear Engineering and Technology
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• v.50 no.5
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• pp.698-708
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• 2018

This article introduces a methodology of designing a wavelet operator suitable for multiscale modeling. The operator matrix transforms states of a multivariable system onto projection space. In addition, it imposes a specific structure on the system matrix in a multiscale environment. To be specific, the article deals with a diagonalizing transform that is useful for decoupled control of a system. It establishes that there exists a definite relationship between the model in the measurement space and that in the projection space. Methodology for deriving the multirate perfect reconstruction filter bank, associated with the wavelet operator, is presented. The efficacy of the proposed technique is demonstrated by modeling the point kinetics nuclear reactor. The outcome of the multiscale modeling approach is compared with that in the single-scale approach to bring out the advantage of the proposed method.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• Journal of Magnetics
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• v.16 no.2
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• pp.108-113
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• 2011

The electron spin resonance lineshape (ESRLS) function for the electron spin resonance linewidth (ESRLW) of $Cr^{3+}$ (S = 3/2) in ferroelectric lithium niobate single crystals doped with 0.05 wt% of Cr, is obtained by using the projection operator technique (POT), developed by Argyres and Sigel. The ESRLS function is calculated to be axially symmetric about the c - axis and analyzed by using the spin Hamiltonian $H_{SP}={\mu}_B(B{\cdot}{^\leftrightarrow_{g}}{\cdot}S)+S{\cdot}{^\leftrightarrow_{D}}{\cdot}S$ with the parameters g = 1.972 and D = $0.395\;cm^{-1}$. In the ca plane, the linewidths show a strong angular dependence, whereas in the ab plane, they are independent of the angle. This result implies that the resonance center has an axial symmetry along the c - axis. Further, from the temperature dependence of the linewidths that is shown, it can be seen that the linewidths increase as the temperature increases, at a frequency of v = 9.27GHz. This result implies that the scattering effect increases with increasing temperature. Thus, the POT is considered to be more convenient to explain the scattering mechanism as in the case of other optical resonant systems.