• 대한수학회보
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• 제57권3호
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• pp.661-676
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• 2020

To understand the interaction of a fluid and a rigid body, we use the concept of B-evolution. Then in a similar way to the usual Navier-Stokes system, we obtain a Helmholtz type decomposition. Using B-evolution theory and the decomposition, we work on the semigroup to analyze the linear part of the system.

• 대한수학회논문집
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• 제9권2호
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• pp.317-325
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• 1994

Suppose X is a complex Banach space and write B(X) for the Banach algebra of bounded linear operators on X, X＊ for the dual space of X, and T＊$\in$ B(X＊) for the dual operator of T. For T $\in$ B(X) write a(T) = dim T$^{-1}$ (0) and $\beta$(T) = codim T(X).(omitted)

• 대한수학회보
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• 제34권1호
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• pp.19-28
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• 1997

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 $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

• 대한수학회지
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• 제45권1호
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• pp.205-219
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• 2008

It is shown that if $A{\geq}0$ and T are two bounded linear operators on a complex Hilbert space H satisfying the inequality $T^*\;AT{\leq}A$ and the condition $AT=A^{1/2}TA^{1/2}$, then there exists the maximum reducing subspace for A and $A^{1/2}T$ on which the equality $T^*\;AT=A$ is satisfied. We concretely express this subspace in two ways, and as applications, we derive certain decompositions for quasinormal contractions. Also, some facts concerning the quasi-isometries are obtained.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.713-723
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• 2009

The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.213-230
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• 2002

We deal with the approximate controllability for semilinear systems with time delay in a Hilbert space. First, we show the existence and uniqueness of solutions of the given systems with the mere general Lipschitz continuity of nonlinear operator f from $R\;\times\;V$ to H. Thereafter, it is shown that the equivalence between the reachable set of the semilinear system and that of its corresponding linear system. Finally, we make a practical application of the conditions to the system with only discrete delay.

• 호남수학학술지
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• 제8권1호
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• pp.21-49
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• 1986

A class of singular quadratic control problem is considered. The state is governed by a higher order system of ordinary linear differential equations and very general nonstandard boundary conditions. These conditions in many important cases reduce to standard boundary conditions and because of the conditions the usual controllability condition is not needed. In the special case where the coefficient matrix of the control variable in the cost functional is a time-independent singular matrix, the corresponding optimal control law as well as the optimal controller are computed. The method of investigation is based on the theory of least-squares solutions of multi-valued operator equations.

• East Asian mathematical journal
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• 제27권3호
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• pp.299-308
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• 2011

The purpose of the present paper is to obtain some subordination and superordination preserving properties involving a certain family of multiplier transformations for meromorphic functions in the open unit disk. The sandwich-type theorems for these linear operators are also considered.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.65-77
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• 2006

By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping $$\sum_{i,j=1}^{N}D_i[a_{ij}(x)D_iy]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0$$ are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.