• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.487-493
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• 2008

A. Di Nola & S.Sessa [8] showed that two compact spaces X and Y are homeomorphic iff the MV -algebras C(X, I) and C(Y, I) of continuous functions defined on X and Y respectively are isomorphic. And they proved that A is a semisimple MV -algebra iff A is a subalgebra of C(X) for some compact Hausdorff space X. In this paper, firstly by use of functorial argument, we show these characterization theorems. Furthermore we obtain some other functorial results between topological spaces and MV -algebras. Secondly as a classical problem, we find a necessary and sufficient condition on a given residuated l-monoid that it is segmenently embedded into an l-group with order unit.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.487-504
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• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.487-494
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• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.487-496
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• 2021

In this paper we show that if A ∈ L(X) and B ∈ L(Y), X and Y complex Banach spaces, then A ⊕ B ∈ L(X ⊕ Y) is subscalar if and only if both A and B are subscalar. We also prove that if A, Q ∈ L(X) satisfies AQ = QA and Q^p = 0 for some nonnegative integer p, then A has property (C) (resp. property (𝛽)) if and only if so does A + Q (resp. property (𝛽)). Finally, we show that A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA and BA ∈ L(X) is subscalar with property (𝛿) then both Lat(BA) and Lat(AC) are non-trivial.

• Communications for Statistical Applications and Methods
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• v.29 no.4
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• pp.487-498
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• 2022

Social network analysis (SNA) techniques have recently been developed to monitor and detect abnormal behaviors in social networks. As a useful tool for process monitoring, control charts are also useful for network monitoring. In this paper, the degree and closeness centrality measures, in which each has global and local perspectives, respectively, are applied to an exponentially weighted moving average (EWMA) chart and a multinomial cumulative sum (CUSUM) chart for monitoring undirected weighted networks. In general, EWMA charts monitor only one variable in a single chart, whereas multinomial CUSUM charts can monitor a categorical variable, in which several variables are transformed through classification rules, in a single chart. To monitor both degree centrality and closeness centrality simultaneously, we categorize them based on the average of each measure and then apply to the multinomial CUSUM chart. In this case, the global and local attributes of the network can be monitored simultaneously with a single chart. We also evaluate the performance of the proposed procedure through a simulation study.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.487-493
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• 2002

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for the n-operators satisfies the equation AX$\_$i/ : Y$\_$i/, for i = 1, 2 …, n. In this article, we obtained the following : Let X = (x$\_$ij/) and Y = (y$\_$ij/) be operators acting on H such that $\varkappa$$\_$ i$\sigma$ (i)/ 0 for all i. Then the following statements are equivalent. (1) There exists a unitary operator A in Alg(equation omitted) such that AX = Y and every E in (equation omitted) reduces A. (2) sup{(equation omitted)}<$\infty$ and (equation omitted) = 1 for all i = 1, 2, ….

• Journal of Power Electronics
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• v.12 no.3
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• pp.487-494
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• 2012

A new low cost high power density photovoltaic power conditioning system (PV PCS) with an energy storage system is proposed in this paper. Its high power density and cost effectiveness can be achieved through the unification of the maximum power point tracker and the battery charger/discharger. Despite the reduced power stage, the proposed system can achieve the same performance in terms of maximum power point tracking and battery charging/discharging as the conventional system. When a utility power failure happens, the proposed system cannot perform maximum power point tracking at the UPS mode. However, the predetermined battery voltage near the maximum power point of the PV array can effectively generate a reasonable PV power even at the UPS mode. Therefore, it features a simpler structure, less mass, lower cost, and fewer devices. Finally, to confirm the operation, validity, and features of the proposed system, a theoretical analysis and experimental results from a single phase AC 220Vrms/1.5kW prototype are presented.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.3
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• pp.487-492
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• 2012

In this study we researched a spotlight in LED lighting. Ordinary LED spotlight was manufactured with characterized property of traveling straightness of LED light source, but multiple use of shell type LED, a yellow band has formed caused by light source interference between the LED. Also, there was a high miscellaneous light efficiency with losing light source homogeneity and efficiency due to light source control uneasiness. The study uses aspheric reflector and aspheric lens, so we can control the light source of LED spotlight with effectively and we reached surface light source by using COB/COM for LED module. Furthermore it can change its use by a reduced scale of light system. It has been designed to make its various application from low power consumption of bicycle lamp, up to high power consumption of automobile lamps and lighthouse.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.487-509
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• 2018

The Truncated Moment Problem (TMP) entails finding a positive Borel measure to represent all moments in a finite sequence as an integral; once the sequence admits one or more such measures, it is known that at least one of the measures must be finitely atomic with positive densities (equivalently, a linear combination of Dirac point masses with positive coefficients). On the contrary, there are more general moment problems for which we aim to find a "signed" measure to represent a sequence; that is, the measure may have some negative densities. This type of problem is referred to as the General Truncated Moment Problem (GTMP). The Jordan Decomposition Theorem states that any (signed) measure can be written as a difference of two positive measures, and hence, in the view of this theorem, we are able to apply results for TMP to study GTMP. In this note we observe differences between TMP and GTMP; for example, we cannot have an analogous to the Flat Extension Theorem for GTMP. We then present concrete solutions to lower-degree problems.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.487-494
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• 2015

A calculation of the Kullback-Leibler information of consecutive order statistics is complicated because it depends on a multi-dimensional integral. Park (2014) discussed a representation of the Kullback-Leibler information of the first r order statistics in terms of the hazard function and simplified the r-fold integral to a single integral. In this paper, we first express the Kullback-Leibler information in terms of the reversed hazard function. Then we establish a generalized result of Park (2014) to an arbitrary consecutive order statistics. We derive a single integral form of the Kullback-Leibler information of an arbitrary block of order statistics; in addition, its relation to the Fisher information of order statistics is discussed with numerical examples provided.