• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.173-183
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• 2015

A radio k-labeling f of a graph G is a function f from V (G) to $Z^+{\cup}\{0\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}k+1$ for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices $x,y{\in}G$. The span of a radio k-labeling f is denoted by sp(f) and defined as max$\{{\mid}f(x)-f(y){\mid}:x,y{\in}V(G)\}$. The radio k-labeling is a radio labeling when k = diam(G). In other words, a radio labeling is an injective function $f:V(G){\rightarrow}Z^+{\cup}\{0\}$ such that $${\mid}f(x)=f(y){\mid}{\geq}diam(G)+1-d(x,y)$$ for any pair of vertices $x,y{\in}G$. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) - 1, a radio k-labeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function $f:V(G){\rightarrow}\{0,1,2,{\ldots}\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}diam(G)$ holds for all $x,y{\in}G$. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and radio antipodal number for the circulant graphs G(4k + 2; {1, 2}).

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.451-465
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• 2016

A Radio labeling of the graph G is a function g from the vertex set V (G) of G to ℤ⁺ such that |g(u) - g(v)| ≥ diam(G) + 1 - d_G(u, v), where diam(G) and d(u, v) are diameter and distance between u and v in graph G respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{g(v) : v ∈ V(G)} = k. We investigate radio number for some families of generalized caterpillar graphs.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.59-74
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• 2017

A radio labeling of a graph G is a function $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ with the property that ${\mid}f(u)-f(v){\mid}{\geq}1+diam(G)-d(u,v)$ for every pair of vertices $u,v{\in}V(G)$, where diam(G) and d(u, v) are diameter and distance between u and v in the graph G respectively. The radio number of a graph G, denoted by rn(G), is the smallest integer k such that G admits a radio labeling. In this paper, we completely determine radio number of all transformation graphs of a path.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.69.1-69.1
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• 2017

According to structure formation simulations, weak shocks with typical Mach number, M<3, are expected to form in merging galaxy clusters. The presence of such shocks has been indicated by X-ray and radio observations of many merging clusters. In particular, diffuse radio sources known as radio relics could be explained by synchrotron-emitting electrons accelerated via diffusive shock acceleration (Fermi I) at quasi-perpendicular shocks. Here we also consider possible roles of stochastic acceleration (Fermi II) by compressive MHD turbulence downstream of the shock. Then we explore a puzzling discrepancy that for some radio relics, the shock Mach number inferred from the radio spectral index is substantially larger than that estimated from X-ray observations. This problem could be understood, if shock surfaces associated with radio relics consist of multiple shocks with different strengths. In that case, X-ray observations tend to pick up the part of shocks with lower Mach numbers and higher kinetic energy flux, while radio emissions come preferentially from the part of shocks with higher Mach numbers and higher cosmic ray (CR) production. We also show that the Fermi I reacceleration model with preexisting fossil electrons supplemented by Fermi II acceleration due to postshock turbulence could reproduce observed profiles of radio flux densities and integrated radio spectra of two giant radio relics. This study demonstrates the CR electrons can be accelerated at collisionless shocks in galaxy clusters just like supernova remnant shock in the interstellar medium and interplanetary shocks in the solar wind.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.45.3-46
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• 2016

Solar activity shows a self-similarity as it has many periods of activity cycle in the time series of long-term observation, such as 13.5, 51, 150, 300 days, and 11, 88 years and so on. Since fractal dimension is a quantitative parameter for this kind of an irregular time series, we applied this method to long-term observations including sunspot number, total solar irradiance, and 3.75 GHz solar radio flux to predict the start and maximum times as well as expected maximum sunspot number for the next solar cycle. As a result, we found that the radio flux data tend to have lower fractal dimensions than the sunspot number data, which means that the radio emission from the sun is more regular than the solar activity expressed by sunspot number. Based on the relation between radio flux of 3.75 GHz and sunspot number, we could calculate the expected maximum sunspot number of solar cycle 24 as 156, while the observed value is 146. For the maximum time, estimated mean values from 7 different observations are January 2013 and this is quite different to observed value of February 2014. We speculate this is from extraordinary extended properties of solar cycle 24. As the cycle length of solar cycle 24, 10.1 to 12.8 years are expected, and the mean value is 11.0. This implies that the next solar cycle will be started at December 2019.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.1
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• pp.36.4-37
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• 2017

Although most of observed properties of giant radio relics detected in the outskirts of galaxy clusters could be explained by relativistic electrons accelerated at merger-driven shocks, a few significant puzzles remain. In some relics the shock Mach number inferred from X-ray observations is smaller than that estimated from radio spectral index. Such a discrepancy could be understood, if either the shock Mach number is nder-estimated in X-ray observation due to projection effects, or if pre-existing electrons with a flat spectrum are re-accelerated by a weak shock, retaining the flat spectral form. In this study, we explore these two scenarios by comparing the results of shock acceleration simulations with observed features of the so-called Toothbrush relic in the merging cluster 1RXS J060303.3. We find that both models could reproduce reasonably well the observed radio flux and spectral index profiles and the integrated radio spectrum. Either way, the broad transverse relic profile requires additional post shock electron acceleration by downstream turbulence.

• ETRI Journal
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• v.17 no.4
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• pp.25-35
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• 1996

This paper derives the symbol error probability for quadrature amplitude modulation(QAM) with L-fold space diversity in Rayleigh fading channels. Two combining techniques, maximal ratio combining(MRC) and selection combining(SC), are considered. The formula for MRC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an additive white Gaussian noise(AWGN) channel over a chi-square distribution with 2L degrees of freedom. The obtained formula overcomes the limitations of the earlier work, which has been limited only to deriving the symbol error rate(SER) of QAM with two branch MRC space diversity. The formula for SC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an AWGN channel over the distribution of the maximum signal-to noise ratio among all of the diversity channels for SC space diversity has been reported yet. Analytical results show that the probability of error decreases with the order of diversity gain per additional branch decreases as the number of branches becomes larger. On the other hand, the performance of 16 QAM with MRC becomes much better than that of SC as the number of branches becomes larger. By giving the order of diversity, L, and the number of signal points, M, we have been able to obtain the SER performance of QAM with general space diversity. These results can be used to determine the order of diversity to achieve the desired SER in land mobile communication system employing QAM modulation.

• Journal of The Korean Astronomical Society
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• v.49 no.4
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• pp.145-155
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• 2016

The Sausage radio relic is the arc-like radio structure in the cluster CIZA J2242.8+5301, whose observed properties can be best understood by synchrotron emission from relativistic electrons accelerated at a merger-driven shock. However, there remain a few puzzles that cannot be explained by the shock acceleration model with only in-situ injection. In particular, the Mach number inferred from the observed radio spectral index, M_radio ≈ 4.6, while the Mach number estimated from X-ray observations, M_X−ray ≈ 2.7. In an attempt to resolve such a discrepancy, here we consider the re-acceleration model in which a shock of M_s ≈ 3 sweeps through the intracluster gas with a pre-existing population of relativistic electrons. We find that observed brightness profiles at multi frequencies provide strong constraints on the spectral shape of pre-existing electrons. The models with a power-law momentum spectrum with the slope, s ≈ 4.1, and the cutoff Lorentz factor, γ_e,c ≈ 3−5×10⁴, can reproduce reasonably well the observed spatial profiles of radio fluxes and integrated radio spectrum of the Sausage relic. The possible origins of such relativistic electrons in the intracluster medium remain to be investigated further.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.5A
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• pp.325-338
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• 2012

In this paper, a radio resource allocation scheme for a multi-hop relay transmission in cognitive radio (CR) system is proposed to support the employment of relay nodes in IEEE 802.22 standard for wireless regional area network (WRAN). An optimization problem is formulated to maximize the number of serving secondary users (SUs) under system constraints such as time-divided frame structure for multiplexing and a single resource-unit to every relay-hop. However, due to mathematical complexity, the optimization problem is solved with a sub-optimal manner instead, which takes three steps in the order of user selection, relay/path selection, and frequency selection. In the numerical analysis, this proposed solution is evaluated in terms of service rate denoting as the ratio of the number of serving SUs to the number of service-requesting SUs. Simulation results show the condition of adopting multi-hop relay and the optimum number of relaying hops by comparing with the performance of 1-hop system.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.08a
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• pp.65-68
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• 2000

In this paper, as a compatible software radio transmission system, Digital-Radio conversion system which can directly change the digital signal generated by the logic circuit into radio signal is proposed. By the vector synthesis method, the digital signals can change directly into radio signal. If such a circuit is realized, RF circuit and an antenna can be composed by the simple one device, and the radio is directly controlled and performed by the software processing which is the essence of software radio. This Digital-Radio conversion system of this paper give many number of communication channels being offered by PN code and offer a hardware design flexibility by digitization, therefore it decrease the percentage ratio of hardware of system and give a more flexible function of software basis. In this paper, this proposed Digital-Radio conversion system is called D/R converter, and the principle of this D/R converter, radio signal generation algorithm is explained and the performance characteristics of proposed algorithm is shown in time base by the computer simulation method.