• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....

• 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.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.380-392
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• 2000

This paper proposes a qualitative reasoning approach for the spatial configuration of mechanisms that could be applied in the early phase of the conceptual design. The spatial configuration problem addressed in this paper involves the relative direction and position between the input and output motion, and the orientation of the constituent primitive mechanisms of a mechanism. The knowledge of spatial configuration of a primitive mechanism is represented in a matrix form called spatial configuration matrix. This matrix provides a compact and convenient representation scheme for the spatial knowledge, and facilitates the manipulation of the relevant spatial knowledge. Using this spatial knowledge of the constituent primitive mechanisms, the overall configuration of a mechanism is described and identified by a spatial configuration state matrix. This matrix is obtained by using a qualitative reasoning method based on sign algebra and is used to represent the qualitative behavior of the mechanism. The matrix-based representation scheme allows handling the involved spatial knowledge simultaneously and the proposed reasoning method enables the designer to predict the spatial behavior of a mechanism without knowing specific dimension of the components of the mechanism.

• Management Science and Financial Engineering
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• v.14 no.1
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• pp.23-34
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• 2008

In this study, we consider stationary waiting times in a Poisson driven single-server m-node queues in series. We assume that service times at nodes are independent, and are either deterministic or non-overlapped. Each node excluding the first node has a finite waiting line and every node is operated under a FIFO service discipline and a communication blocking policy (blocking before service). By applying (max, +)-algebra to a corresponding stochastic event graph, a special case of timed Petri nets, we derive the explicit expressions for stationary waiting times at all areas, which are functions of finite buffer capacities. These expressions allow us to compute the performance measures of interest such as mean, higher moments, or tail probability of waiting time. Moreover, as applications of these results, we introduce optimization problems which determine either the biggest arrival rate or the smallest buffer capacities satisfying probabilistic constraints on waiting times. These results can be also applied to bounds of waiting times in more general systems. Numerical examples are also provided.

• Journal for History of Mathematics
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• v.28 no.6
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• pp.301-310
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• 2015

Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.

• Journal of the Korean Institute of Gas
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• v.3 no.3 s.8
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• pp.29-33
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• 1999

ln this study, a computerized prototype program was developed with frequency analysis system as a main system and data base as sub-items to utilize data. Through use of gate-by-gate analysis and minimal cut set using boolean algebra, the frequency analysis program peformed the qualitative approach for the accident development path and a quantitative risk analysis. In conclusion, it is thought that the resulting installation will be effective for lessening the probability of accidents through use of this lower cost software.

• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 2014

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• The Journal of the Korea Contents Association
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• v.11 no.9
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• pp.63-75
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• 2011

A number of process algebras have been proposed to develop distributed mobile real-time systems: pi-Calculus, Mobile Ambients Calculus, Bigraph, etc. However, as the systems get large and complex, the algebras become less suitable for understanding the interactions and mobility of the processes of the systems due to the size and complexity. Therefore it is necessary to handle the size and complexity for systematic understanding of the systems. This paper handles the size and complexity with a method of abstraction on sequences of interactions and movements of processes in the systems, which can be further organized in the form of hierarchically structured lattices, namely, Prism. The theoretical principle of the abstraction is based on a new concept of Behavior Ontology, which is extended from Active ontology. Prism allows the systems to be analyzed in the perspective of the lattices in Prism, which are characterized by the hierarchically organized behavioral properties of the developing systems, for systematic understanding the systems. In this way, the complexity of the interactions and the movements can be handled systematically in the semantically and hierarchically organized structure of the behavior.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.5_6
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• pp.335-346
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• 2004

PtolemyII is an environment that supports heterogeneous modeling and design of concurrent systems such as embedded system. PtolemyII has several Domains which are physical rules to determine the way of communicating between components. PtolemyII has 11 domains such as PetriNet, Timed Multitasking, SR etc. Components of System can be specified using appropriate domains for their properties. Communicating Sequential Processes(CSP) is implemented as formally designed CSP domain, in PtolemyII. But CCS didn't be implemented as a domain. It is a kind of Process Algebra language which can be used for specifying and verifying concurrent systems formally. Thus, in this paper we implemented CCS domain. And that permitted developers using PtolemyII to use the same modeling pattern used in PtolemyII and to make system specifications in the base of the formal semantics of CCS. This caused the diversity of PtolemyII domains and the power of expression was improved. This paper will explain the structure of CCS domain implemented in PtolemyII and the way of implementing it.