• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.225-243
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• 2000

We explain the notion of complete system and how it naturally arises from the equivalence problem of G-structures. Then we construct a complete system of 3rd order for the infinitesimal CR automorphisms of CR manifold of nondegenerate Levi form.

• Journal of Electrical Engineering and information Science
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• v.2 no.5
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• pp.1-8
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• 1997

The main purpose of the Boolean equivalence problem is to verify that two Boolean expressions have the same functionality. Simulation has been extensively used as the standard method for the equivalence problem. Obviously, the number of tests required to perform a satisfactory coverage grows exponentially with the number of input variables. However, formal methods as opposed to simulation are getting more attention from the community. We propose a new algorithm called the Cover-Merge Algorithm based on a derivational method using the concept of cover and merge for the equivalence problem and investigate its theoretical aspects. Because of the difficulty of the problem, we emphasize simplification techniques in order to reduce the search space or problem size. Heuristics based on types of merges are developed to speed up the derivation process by allowing simplifications. In comparison with widely used technique called Binary Decision Diagram or BDD, the algorithm proposed outperforms BDD in nearly all cases of input including standard benchmark problems.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.505-511
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• 2007

Recently, the equivalent relations between a symmetric dual problem and a matrix game B(x, y) were given in [6: D.S. Kim and K. Noh, J. Math. Anal. Appl. 298(2004), 1-13]. Using more simpler form of B(x, y) than one in [6], we establish the equivalence relations between a symmetric dual problem and a matrix game, and then give a numerical example illustrating our equivalence results.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.245-251
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• 2000

Assume that two boundaries of worm domains, which are parpametrizd by harmonic functions, are CR equivalent. Then we determine the Taylor expansion of CR equivalence mapping and get a relation of harmonic functions.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.405-412
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• 1992

The problem we consider in this paper is more demanding than the problem of input-output linearization with state equivalence recently solved by Cheng, Isidori, Respondek, and Tarn. We request that the MIMO nonlinear system, for which the problem of input-output linearization with state-equivalence is solvable, can be decoupled. In exchange for further requirement like this, our problem produces more usable and informative results than the problem of input-output linearization with state-equivalence. We present the necessary and sufficient conditions for our problem to be solvable. We characterize each of the nonlinear systems satisfying these conditions by a set of parameters which are invariant under the group action of state feedback and transformation. Using this set of parameters, we can determine directly the unique one, among the canonical forms of decouplable and controllable linear systems, to which a nonlinear system can be transformed via appropriate state feedback and transformation. Finally, we present the necessary and sufficient conditions for our problem to be solvable with internal stability, that is, for stable decoupling.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.563-589
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• 2019

Let W and V be manifolds of dimension m + 2, M a locally flat submanifold of V whose dimension is m. Let $f:W{\rightarrow}V$ be a homotopy equivalence. The problem we study in this paper is the following: When is f homotopic to another homotopy equivalence $g:W{\rightarrow}V$ such that g is transverse regular along M and such that $g{\mid}g^{-1}(M):g^{-1}(M){\rightarrow}M$ is a simple homotopy equivalence? $L{\acute{o}}pez$ de Medrano (1970) called this problem the weak h-regularity problem. We solve this problem applying the codimension two surgery theory developed by the author (1973). We will work in higher dimensions, assuming that $$m{\geq_-}5$$.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.773-785
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• 1999

Shifts of finite type are represented by nonnegative integral square matrics, and conjugacy between two shifts of finite type is determined by strong shift equivalence between the representing nonnegative intergral square matrices. But determining strong shift equivalence is usually a very difficult problem. we develop splittings and amalgamations of nonnegative integral matrices, which are analogues of those of directed graphs, and show that two nonnegative integral square matrices are strong shift equivalent if and only if one is obtained from a higher matrix of the other matrix by a series of amalgamations.

• The Mathematical Education
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• v.48 no.3
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• pp.235-263
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• 2009

The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.

• Journal of KIISE:Software and Applications
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• v.30 no.7_8
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• pp.642-648
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• 2003

In this paper, we are interested in checking equivalence of FSMs(finite state machines). Two FSMs are equivalent if and only if their responses are always equal with each other with respect to the same external stimuli. Equivalence checking FSMs makes complicated FSM be substituted for simpler one, if they are equivalent. We can also determine the system satisfies the requirements, if they are all written in FSMs. In this paper, we regard equivalence checking problem as model checking one. For doing so, we construct the product model $M ={M_A} {\beta}{M_B} from two FSMs ${M_A} and {M_B}$. And we also get the temporal logic formula ${\Phi}$ from the equivalence checking definition. Then, we can check with model checker whether if satisfies ${\Phi}$, written $M= {.\Phi}$. Two FSMs are equivalent, if $M= {.\Phi}$ Otherwise, it is not equivalent. In that case, model checker generates counterexamples which explain why FSMs are not equivalent. In summary, we solve the equivalence checking problem with model checking techniques. As a result of applying to several examples, we have many satisfiable results.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.201-205
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• 2019

This note provides the solution equivalence of general minimum variance and minimax disparity problems for OWA operator. This result generalize a main theorem of Liu [International Journal of Approximate Reasoning, 48 (2008) 598-627.]