• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.793-803
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• 2005

In this paper, we study the effectiveness of college mathematics education by counseling freshman. And we discuss the effectiveness that the college mathematics education can be promoted throughout counseling freshman and by teaching examples in engineering mathematics in courses of calculus and differential equation and linear algebra.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.621-629
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• 2008

Let R be a prime ring of characteristic different from 2, C the extended centroid of R, and $\delta$ a generalized derivations of R. If [[$\delta(x)$, x], $\delta(x)$] = 0 for all $x\;{\in}\;R$ then either R is commutative or $\delta(x)\;=\;ax$ for all $x\;{\in}\;R$ and some $a\;{\in}\;C$. We also obtain some related result in case R is a Banach algebra and $\delta$ is either continuous or spectrally bounded.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.233-249
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• 2015

This paper is concerned with applications of representations of the Lie group of class $D_4$ to PDE. A realization of all irreducible finite-dimensional representations of $D_4$ is found and their application to a study of solutions of some systems of partial differential equations is given.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.41-48
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• 1990

Let D' : $C^n$[0, 1] ${\rightarrow}$ M be a second order derivation from the Banach algebra of n times continuously differentiable functions on [0, 1] into a Banach $C^n$[0, 1]-module M and let D be the primitive of D'. If D' is continuous and D'(z) lies in the 1-differential subspace, then it is completely determined by D(z) and D'(z) where z(t)=t, $0{\leq}t{\leq}1$.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.663-677
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• 2022

This present paper extends some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Kannan type mappings. Non-trivial examples are further provided to support the hypotheses of our results.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.11
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• pp.505-513
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• 2001

This paper presents the new three-level optimal control scheme for the large scale nonlinear systems, which is based on fast walsh transform. It is well known that optimization for nonlinear systems leads to the resolution of a nonlinear two point boundary value problem which always requires a numerical iterative technique for their solution. However, Three-level costate coordination can avoid two point boundary condition in subsystem. But this method also has the defect that must solve high order differential equation in intermediate level. The proposed method makes use of fast walsh transform, therefore, is simple in computation because of solving algebra equation instead of differential equation.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.493-510
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• 2010

This paper presents effects of anisotropy and curvature on free vibration characteristics of cross-ply laminated composite cylindrical shallow shells. Shallow shells have been considered for different lamination thickness, radius of curvature and elasticity ratio. First, kinematic relations of strains and deformation have been showed. Then, using Hamilton's principle, governing differential equations have been obtained for a general curved shell. In the next step, stress-strain relation for laminated, cross-ply composite shells has been given. By using some simplifications and assuming Fourier series as a displacement field, differential equations are solved by matrix algebra for shallow shells. The results obtained by this solution have been given tables and graphs. The comparisons made with the literature and finite element program (ANSYS).

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.211-222
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• 2023

In this paper, we study the following hybrid Caputo-Fabrizio fractional differential equation: ^𝐶𝓕_α𝕯^θ_ϑ [ω(ϑ) - 𝕱(ϑ, ω(ϑ))] = 𝕲(ϑ, ω(ϑ)), ϑ ∈ 𝕵 := [a, b], ω(α) = 𝜑_α ∈ ℝ, The result is based on a Dhage fixed point theorem in Banach algebra. Further, an example is provided for the justification of our main result.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.131-155
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• 2015

The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.