• East Asian mathematical journal
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• v.16 no.1
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• pp.135-145
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• 2000

The purpose of this paper is to study the Chern-type problem of the complete space-like submanifolds of an indefinite complex space form.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.517-532
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• 2020

In this paper, we consider a class of nonlocal problems with indefinite weights in Orlicz-Sobolev space. Under some suitable conditions on the nonlinearities, we establish some existence results using variational techniques and Ekeland's variational principle.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.85-97
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• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

• Management Science and Financial Engineering
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• v.7 no.2
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• pp.13-30
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• 2001

This paper discusses a paradox in an Indefinite Quadratic transportation Problem. Here, the objective function is the product of two linear functions. A paradox arises when the transportation problem admits of a total cost which is lower than the optimum cost, by transporting larger quantities of goods over the same route. A sufficient condition for the existence of a paradox is established. Paradoxical Range of flow is obtained for any given flow in which the corresponding objective function value is less than the optimum value of the given transportation problem. It is illustrated with the help of a numerical example.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1145-1168
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• 1999

The purpose of this paper is to study the complete submanifolds with restricted space-like and time-like holomorphic bisectional curvatures in an indefinite locally symmetric K hler manifold.

• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.329-343
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• 2013

Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Takebe Katahiro (1664-1739) and Nakane Genkei (1662-1733), among a great number of mathematicians in Wasan, maybe the most famous ones. Taking Takebe and Nakane's indefinite problems as examples, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to these problems which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of Chinese tradition deeper.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.811.1-818
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• 2001

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1464-1468
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• 1997

We propose a decentralized state estimation method in the multisensor state estimation problem. The proposed method bounds teh maximum energy gain from uknown external disturbances to the estimation errors in the suboptimal case. And we formulate aternative H/sip .inf./ filter gain equatiions with teh idea that the suboptimal H.$^{\infty}$ filter is the special form of Kalman filter filter whose state equations are defined in indefinite inner product spaces. Using alternative filter gain equations we design the decentralized $H^{\infty}$ state estimator which is composed of local filters and central fusion filter that are suboptimal in the $H^{\infty}$ sense. In addition, the proposed update equations between global and local data can reduce unnecessary calculation burden efficently.y.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.104-109
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• 2002

A new robust Kalman filter is designed for the linear discrete-time system with norm-bounded parametric uncertainties. Sum quadratic constraint, which describes the uncertainties of the system, is converted into an indefinite quadratic form to be minimized in indefinite inner product space. This minimization problem is solved by the new robust Kalman filter. Since the new filter is obtained by simply modifying the conventional Kalman filter, robust filtering scheme can be more readily designed using the proposed method in comparison with the existing robust Kalman filters. A numerical example demonstrates the robustness and the improvement of the proposed filter compared with the existing filters.