• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.297-304
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• 2012

There are several types of orders in a Quaternion algebra. Generally, zeta functions defined on orders of a Quaternion algebra give some informations on the ideal theory of orders. In this study, we investigate functional equalities between the zeta functions defined on orders of a Quaternion algebra.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.125-133
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• 2002

Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.7A
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• pp.562-567
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• 2009

In this paper, two-hop beamforming relay system, with source, relay, and destination nodes, is considered and the transmit- and receive-beamforming vectors and the relay processing matrix are designed for minimizing a mean square error (MMSE) between the transmit and receive signals. Here, to reduce the transmit power of the source or the relay, two local inequality constraints are involved with MMSE problem. By adopting the Lagrange method, closed formed Karush-Kuhn-Tucker (KKT) conditions (equalities) are derived and an iterative algorithm is developed to solve the entangled KKT equalities. Due to the inequality power constraints, the source or the relay can reduce its transmit power when the received signal-to-noise ratios (SNRs) of the first- and the second-hop are different. Meanwhile, the destination can achieve almost identical bit-error-rate performance compared to an optimal beamforming system maximizing the received SNR. This claim is supported by a computer simulation.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.315-328
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• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

• Journal of Information Processing Systems
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• v.12 no.2
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• pp.214-225
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• 2016

Global value numbering (GVN) is a method for detecting equivalent expressions in programs. Most of the GVN algorithms concentrate on detecting equalities among variables and hence, are limited in their ability to identify value-based redundancies. In this paper, we suggest improvements by which the efficient GVN algorithm by Gulwani and Necula (2007) can be made to detect expression equivalences that are required for identifying value based redundancies. The basic idea for doing so is to use an anticipability-based Join algorithm to compute more precise equivalence information at join points. We provide a proof of correctness of the improved algorithm and show that its running time is a polynomial in the number of expressions in the program.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.779-791
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• 2016

Transfer of homological properties under base change is a classical field of study. Let $R{\rightarrow}S$ be a ring homomorphism. The relations of Gorenstein projective (or Gorenstein injective) dimensions of unbounded complexes between $U{\otimes}^L_RX$(or $RHom_R(X,U)$) and X are considered, where X is an R-complex and U is an S-complex. In addition, some sufficient conditions are given under which the equalities $G-dim_S(U{\otimes}^L_RX)=G-dim_RX+pd_SU$ and $Gid_S(RHom_R(X,U))=G-dim_RX+id_SU$ hold.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.7
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• pp.587-591
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• 2013

This paper addresses the robust fault tolerant controller design problems of static output systems with disturbance. The fault is expressed by the abrupt chattering of system parameters. The design conditions are derived in terms of linear matrix inequalities and linear matrix equalities. An illustrative example is provided to verify performances of the proposed controller.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.6
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• pp.347-353
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• 2003

In models of imperfect competition of deregulated electricity markets, the key task is to find the Nash equilibrium(NE). The approaches for finding the NE have had two major bottlenecks: computation of mixed strategy equilibrium and treatment of multi-player games. This paper proposes a payoff matrix approach that resolves these bottlenecks. The proposed method can efficiently find a mixed strategy equilibrium in a multi-player game. The formulation of the m condition for a three-player game is introduced and a basic computation scheme of solving nonlinear equalities and checking inequalities is proposed. In order to relieve the inevitable burden of searching the subspace of payoffs, several techniques are adopted in this paper. Two example application problems arising from electricity markets and involving a Cournot and a Bertrand model, respectively, are investigated for verifying the proposed method.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.127-146
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• 2004

In this paper we consider a heat flow in an inhomogeneous. body without internal source. There exists special initial and boundary conditions in this system and we intend to find a convenient coefficient of heat conduction for this body so that body cool off as much as possible after definite time. We consider this problem in a general form as an optimal control problem which coefficient of heat conduction is optimal function. Then we replace this problem by another in which we seek to minimize a linear form over a subset of the product of two measures space defined by linear equalities. Then we construct an approximately optimal control.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.73-90
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• 1998

In this paper we introduce and study a number of new classes of quasi variational inequalities. using essentially the projection technique and its variant forms we prove that the gen-eralized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations(normal maps). This equivalence enables us to suggest a number of iterative algorithms solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational in-equalities we obtain a class of quasi variational inequalities studied by Siddiqi Husain and Kazmi [35] but there are several inaccuracies in their formulation of the problem the statement and the proofs of the problem the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of thir results can be obtained as special cases from our main results.