• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.59-71
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• 2016

To obtain more accurate approximation of the true images in the deblurring problems, the weighted global generalized cross validation(GCV) function to the inverse problem with multiple right-hand sides is suggested as an efficient way to determine the regularization parameter. We analyze the experimental results for many test problems and was able to obtain the globally useful range of the weight when the preconditioned global conjugate gradient linear least squares(Gl-CGLS) method with the weighted global GCV function is applied.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.93-104
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• 2007

It is well known that a suspension bridge may display certain oscillations under external aerodynamic forces. Under the action of a strong wind, in particular, a narrow and very flexible suspension bridge can undergo dangerous oscillations. The collapse of the Tacoma Narrows suspension bridge caused by a wind blowing at a speed of 42 miles per hour, is one of the most striking examples. In this paper, we study models describing oscillations in suspension bridges and known results.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.129-135
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• 2012

The aim of this paper is to establish the well-known and very useful classical Saalsch$\ddot{u}$tz's theorem for the series $_3F_2$(1) by following a different method. In addition to this, two summation formulas closely related to the Saalsch$\ddot{u}$tz's theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series $_3F_2$(1) and $_4F_3(1)$ already available in the literature.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.97-104
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• 1997

The large deviations theorem of Cramer is extended to conditional probabilities in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. The probability that the first falls outside a certain convex set given that the second is fixed is shown to decrease with the sample size at an exponential rate which depends on the Kullback-Leibler distance between two distributions in an associated exponential familiy of distributions. Examples are given which include a method of computing the Bahadur exact slope for tests of certain composite hypotheses in exponential families.

• East Asian mathematical journal
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• v.36 no.2
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• pp.291-315
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• 2020

In this study, the geometric model of 11 factorization formulas presented in the 2015 revised national curriculum was constructed and the necessary mathematical conditions were derived in the process. As a result of the study, all of the 11 factorization formulas are geometrically modeled and 12 conditions are derived in the process. However, the basic method of directly cutting and attaching a given shape was limited to not being able to make a rectangle or rectangular parallelepiped. Therefore, the problem was solved by changing the perspective and focusing on whether rectangle or rectangular parallelepiped with the same area or volume could be constructed.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.243-251
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• 2017

In this paper, we solve the additive ${\rho}-functional$ equations (0.1) $f(x+y)+f(x-y)-2f(x)={\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x))$, and (0.2) $2f(\frac{x+y}{2})+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$, where ${\rho}$ is a fixed (complex) number with ${\rho}{\neq}1$, Using the direct method, we prove the Hyers-Ulam stability of the additive ${\rho}-functional$ equations (0.1) and (0.2) in ${\beta}-homogeneous$ (complex) F-spaces.

• Journal of Korea Society of Industrial Information Systems
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• v.7 no.1
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• pp.75-80
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• 2002

We investigate sorry: asymptotic stabilities of the zero solution for the perturbed linear differential system dx/dt=A(t)x+e(t, x)+f(t,x), by using Perron's method and integral inequalities, etc. and we also find some sufficient conditions that ensure some asymptotic stabilities of the zero solution of the system And hence we obtain several results of it.

• School Mathematics
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• v.10 no.4
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• pp.625-648
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• 2008

We collected the data through the following process. 36 third-grade middle school students are selected, and we conducted ex-ante interviews for researching how they understand the nature of proof. Based on the results of survey, then we chose two students we took a lesson with the Branford's among the 36 samples. After sampling, historic-genetic geometry education, inspected carefully whether the Branford's method helps the students.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.73-78
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• 1998

Let $H_1$ ($\Delta$, M) be the family of all 1-1 holomorphic mappings of the unit disk $\Delta\; \subset\; C$ into a complex manifold M. Following the method of Royden, Hahn introduces a new pseudo-differential metric $S_{M}$ on M. The present paper is to study the product property of the metric $S_{M}$ when M is given by the product of two domains $D_1$ and $D_2$ in the complex plane C, thus investigating the hyperbolicity of the product domain $D_1 \;\times\; D_2$ with respect to $S_{M}$ metric.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.