• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.609-615
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• 2012

In the current paper, we establish the relationship between the powers of an invertible matrix and the powers of its inverse. More precisely, we prove that if A is an invertible matrix and, if $A^n\;=\;(A_{i,j}(n))$ for all positive integer n, then $A^{-n}\;=\;(A_{i,j}{(-n))$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.19-25
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• 2012

The purpose of this paper is to derive powers $A^{n}$ using a system of recursive sequences for a given $2{\times}2$ matrix A. Introducing a recursive sequence we have a quadratic equation. Solutions to this quadratic equation are related with eigenvalues of A. By solving this quadratic equation we can easily obtain an explicit form of $A^{n}$. Our method holds when A is defined not only on the real field but also on the complex field.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.285-290
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• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.27 no.5
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• pp.430-437
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• 2016

In general, noise measurement results show larger random ripple than those of the network analyzer. The reason for the lager random ripple of the noise measurements is considered that the general noise measurements uses absolute measured noise powers, while the network analyzer measures using a ratio of the measured powers. In this paper, a novel measurement method of noise correlation matrix using relative noise ratios is proposed. Proposed method measures the five noise powers of DUT for the five input impedance variations and the four relative noise ratios are formed using the five measured noise powers. The four noise ratios are used to compute the noise correlation matrix and noise parameters. The resulting noise parameters for a 0.5 dB attenuator show good agreements with theoretical values calculated by S-parameters. Also, the noise parameters of an active DUT with a noise figure of less than 1 dB are measured and the measured results show a small random ripple as expected and their values are physically acceptable. In conclusion, the proposed method can be applied to the noise parameter measurements for DUT with a noise figure below 1 dB.

• Proceedings of the KIPE Conference
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• 1997.07a
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• pp.228-232
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• 1997

The relation between instantaneous active/reactive powers and currents is defined by voltage mapping matrix in three-phase four-wire systems. Control strategies for an active filter without energy storage components are proposed on the basis of mapping matrices. It can compensate for the zero-sequence current, irrespectively of whether or not a zero-sequence voltage exists in a three-phase four-wire system.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.329-332
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• 1991

This paper presents an algorithm to reduce the time to solve Power Equations using a Neural Net. The Neural Net is trained with samples obtained through the conventional AC Load Flow. With these samples, the Neural Net is constructed and has the function of a linear interpolation network. Given arbitrary load level, this Neural Net generates voltage magnitudes and angles which are linear interpolation of real and reactive powers. Obtained voltage magnitudes and angles are substituted to Power Equations, Real and reactive powers are found. Thus, a new sample is generated. This new experience modifies weight matrix. Continuing to modify the weight matrix, the correct solution is achieved. comparing this method with AC Load flow, this method is faster. If we consider parallel processing, this method is far faster than conventional ones.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.686-710
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• 2019

This work proposes a model to solve the problem of Network Coding over a one-session multicast network. The model is based on a system of restrictions that defines the packet flows received in the sink nodes as functions of the outgoing flows from the source node. A multicast network graph is used to derive a directed labeled line graph (DLLG). The successive powers of the DLLG adjacency matrix to the convergence in the null matrix permits the construction of the jump matrix Source-Sinks. In its reduced form, this shows the dependency of the incoming flows in the sink nodes as a function of the outgoing flows in the source node. The emerging packets for each outgoing link from the source node are marked with a tag that is a linear combination of variables that corresponds to powers of two. Restrictions are built based on the dependence of the outgoing and incoming flows and the packet tags as variables. The linear independence of the incoming flows to the sink nodes is mandatory. The method is novel because the solution is independent of the Galois field size where the packet contents are defined.

• Journal of Electrical Engineering and Technology
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• v.3 no.4
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• pp.491-498
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• 2008

In this paper a decoupled control of a doubly-fed induction machine(DFIM) feed by a matrix converter is presented. It provides a robust regulation of the stator side active and reactive powers by the direct and quadratic components of the stator current vector, presented in a line-voltage-oriented reference frame. In this case, the stator windings are directly connected to the line grid, while the rotor windings are supplied by this later through a matrix converter controlled by a space vector modulation technique. The proposed solution is suitable for both energy generation and electrical drive applications with restricted speed variation range.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2107-2117
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• 2017

We study the quasi-commutativity in relation with powers of coefficients of polynomials. In the procedure we introduce the concept of ${\pi}$-quasi-commutative ring as a generalization of quasi-commutative rings. We show first that every ${\pi}$-quasi-commutative ring is Abelian and that a locally finite Abelian ring is ${\pi}$-quasi-commutative. The role of these facts are essential to our study in this note. The structures of various sorts of ${\pi}$-quasi-commutative rings are investigated to answer the questions raised naturally in the process, in relation to the structure of Jacobson and nil radicals.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.4
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• pp.374-387
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• 1989

The decoding method of Binary BCH Codes using symmetric matrix is proposed in this paper. With this method, the error-locator-polynomial is composed by symmetric matrix which consists of the powers of the unknown X plus the synfromes as its elements. The symmetric matirx can also be represented in terms of the unknown X. But the each coefficients of the error-locator polynomial represents the matirx with the syndromes as its entries. By utilizing this proposed algorithm, the device for decoding circuit of the (63, 45) BCH Code for t=3 has been implemented for demonstration.