• 전자공학회논문지S
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• 제34S권10호
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• pp.52-58
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• 1997

In this paper, we consider methods of robust stabilization of the interval plant with a PID controller. Suppose that we know apriori a sign of the coefficients of the numerator of the PID controller. Under this condition, it sufficies to make eight polynomials stable for robust stabilization of the interval plant with a minimum phase PID controller. In addition, with a nonminimum phase PID controller, it suffices to make different eight polynomials stable. Especially, with the nonminimum phase PID controller it is shown that stabilization of eight plants is necessary and sufficient for robust stabilization of the interval plants.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• 동의생리병리학회지
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• 제25권6호
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• pp.1108-1112
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• 2011

Voice can be widely used to classify the four constitution types and to recognize one's health condition from extracting meaningful features as physical quantity in traditional Korean medicine or Western medicine. In this paper, we proposed the method to update the standard operating procedure (SOP) to acquire and record voices for extracting stable vocal features since they are sensitive to the variation of a subject's utterance. At first, we obtained pitch frequencies from vowels and the sentence and intensity form the sentence as features with voices acquired under subjects' utterance conditions and then the deviation ratios of features from median values according to the utterance conditions were obtained and the condition to minimize the ratio was selected as a new SOP. As a result, we decided the SOP for a subject to utter vowels with the length of 2s~1s and sentences with over 2s interval between them after practice, in consideration of the deviation and qualitative requirements. Stable voice features obtained from updated SOP produce accurate diagnosis, which will be developed and simplified for using in the u-Healthcare system of personalized medicine.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.231-244
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• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.

• Management Science and Financial Engineering
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• 제2권1호
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• pp.103-122
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• 1996

This paper presents an easily used graphical procedure for simultaneous estimation of the index, skewness, scale, and location parameters of the stable laws. First, the index $\alpha$ and skewness $\beta$ are estimated through the joint use of a tail length statistic $\widetilde{K_t}$ and a skewness statistic $\widetilde{K_s}$, both of which are functions of order statistics. Next, the function of order statistics needed for estimation of scale $\sigma$ and location $\mu$ are determined from a nomogram indexed on the estimates of $\alpha$ and $\beta$. Some applications and examples are provided.

• Bulletin of the Korean Chemical Society
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• 제35권12호
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• pp.3567-3570
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• 2014

The most stable adsorption structures and energies of four tautomers of 3-methyl-5-pyrazolone (keto-1, enol-1, keto-2, and enol-2) on Ge(100) surfaces were investigated using density functional theory (DFT) calculations. The enol-1, keto-2, and enol-2 tautomers, but not the keto-1 tautomer, were found to exhibit stable adsorption structures on the Ge(100)-$2{\times}1$ surface. Of these three adsorption structures, that of enol-2 is the most stable.

• 대한수학회보
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• 제34권1호
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• pp.1-8
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• 1997

Let G be a finiteg oroup. We denote BG a classifying space of G, which a contractible universal principal G bundle EG. The stable type of BG does not determine G up to isomorphism. A simple example [due to N. Minami]is given by $Q_{4p} \times Z/2$ and $D_{2p} \times Z/4$ where ps is an odd prime, $Q_{4p} is the generalized quarternion group of order 4p and $D_{2p}$ is the dihedral group of order 2p. However the paper [6] gives us a necessary and sufficient condition for $BG_1$ and $BG_2$ to be stably equivalent localized et pp. The local stable type of BG depends on the conjegacy classes of homomorphisms from the p-groups Q into G. This classification theorem simplifies if G has a normal sylow p-subgroup. Then the stable homotopy type depends on the Weyl group of the sylow p-subgroup.

• 제어로봇시스템학회논문지
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• 제12권6호
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• pp.517-523
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• 2006

This paper is focused on a robust saturation controller for the stable linear time-invariant (LTI) system involving both actuator's saturation and structured real parameter uncertainties. Based on affine quadratic stability and multi-convexity concept, a robust saturation controller is newly proposed and the linear matrix inequality (LMI)-based sufficient existence conditions for this controller are presented. The controller suggested in this paper can analytically prescribe the lower and upper bounds of parameter uncertainties, and guarantee the closed-loop robust stability of the system in the presence of actuator's saturation. Through numerical simulations, it is confirmed that the proposed robust saturation controller is robustly stable with respect to parameter uncertainties over the prescribed range defined by the lower and upper bounds.

• Structural Engineering and Mechanics
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• 제19권4호
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• pp.413-423
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• 2005

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.