• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.115-130
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• 2010

Let $\cal{A}$ be a unital Banach algebra. If f : $\cal{A}{\rightarrow}\cal{A}$ is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : $\cal{A}{\rightarrow}\cal{A}$ is anexactly quadratic derivation. On the other hands, let $\cal{A}$ and $\cal{B}$ be Banach algebras.Any approximately generalized homomorphism f : $\cal{A}{\rightarrow}\cal{B}$ corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.101-113
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• 2016

In this article, we considered the stability of the following (${\alpha}$, ${\beta}$, ${\gamma}$)-derivation $${\alpha}D[x,y]={\beta}[D(x),y]+{\gamma}[x,D(y)]$$ and homomorphisms associated to the quadratic type functional equation $$f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A$$, where ${\sigma}$ is an involution of the Lie $C^*$-algebra A and k is a fixed positive integer. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.887-902
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• 2023

In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation f(ax + by) + abf(x - y) = (a + b)(af(x) + bf(y)), where ab ≠ 0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y²] + [x², f(y)] on a 𝜌-complete convex modular *-algebra χ_𝜌 by using ∆₂-condition via convex modular 𝜌.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.893-907
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• 2015

The Hyers-Ulam-Rassias stability of the k-th partial ternary quadratic derivations is investigated in non-Archimedean Banach ternary algebras and non-Archimedean $C^*$-ternary algebras by using the fixed point theorem.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.693-699
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• 2016

The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kummer using a differential equation approach.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.151-163
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• 1998

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws, acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, character and movement state of various quadratic function graph types can be used. Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Then, students understand the mathematical concepts and the correct quadratic function graph correctly. Consquently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the quadratic function graph", which exists in mathematical curriculum the middle school. When this program is used for students, it is expected the following educational effect. 1, Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 2. This program will cause students to form the mathematical concepts correctly. 3. By visualizing the process of drawing the quadratic function graph, students understand the quadratic function graph structually. 4. Through the feedback, the recognition ability of the trigonometric function can be improved. 5. It is possible to change the teacher-centered instruction into the student-centered instruction. For the purpose of increasing the efficiencies and qualities of mathmatics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, tearchers have to use the CIA program carefully.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.45-60
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• 2017

This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal, and comparison analysis between optimal and suboptimal estimators is presented.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.229-240
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• 2002

Whether to use linear or quadratic model in the analysis of regression data is one of the important problems in classical regression model and measurement error model (MEM). In MEM, four goodness of fit test statistics are available In solving that problem. Two are from the derivation of estimators of quadratic MEM, and one is from that of the general $k^{th}$-order polynomial MEM. The fourth one is derived as a variation of goodness of fit test statistic used in linear MEM. The purpose of this paper is to find the most powerful test statistic among them through the small-scale simulation.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.505-514
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• 2008

In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.79-86
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• 1998

The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized. In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of applications to the NEACRP PWR rod ejection benchmark problem.