• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.557-564
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• 2010

By using an idea of C$\u{a}$dariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form $f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}$ given by f(x, y) = $ax^2\;+\;by^2$ is a solution of the above functional equation.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1996.10a
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• pp.14-14
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• 1996

In order to understand the tidal hydrodynamics of the Yellow Sea and Parts of the East China Sea, we have developed a three-dimensional, fine resolution, nonlinear, harmonic finite element model. Major four tidal constituents, M$_2$, S$_2$, K$_1$ and O$_1$ are used as forcing along the open boundary. Due to the shallowness of the region, tidal results are strongly affected by the bottom roughness coefficients, especially for the quadratic form. (omitted)

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.167-182
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• 2018

In this paper, we prove the optimal inequalities for the generalized normalized ${\delta}$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (${\kappa},{\mu}$)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.218-223
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• 1997

The technique used is the active structural acoutrol (ASAC)approach which involves controlling the acoustic response of a panel-cavity covpled system by applying oscillating force inputs in the form of prezoelectric actuators directly to the flexible panel. The linear quadratic Gaussian control scheme is used for attenuating nosie inside the rectangular enclosure causing by flexible wall vibration. Results indicated the application of control inputs to the radiating wall resukted in considerable noise reductions inside the cavity. Auso,the possibility of application to the more complicated fluid-structure coupled system is verified.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.521-537
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• 1994

We consider the Schrodinger equation of quantum mechanics $$ i\hbar\frac{\partial t}{\partial}\Gamma(t, \vec{\eta}) = -\frac{2m}{\hbar}\Delta(t, \vec{\eta}) + V(\vec{\eta}\Gamma(t, \vec{\eta}) (1.1) $$ $$ \Gamma(0, \vec{\eta}) = \psi(\vec{\eta}), \vec{\eta} \in R^n $$ where $\Delta$ is the Laplacian on $R^n$, $\hbar$ is Plank's constant and V is a suitable potential.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.195-205
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• 2004

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

• The Korean Journal of Applied Statistics
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• v.5 no.1
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• pp.29-39
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• 1992

A testing and estimation procedure is considered for changes at unknown time point in simple linear regression model. A test statistic of quadratic form is suggested. We also discuss the asymptotic distribution and its level control. The proposed method is compared with the likelihood ratio test through a example.

• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.637-644
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• 2001

We investigated two kinds of mean square error (MSE) estimator of homogeneous linear estimator (HLE) for the population total under stratified multi-stage sampling. One is studied when the second stage variance component is estimable and the other is found in cafe it is not estimable. The proposed estimators are necessary forms of non-negative unbiased MSE estimators of HLE.

• International Journal of Control, Automation, and Systems
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• v.4 no.3
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• pp.281-292
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• 2006

The design and implementation of Generalized Minimum Variance control laws for nonlinear multivariable systems that can include severe nonlinearities is considered. The quadratic cost index minimised involves dynamically weighted error and nonlinear control signal costing terms. The aim here is to show the controller obtained is simple to design and implement. The features of the control law are explored. The controller obtained includes an internal model of the process and in one form is a nonlinear version of the Smith Predictor.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.175-179
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• 2013

In this note, we show that every linear BCI-algebra (X; *, $e$), $e{\in}X$, has of the form $x*y=x-y+e$ where $x,\;y{\in}X$, where X is a field with $\left|X\right|{\geq}3$.