• Journal of the Korean Society for Precision Engineering
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• v.32 no.3
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• pp.253-261
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• 2015

A parallel mechanism with redundancy can be regarded as a means for not only maximizing the benefits of parallel mechanisms but also overcoming their drawbacks. We proposed a novel parallel mechanism by eliminating an unnecessary degree of freedom of the configuration space. Because of redundancy, however, the solution for the inverse kinematics of the developed parallel mechanism is infinite. Therefore, we defined a cost function that can minimize the movement time to the target orientation and found the solution for the inverse kinematics by using a numerical method. In addition, we proposed a method for determining the boundary of the geometric singularity in order to avoid singularities.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.11-17
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• 1989

In [1], Johnson and Lapidus introduced a family { $A_{t}$ :t>0} of Banach algebras of functionals on Wiener space and showed that for every F in $A_{t}$ , the analytic operator-valued function space integral $K_{\lambda}$$^{t}$ (F) exists for all nonzero complex numbers .lambda. with nonnegative real part. In [2,3] Johnson and Lapidus introduced a noncommtative multiplication having the property that if F.mem. $A_{t}$ $_{1}$ and G.mem. $A_{t}$ $_{2}$ then $F^{*}$G.mem. A$t_{1}$+$_{t}$ $_{2}$ and (Fig.) Note that for F, G in $A_{t}$ , $F^{*}$G is not in $A_{t}$ but rather is in $A_{2t}$ and so the multiplication * is not internal to the Banach algebra $A_{t}$ . In this paper we introduce an internal noncommutative multiplication on $A_{t}$ having the property that for F, G in $A_{t}$ , F G is in $A_{t}$ and (Fig.) for all nonzero .lambda. with nonnegative real part. Thus is an auxiliary binary operator on $A_{t}$ .TEX> .

• School Mathematics
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• v.17 no.1
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• pp.19-33
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• 2015

This study examined mathematics class using the CAS(Computer Algebra Systems, CAS) targeted for high school first grade students. We examined what kind of transforming of representations got up according to mathematics subject contents at this classroom. This study analyzed 15 math lessons during one month and the focus of analysis was on the classroom teacher. In particular, for transformations among representations this study mainly investigated from theoretical frameworks such as transparent and opaque representation of Lesh, Behr & Post(1987), descriptive and depictive representation of Kosslyn(1994). According to the results of this study, CAS technology affected the transforming of representations in high school math class and this transforming of representations improved the students' thinking and understanding of mathematical concepts and provided the opportunity to create the representation of individual student. Such results of this study suggest the importance of CAS technology's role in transforming of representations. and they offer the chance to reconsider the fact that CAS technology could be used to improve students' ability of transforming representations at the mathematics class.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1297-1303
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• 2015

We study Samelson products on models of function spaces. Given a map $f:X{\rightarrow}Y$ between 1-connected spaces and its Quillen model ${\mathbb{L}}(f):{\mathbb{L}}(V){\rightarrow}{\mathbb{L}}(W)$, there is an isomorphism of graded vector spaces ${\Theta}:H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W))){\rightarrow}H_*({\mathbb{L}}(W){\oplus}Der({\mathbb{L}}(V),{\mathbb{L}}(W)))$. We define a Samelson product on $H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W)))$.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.437-456
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• 2003

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.499-510
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• 2009

For a Borel function ${\psi}:\mathbb{R}{\times}\mathbb{R}{\rightarrow}\mathbb{R}$ satisfying the functional equation $\psi$ (s + t, u + v) + $\psi$(s - t, u - v) = $2\psi$(s, u) + $2\psi$(t, v), we show that it satisfies the functional equation $$\psi$$(s, t) = s(s - t)$$\psi$$(1, 0) + $$st\psi$$(1, 1) + t(t - s)$$\psi$$(0, 1). Using this, we prove the stability of the functional equation f(ax + ay, bz + bw) + f(ax - ay, bz - bw) = 2abf(x, z) + 2abf(y,w) in Banach modules over a unital $C^*$-algebra.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.569-608
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• 1994

The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

• The Journal of Korean Association of Computer Education
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• v.15 no.1
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• pp.65-72
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• 2012

Generally, a logic function has many factored forms. The problem of finding more compact factored form is one of the basic operations in logic synthesis. In this paper, we present a new method for factoring Boolean functions to assist in educational logic designs. Our method for factorization is to implement two-cube Boolean division with supports of an expression. The number of literals in a factored form is a good estimate of the complexity of a logic function. Our empirical evaluation shows the improvements in literal counts over previous other factorization methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.81-90
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• 1993

The optimum design of a structure requires the determination of the economical member size and shape of the structure which satisfies the design condition and function. In this study, the process of design automatization of three-dimensional truss structure introduces the optimization technique tests its application in the design automatization, proposes its application method and applies the example structure of the parabolic antenna truss. Using the Formex Algebra of configuration function, the structure's mesh-generation is automatized. By using the program developed in this study, the input member array, member size and load condition designer can generate the input data file for the structure analysis and optimum design. This study is aimed at the development of a design automatization system that search for tile optimum value of a structure design by observing the structure's sensitivity from the modification of member array and member property.