• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1247-1257
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• 2016

In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.53-63
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• 1993

We consider various types of weak convergence for sums of sign-invariant random variables. Some results show a similarity between independence and sign-invariance. As a special case, we obtain a result which strengthens a weak law proved by Rosalsky and Teicher [6] in that some assumptions are deleted.

• 대한수학회보
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• 제53권3호
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• pp.723-732
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• 2016

We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifold. Moreover, we determine 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds which admit a certain kind of proper biharmonic foliation.

• 전기의세계
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• 제23권1호
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• pp.69-72
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• 1974

This paper deals with an analytical design of a feedback regulator with vector input is discrete linear time-invariant systems. We have derived some relations such that the eigenvalues of a system plant with vector input under the time-optimal control strategy can be arbitrarily changed by the characteristics of the minor loop compensator which is indroduced in the feedback path.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.127-143
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• 2015

In this paper, we consider a modified inexact Newton method for solving a nonlinear system F(x) = 0 where $F(x):R^n{\rightarrow}R^n$. The basic idea is to accelerate convergence. A semi-local convergence theorem for the modified inexact Newton method is established and an affine invariant version is also given. Moreover, we test three numerical examples which show that the modified inexact scheme is more efficient than the classical inexact Newton strategy.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.453-459
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• 2004

A left-invariant flat Riemannian connection on a Lie group makes its Lie algebra a left symmetric algebra compatible with an inner product. The left symmetric algebra is decomposed into trivial ideal and a subalgebra of e(l). Using this result, the Lie group is embedded isomorphically into the direct product of O(l) $\times$ $R^{k}$ for some nonnegative integers l and k.

• 한국농공학회지
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• 제38권3호
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• pp.112-126
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• 1996

This study was conducted to develop an optimal runoff bydrograph model by comparison of the peak discharge and time to peak between observed and simulated flows derived by four different models, that is, linear time-invariant, linear time-variant, nonlinear time-invariant and nonlinear time-variant models under the conditions of heavy rainfalls with regionally uniform rainfall intensity in short durations at nine small watersheds. The results obtained through this study can be summarized as follows. 1. Parameters for four models including linear time-invariant, linear time-variant, nonlinear time-invariant and nonlinear time-variant models were calibrated using a trial and error method with rainfall and runoff data for the applied watersheds. Regression analysis among parameters, rainfall and watershed characteristics were established for both linear time-invariant and nonlinear time-invariant models. 2. Correlation coefficients of the simulated peak discharge of calibrated runoff hydrographs by using four models were shown to be a high significant to the peak of observed runoff graphs. Especially, it can be concluded that the simulated peak discharge of a linear time-variant model is approaching more closely to the observed runoff hydrograph in comparison with those of three models in the applied watersheds. 3. Correlation coefficients of the simulated time to peak of calibrated runoff hydrographs by using a linear time-variant model were shown to be a high significant to the time to peak of observed runoff hydrographs than those of the other models. 4. The peak discharge and time to peak of simulated runoff hydrogaphs by using linear time-variant model are verified to be approached more closely to those of observed runoff hydrographs than those of three models in the applied watersheds. 5. It can be generally concluded that the shape of simulated hydrograph based on a linear time-variant model is getting closer to the observed runoff hydrograph than those of three models in the applied watersheds. 6. Simulated hydrographs using the nonlinear time-variant model which is based on more closely to the theoritical background of the natural runoff process are not closer to the observed runoff hydrographs in comparison with those of three models in the applied watersheds. Consequently, it is to be desired that futher study for the nonlinear time-variant model should be continued with verification using rainfall-runoff data of the other watersheds in addition to the review of analyical techniques.

• 호남수학학술지
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• 제32권4호
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• pp.633-642
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• 2010

In this note, we introduce the definition of the generalized analogue of Wiener measure on the space C[a, b] of all real-valued continuous functions on the closed interval [a, b], give several examples of it and investigate some important properties of it - the Fernique theorem and the existence theorem of scale-invariant measurable subsets on C[a, b].

• 대한수학회보
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• 제35권2호
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• pp.227-234
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• 1998

Criteria are derived for the existence of a unique invariant oprobability distribution of a class of nonlinear pth-order autoregressive oprocesses, which reformulate those of Tweedie's. It will be shown that the criteria in this paper are easily applicable to the linear or piecewise linear case so that some of the earlier results are immediate consequences of our main results.

• 대한수학회보
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• 제46권3호
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• pp.477-487
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• 2009

We define a quarter symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, noninvariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection.