• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.803-829
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• 1998

We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

• Steel and Composite Structures
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• v.28 no.6
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• pp.671-679
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• 2018

The paper is devoted to the stability analysis of a simply supported five layer sandwich beam. The beam consists of five layers: two metal faces, the metal foam core and two binding layers between faces and the core. The main goal is to elaborate a mathematical and numerical model of this beam. The beam is subjected to an axial compression. The nonlinear hypothesis of deformation of the cross section of the beam is formulated. Based on the Hamilton's principle the system of four stability equations is obtained. This system is approximately solved. Applying the Bubnov-Galerkin's method gives an ordinary differential equation of motion. The equation is then numerically processed. The equilibrium paths for a static and dynamic load are derived and the influence of the binding layers is considered. The main goal of the paper is an analytical description including the influence of binding layers on stability, especially on critical load, static and dynamic paths. Analytical solutions, in particular mathematical model are verified numerically and the results are compared with those obtained in experiments.

• The Korean Journal of Applied Statistics
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• v.21 no.3
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• pp.485-495
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• 2008

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will present explicit pricing formulas for these floating-strike lookback options with flexible monitoring periods. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying asset pays dividends continuously at a rate proportional to its price.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.361-376
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• 2000

Our purpose is to seek that the reachable set of the semilinear system $\frac{d}{dt}x(t){\;}={\;}Ax(t){\;}+{\;}f(t,x(t)){\;}+{\;}Bu(t)$ is equivalent to that of its corresponding to linear system (the case where f=0).Under the assumption that the system of generalized eigenspaces of A is complete, we will show that the reachable set corresponding to the linear system is independent of t in case A generates $C_0-semigroup$. An illustrative example for retarded system with time delay is given in the last section.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.537-549
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• 2006

MAA Digital library Workshop, October 6-8, 2006 was held at the newly completed Carriage House Conference Center at MAA Headquarters. This workshop is designed to inform participants about the Mathematical Sciences Digital Library (MathDL), the new MAA Math Gateway project, and the National Science Digital Library (NSDL) and to enable participants to conduct short sessions publicizing these online resources at MAA Section Meetings. The workshop was conducted by Lang Moore, David Smith, and Eileen McIlvain. Major support is being provided by the National Science Foundation through the National Science Digital Library Program. We introduce what was in there and how we properly use and publicize them and add what we could do.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.99-117
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• 1998

Let $(B, H, p_1)$ be an abstract Wiener space and $F(B)$ the Fresnel class on $(B, H, p_1)$ which consists of functionals F of the form : $$ F(x) = \int_{H} exp{i(h,x)^\sim} df(h), x \in B, $$ where $(\cdot, \cdot)^\sim$ is a stochastic inner product between H and B, and f is in $M(H)$, the space of complex Borel measures on H. We introduce an $L_1$ analytic Fourier-Feynman transforms for functionls in $F(B)$. Furthermore, we introduce a convolution on $F(B)$, and then verify the existence of the $L_1$ analytic Fourier-Feynman transform for the convolution product of two functionals in $F(B)$, and we establish the relationships between the $L_1$ analytic Fourier-Feynman tranform of the convolution product for two functionals in $F(B)$ and the $L_1$ analytic Fourier-Feynman transforms for each functional. Finally, we show that most results in [7] follows from our results in Section 3.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.25-33
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• 2009

Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$, then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$-space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.

• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.11-25
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• 2019

The present paper utilizes auxiliary information to neutralize the effect of non-response for estimating the population mean. Improved ratio type estimators for population mean have been proposed and their properties are studied. These estimators are suggested for both single phase sampling and two phase sampling in presence of non-response. Empirical studies are conducted to validate the theoretical results and demonstrate the performance of the proposed estimators. The proposed estimators are shown to perform better than those used by Cochran (Sampling Techniques (3rd ed), John Wiley & Sons, 1977), Khare and Srivastava (In Proceedings-National Academy Science, India, Section A, 65, 195-203, 1995), Rao (Randomization Approach in Incomplete Data in Sample Surveys, Academic Press, 1983; Survey Methodology 12, 217-230, 1986), and Singh and Kumar (Australian & New Zealand Journal of Statistics, 50, 395-408, 2008; Statistical Papers, 51, 559-582, 2010) under the derived optimality condition. Suitable recommendations are put forward for survey practitioners.

• International Journal of Computer Science & Network Security
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• v.21 no.2
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• pp.88-92
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• 2021

A method and a mathematical algorithm for finding a quasi-optimal assignment plan with rectangular efficiency matrices are proposed. The developed algorithm can significantly reduce the time and computer memory consumption for its implementation in comparison with optimal methods.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.81-96
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• 2014

Now, most of programs developed were presented as form of item pool by dividing problems by section and level for the level differentiated course, so the utilization is decreasing at the field caused by unconsidered school underachievement elements by achievement. Especially, the study on teaching materials and effective measures map for mid-low level students with low utilization is more urgent. Therefore, in this study we will promote teaching method for improving learning achievement at high school. The development teaching materials(the performance evaluation and diagnostic assessment, reconstruction of textbooks) will be applied to classes for the underachieving students directly, and the achievement in the experimental class was significantly improved compared to the comparative class and the meaningful conclusions could be drawn as results of conducting same assessment based on the experimental class and the comparative class.