• 대한수학회지
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• 제50권6호
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• pp.1349-1367
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• 2013

The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.

• Journal of Korean Neurosurgical Society
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• 제60권2호
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• pp.269-272
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• 2017

We report a patient with a wooden foreign body granuloma in the intervertebral disc space being symptomatic 17 years after a paraspinal penetrant trauma. According to the our result of the search for wooden foreign body granulomas, this is the first case suffered from a wooden foreign body granuloma in the intervertebral disc space that reported in the literature. In this report, we emphasized the importance of rigorous examination and follow up in paraspinal wooden penetrant traumas.

• Structural Engineering and Mechanics
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• 제15권6호
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• pp.735-752
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• 2003

The quasi-static and dynamic responses of a linear viscoelastic circular beam on Winkler foundation are studied numerically by using the mixed finite element method in transformed Laplace-Carson space. This element VCR12 has 12 independent variables. The solution is obtained in transformed space and Schapery, Dubner, Durbin and Maximum Degree of Precision (MDOP) transform techniques are employed for numerical inversion. The performance of the method is presented by several quasi-static and dynamic example problems.

• 호남수학학술지
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• 제24권1호
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.177-195
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• 2021

In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.731-742
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• 2022

In this paper, we present a new mixed type iterative process for approximating the common fixed points of single-valued nonexpansive mapping and multi-valued nonexpansive mapping in a CAT(0) space. We demonstrate strong and weak convergence theorems for the new iterative process in CAT(0) spaces, as well as numerical results to support our theorem.

• 대한수학회보
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• 제44권3호
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• pp.429-438
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• 2007

In this paper, we study the position vectors of a spacelike W-curve (or a helix), i.e., curve with constant curvatures, with spacelike, timelike and null principal normal in the Minkowski 3-space $\mathbb{E}_1^3$. We give some characterizations for spacelike W - curves whose image lies on the pseudohyperbolical space $\mathbb{H}_0^2$ and Lorentzian sphere $\mathbb{S}_1^2$ by using the positions vectors of the curve.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• 대한수학회지
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• 제59권4호
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• pp.651-684
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• 2022

Let G be an arbitrary, connected, simply connected and unimodular Lie group of dimension 3. On the space 𝔐(G) of left-invariant Lorentzian metrics on G, there exists a natural action of the group Aut(G) of automorphisms of G, so it yields an equivalence relation ≃ on 𝔐(G), in the following way: h₁ ≃ h₂ ⇔ h₂ = 𝜙^*(h₁) for some 𝜙 ∈ Aut(G). In this paper a procedure to compute the orbit space Aut(G)/𝔐(G) (so called moduli space of 𝔐(G)) is given.

• 대한수학회지
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• 제61권4호
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.