• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.525-538
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• 1998

Recently, a stability theorem for the Feynman integral as a bounded linear operator on$ L_2$($R^{d}$ /) with respect to measures whose positive and negative variations are in the generalized Kato class was proved. We study a stability theorem for the Feynman integral with respect to measures whose positive variations are in the class of $\sigma$-finite smooth measures and negative variations are in the generalized Kato class. This extends the recent result in the sense that the class of $\sigma$-finite smooth measures properly contains the generalized Kato class.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.2995-3006
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• 1993

An automatic mesh generation scheme has been developed for finite element analysis with two-dimensional, quadrilateral elements. The basic strategies of the method are to transform the analysis domain into loops with key nodes and the loops are recursively subdivided into subloops with the use of best split lines. Finally by using the basic loop operators, the meshes are completed. In this algorithm an eight-node loop operator is proposed, which is useful in the area where the change of element size is large and the splitting criteria for subdividing the loops have also been modified to the existing algorithms. Lines, arcs, and cubic spline curves are used to define the boundaries of analysis domain. Sample meshes for several geometries are presented to demonstrate the robustness of the algorithm.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.549-565
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• 2016

A Hilbert space operator $T{\in}{\mathfrak{B}}(\mathfrak{H})$ is said to be n-*-paranormal, $T{\in}C(n)$ for short, if ${\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}$ for all $x{\in}{\mathfrak{H}}$. We proved some properties of class C(n) and we proved an asymmetric Putnam-Fuglede theorem for n-*-paranormal. Also, we study some invariants of Weyl type theorems. Moreover, we will prove that a class n-* paranormal operator is finite and it remains invariant under compact perturbation and some orthogonality results will be given.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.627-645
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• 2007

We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by $L_vu\;:=-{\Delta}u+a(x,\;y)u_x+b(x,\;y)u_y+d(x,\;y)u$, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator $L_cu$ is constructed by using the leading term of $L_vu$ plus the constant reaction term such that $L_cu\;:=-{\Delta}u+d_cu$. Using the field of values arguments, we show that the eigenvalues of the preconditioned matrix are clustered at some number. Some numerical evidences are also provided.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

• Coupled systems mechanics
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• v.8 no.2
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• pp.147-168
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• 2019

This work aims to simulate three-dimensional heavy oil flow in a reservoir with heater-wells. Mass, momentum and energy balances, as well as correlations for rock and fluid properties, are used to obtain non-linear partial differential equations for the fluid pressure and temperature, and for the rock temperature. Heat transfer is simulated using a two-equation model that is more appropriate when fluid and rock have very different thermal properties, and we also perform comparisons between one- and two-equation models. The governing equations are discretized using the Finite Volume Method. For the numerical solution, we apply a linearization and an operator splitting. As a consequence, three algebraic subsystems of linearized equations are solved using the Conjugate Gradient Method. The results obtained show the suitability of the numerical method and the technical feasibility of heating the reservoir with static equipment.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.53-56
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• 2002

Suppose { $X_{n}$}$_{n=1}$$^{\infty}$ sequence of finite dimensional Banach spaces and suppose that X is either a closed subspace of (equation omitted) or a closed subspace of (equation omitted) with p>2. We show that every bounded linear operator from X to a Banach space Y of cotype q(2$\leq$q〈p) is compact.t.t.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.711-722
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• 2016

We study Toeplitz operators $T_{\nu}$ on generalized Fock spaces $F^2_{\phi}$ with a locally finite positive Borel measures ${\nu}$ as symbols. We characterize operator-theoretic properties (boundedness and compactness) of $T_{\nu}$ in terms of the Fock-Carleson measure and the Berezin transform ${\tilde{\nu}}$.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.363-372
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• 2010

In this paper, we introduce and study the generalized inverse $A^{(1,2)}_{T,S}$ with the prescribed range T and null space S of an adjointable operator A from one Hilbert $C^*$-module to another, and get some analogous results known for finite matrices over the complex field or associated rings, and the Hilbert space operators.