• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1489-1492
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• 2009

Nagata[3] and Higman[1] showed that nil-algebra of the nilindex n is nilpotent of finite index. In this paper we show that the bounded degree of the nilpotency is less than or equal to $2^n-1$. Our proof needs only some elementary fact about Vandermonde determinant, which is much simpler than Nagata's or Higman's proof.

• 한국CDE학회논문집
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• 제11권1호
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• 제어로봇시스템학회논문지
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• 제6권3호
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• pp.241-247
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• 2000

The reference model of an MRC (model reference control) provides the desired trajectory a plant should follow and thus the design of a reference model has a significant effect on control performance. In most control systems control input to a plant has some bounds and it is preferable to make use of as large control inputs as possible within the range of no saturation. In this paper a new approach of selecting the reference model is proposed for bounded control inputs. Design variables of the reference model are determined in such a way that maximizes the performance index within the range of no saturation. Moreover this variable reference model is regularly updated during control. This scheme is verified by application to the servo motor position control system in various simulations. The responses of the MRC with a variable reference model show better tracking performance than that with a fixed reference mode. Moreover by adjusting the update interval of the reference model the control performance can be further improved.

• 대한수학회보
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• 제56권2호
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• pp.365-371
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• 2019

If 𝖃 is a class of groups, denote by F𝖃 the class of groups G such that for every $x{\in}G$, there exists a normal subgroup of finite index H(x) such that ${\langle}x,h{\rangle}{\in}$ 𝖃 for every $h{\in}H(x)$. In this paper, we consider the class F𝖃, when 𝖃 is the class of nilpotent-by-finite, finite-by-nilpotent and periodic-by-nilpotent groups. We will prove that for the above classes 𝖃 we have that a finitely generated hyper-(Abelian-by-finite) group in F𝖃 belongs to 𝖃. As a consequence of these results, we prove that when the nilpotency class of the subgroups (or quotients) of the subgroups ${\langle}x,h{\rangle}$ are bounded by a given positive integer k, then the nilpotency class of the corresponding subgroup (or quotient) of G is bounded by a positive integer c depending only on k.

• 대한수학회보
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• 제55권3호
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• pp.913-920
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• 2018

Let R be a 2-primal strongly 2-nil-clean ring. We prove that every square matrix over R is the sum of a tripotent and a nilpotent matrices. The similar result for rings of bounded index is proved. We thereby provide a large class of rings over which every matrix is the sum of a tripotent and a nilpotent matrices.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.243-257
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• 2008

We seek the sign changing periodic solutions of the nonlinear wave equation $u_{tt}-u_{xx}=a(x,t)g(u)$ under Dirichlet boundary and periodic conditions. We show that the problem has at least one solution or two solutions whether $\frac{1}{2}g(u)u-G(u)$ is bounded or not.

• 대한수학회보
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• 제40권1호
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• pp.91-99
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• 2003

In this paper, we show that if the ring of a Merits context (A, B, M, N, ${\psi},\;{\phi}$) with zero pairings is a strongly $\pi$-regular ring of bounded index if and only if so are A and B. Furthermore, we extend this result to the ring of a Merits context over quasi-duo strongly $\pi$-regular rings.

• 대한수학회지
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• 제56권5호
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• pp.1419-1439
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• 2019

In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.147-166
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• 1997

The convergence of the power sequence of an $n{\times}n$ fuzzy matrix has been studied. Some theoretical necessary and sufficient con-ditions have been established for the power sequence to be convergent generally. Furthermore as one of our main concerns the convergence index was studied in detail especially for some special types of Boolean matrices. Also it has been established that the convergence index is bounded by $(n-1)^2+1$ from above for an arbitrary $n{\times}n$ fuzzy matrix if its power sequence converges. Our method is concentrated on the limit behavior of the power se-quence. It helped us to make our proofs be simpler and more direct that those in pure algebraic methods.

• 대한수학회논문집
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• 제9권3호
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• pp.593-598
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• 1994

In this note we give some results on the jump (due to Kato [5] and West [7]) of a semi-Fredholm operator. Throughout this note, suppose X is an Banach space and write L(X) for the set of all bounded linear operators on X. A operator $T \in L(x)$ is called upper semi-Fredholm if it has closed range with finite dimensional null space, and lower semi-Fredholm if it has closed range with its range of finite co-dimension. It T is either upper or lower semi-Fredholm we shall call it semi-Fredholm and Fredholm it is both. The index of a (semi-) Fredholm operator T is given by $$ index(T) = n(T) = d(T),$$ where $n(T) = dim T^{-1}(0)$ and d(T) = codim T(X).