• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.655-656
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• 2008

This research presents a topology optimization to minimize eddy current loss maintaining mechanical robustness of structure part in electrical machines A design sensitivity equation for the topology optimization is derived by employing the discrete system equations combined with the adjoint variable method. As a numerical example, frame design of a C-core actuator is performed by the proposed method.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.405-435
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• 2017

We deal with a sensitivity analysis of an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. By using the material derivative method and adjoint variables for a shape sensitivity analysis, we derive the shape gradient of the design functional for the model problem.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.669-670
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• 1994

Let $E \to M$ be a hermitian holomorphic vector bundle over a compact (complex) hermitian manifold M of complex dimension n, and let $$ d"_p(E) : 0 \to A^{p,0}(E) \to A^{p,1}(E) \to \cdots \to A^{p,n}(E) \to 0$$ be the Dolbeault complex. Then $A^{p,q}(E)$ become a prehibert space so that the formal adjoint $\delta"$ of $d"$ and the "Laplacian" $\Delta" = \delta" d" + d" \delta"$ are defined.quot; d" + d" \delta"$ are defined.;$ are defined.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.527-544
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• 1999

The generalized Hardie-Jansen product and its dual are defined and the fundamental results on these products are obtained. By studying the adjoint maps, we give proofs to them. Moreover we characterize the generalized Hardie-jansen product making use of the ${\Gamma}W$-Whitehead product. We also obtain a characterization of the dual of the generalized Hardie-Jansen product using $({\Gamma}W)$-Whitehead product.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1249-1269
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• 2018

This paper provides a method to study the nonnegativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and nonnegative, we can study the complex powers using an appropriate locally convex space. In this case, the initial operator also will be nonnegative and we will be able to study its powers. In particular, we have applied this method to Bessel-type operators.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.3B no.2
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• pp.79-83
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• 2003

The topology optimization for the magnet design is studied. The magnet design in the C-core actuator is investigated by using the derived topology optimization algorithm and finite element method. The design sensitivity equation for the topology optimization is derived using the adjoint variable method and the continuum approach.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.35-41
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• 1995

We consider the linear differential equations y〃'＋ P($\chi$)y'＋Q($\chi$)y=0 (1)(y"＋P($\chi$)y)'-Q($\chi$)y =0 (2) Where (2) in the adjoint of (1) and P($\chi$), Q($\chi$) are continuous functions satisfying P($\chi$)$\geq$0, Q($\chi$)$\leq$0, P($\chi$)-Q($\chi$)$\geq$0 on [a, ${\alpha}$). (3) In this, we show that a condition a oscillatory of(1).(omitted)

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.6
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• pp.1020-1026
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• 1994

This paper presents a technique to optimize the shape of waveguide components in H-plane. The technique utilizes the numerical optimization process which employs the vector finite element method. In the optimization process, the sensitivity of an objective function with respect to design variables is computed by introducting adjoint variables, which makes the computation easy. The steepest descent method is then employed to update design variables. As a numerical example, an H-plane waveguide teejunction was considered to obtain optimized shape. Comparison between the initial and optimized shape was made.