• Economic and Environmental Geology
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• v.32 no.4
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• pp.379-384
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• 1999

In order to know the characteristics of attenuation of coda wave in the Kyungsang Sedimetary Basin, quality faclity factor for coda wave (coda Q) is estimated from the earthquake data recorded in the KIGAM local seismic network. Thesingle scattering model for coda wave generation is adopted is adopted in estimating coda Q. In the present study, coda Q(Qc)is estimated in the range of $\alpha$=1.5~3.0, where $\alpha$ denotes the normalized time to S-wave travel time and expressed in terms of frequency (f). The deduced function in the range of 1 to 25 Hz is Qc=36.8283$f^{1.15095}$ which represents the strong dependence of coda Q on frequency. It is found that the difference of Qc between U-D, N-S, and E-W components is negligible. This fact suports the back scattering therory that coda wave originates from scattered waves by randomly distributed heterogenities in the crust On the other hand, it is observed that the coda Q increases with increasing epicentral distence. This observation suggests that QC increases with depth.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.55-107
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k,\;q=e^{{\pi}i\tau}$. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, $\frac{q^{1/8}}{1}+\frac{-q}{1+q}+\frac{-q^2}{1+q^2}+\cdots$ ([1]) is transcendental.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Journal of The Korean Astronomical Society
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• v.36 no.3
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• pp.89-95
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• 2003

Observations of dark matter dominated dwarf and low surface brightness disk galaxies favor density profiles with a flat-density core, while cold dark matter (CDM) N-body simulations form halos with central cusps, instead. This apparent discrepancy has motivated a re-examination of the microscopic nature of the dark matter in order to explain the observed halo profiles, including the suggestion that CDM has a non-gravitational self-interaction. We study the formation and evolution of self-interacting dark matter (SIDM) halos. We find analytical, fully cosmological similarity solutions for their dynamics, which take proper account of the collisional interaction of SIDM particles, based on a fluid approximation derived from the Boltzmann equation. The SIDM particles scatter each other elastically, which results in an effective thermal conductivity that heats the halo core and flattens its density profile. These similarity solutions are relevant to galactic and cluster halo formation in the CDM model. We assume that the local density maximum which serves as the progenitor of the halo has an initial mass profile ${\delta}M / M {\propto} M^{-{\epsilon}$, as in the familiar secondary infall model. If $\epsilon$ = 1/6, SIDM halos will evolve self-similarly, with a cold, supersonic infall which is terminated by a strong accretion shock. Different solutions arise for different values of the dimensionless collisionality parameter, $Q {\equiv}{\sigma}p_br_s$, where $\sigma$ is the SIDM particle scattering cross section per unit mass, $p_b$ is the cosmic mean density, and $r_s$ is the shock radius. For all these solutions, a flat-density, isothermal core is present which grows in size as a fixed fraction of $r_s$. We find two different regimes for these solutions: 1) for $Q < Q_{th}({\simeq} 7.35{\times} 10^{-4}$), the core density decreases and core size increases as Q increases; 2) for $Q > Q_{th}$, the core density increases and core size decreases as Q increases. Our similarity solutions are in good agreement with previous results of N-body simulation of SIDM halos, which correspond to the low-Q regime, for which SIDM halo profiles match the observed galactic rotation curves if $Q {\~} [8.4 {\times}10^{-4} - 4.9 {\times} 10^{-2}]Q_{th}$, or ${\sigma}{\~} [0.56 - 5.6] cm^2g{-1}$. These similarity solutions also show that, as $Q {\to}{\infty}$, the central density acquires a singular profile, in agreement with some earlier simulation results which approximated the effects of SIDM collisionality by considering an ordinary fluid without conductivity, i.e. the limit of mean free path ${\lambda}_{mfp}{\to} 0$. The intermediate regime where $Q {\~} [18.6 - 231]Q_{th}$ or ${\sigma}{\~} [1.2{\times}10^4 - 2.7{\times}10^4] cm^2g{-1}$, for which we find flat-density cores comparable to those of the low-Q solutions preferred to make SIDM halos match halo observations, has not previously been identified. Further study of this regime is warranted.

• Proceedings of the Korean Vacuum Society Conference
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• 2005.08a
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• pp.40-40
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• 2005

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.287-303
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• 1999

The general solution of the functional equation f1(pr, qs) + f2(ps, qr) = g(p,q) + h(r,s) for p, q, r, s $\in$] 0, 1[will be investigated without any regularity assumptions on the unknown functions f1, f2, g, h:]0.1[->R.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.95-101
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• 2014

An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.7
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• pp.192-199
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• 2018

This study was conducted to examine the nursing image types and characteristics of nurses perceived by nursing college students by applying the Q methodology and to manage effective nursing education and clinical education. The survey was conducted from May 15, 2017 to May 24, 2017, and the data collection for the Q population composition was based on in-depth interviews and literature review. First, nursing college students were searched for convenience and 158 statements were obtained based on open questionnaires and 64 statements extracted from in-depth interviews and after a literature review. To select the Q sample, Q population was categorized by taking several repeated readings. Five categories were developed from these processes: quality and role, social awareness, professionalism, uniqueness, and working conditions. The selected statements were reviewed and revised by experts and 35 Q samples were finally selected. Based on this, 46 students in one nursing college classified 35 Q statements, and analyzed data using PC QUANL program. The results of the study were as follows: 2) Type I-1: Job related anxiety, Type I-2: cold and professional, Type II-1: Complaint of treatment and Type II-2: Profession-Unacceptable. These results are expected to provide useful data for understanding the characteristics of nurses' images and provide data enabling development of image improvement strategies of nursing education and clinical education.

• KIEE International Transactions on Electrophysics and Applications
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• v.4C no.1
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• pp.21-25
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• 2004

From the gradual increasing state of charge (GISOC) observations, electrochemical behavior of multi-walled carbon nanotube│(lM LiP $F_{6}$ , EC,DEC,DME 3:5:5 volume ratio)│lithium cells was evaluated using the galvanostatic charge-discharge process. A MWCNT delivers a specific charge capacity of 1,300 mAh/g in a Li cell when cycled up to an end voltage of 0 V (vs. Li/L $i^{＋}$ )at a constant current rate every 10 hours. However, in the present study, the specific discharge capacity obtained is 338 mAh/g, thus amounting to a coulombic efficiency of only 26％. Further, when the MWCNT│Li cells were tested using the GISOC method, two distinguishable linear-fit ranges were observed due to the intercalation/deintercalation of lithium, which were found to have II $E_1$, IIC $s_1$ and II $E_2$of 27.3％, 372 mAh/g, and 25.5％, respectively. Q $c_1$, could be calculated from the data of IIE and IICs of each range by the modified equation "II $C_{sum}$= $\Sigma$( $Q_{C}$- $Q_{D}$)=(II $E_{1}$$^{-1}$ ) $Q_{Dl}$ ＋(II $E_2$$^{-1}$ -1) ( $Q_{D2}$- $Q_{Dl}$ ) ＋ IIC $s_1$= $Q_{Cl}$ - $Q_{Dl}$ ". Results of the GISOC method could be converted to the results of galvanostatic charge-discharge process, irrespective of the state of charge of the cell or battery.ery.y.y.

• Proceedings of the Korean Vacuum Society Conference
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• 2005.02a
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• pp.47-47
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• 2005