• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.5
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• pp.87-93
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• 2014

For n/m=qm+r, there is no simple divisibility rule for simple m=7 such that is the n multiply by m? This problem can be more complex for two or more digits of m. The Dunkels method has been known for generalized divisibility test method, but this method can not compute very large digits number that can not processed by computer. This paper suggests simple and exact divisibility method for m completely irrelevant n and m of digits. The proposed method sets $r_1=n_1n_2{\cdots}n_l(mod m)$ for $n=n_1n_2n_3{\cdots}n_k$, $m=m_1m_2{\cdots}m_l$. Then this method computes $r_i=r_{i-1}{\times}10+n_i(mod m)$, $i=2,3,{\cdots}k-l+1$ and reduces the digits of n one-by-one. The proposed method can be get the quotient and remainder with easy, fast and correct for various n,m experimental data.

• 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.

• Korean Journal of Materials Research
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• v.7 no.3
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• pp.213-217
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• 1997

AOhf(Hcousto-r)l)tic niodulator) with :!OOlIiz freclucncl- and Sfi(;(Seconrl harmonic generation) green lasel-Lvith 53% nm wavelength were used for Il\'IIII~Dii.it,ii v~ilco disk recorder) FOI rhe appli~aptin of high densit]. optical recording, a high po\ver I ~ c r is r c ~ ~ l i ~ i l - u l ic I !tic. s\-sti,m a n d optic.,~I io;iting l,t)c>rs of each optical device must have a high laser damage threshoid hie rn;itie ant] retlwtive coatings on a $TeO_{2}$ singlc crystal. which is used as an acoustooptic material, by E-beam evaporation method. Laser damage threshold \vas nicdsureci hy Ar laser with the input power oi 0.55LV 1,aser damage threiholti 01 $ZrO_{2}$ and $SiO_{2}$. filn-is were higher than $AI_{2}O_{3}$ f i l m U'e also investigated a long--tern1 stability of the output po\ver of St{(; green laser

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.827-833
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• 2017

In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

• Journal of the Korean Association of Geographic Information Studies
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• v.11 no.1
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• pp.155-166
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• 2008

The quantitative bivariate spatial pattern analysis was applied for the water quality and nutrients data of Masan Bay, and for this analysis Pearson's r as aspatial correlation measurement, Moran's I as spatial association measurement and L index as integration of aspatial and spatial measurement methods were used. To understand the aspatial and spatial characteristics implicated in L index, Pearson's r as well as Moran's I were classified into 3 types respectively, and Pearson's r and Moran's I were combined with 9 types, and also quantile of L index value was used for each of those 9 types. Finally, these types were defined as 5 groups having not overlapped L index range. According to the application result of L index groups, bivariate water quality and nutrients showed no aspatial correlation regardless of spatial association in February and July, but they showed aspatial correlation having clustered spatial pattern in May and November. The result of this study providing the guideline for the interpretation of aspatial correlation and spatial association using L index is expected to be helpful for the marine environment pattern analysis using quantitative index for further study.

• Journal of the Mineralogical Society of Korea
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• v.16 no.3
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• pp.223-232
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• 2003

The co-precipitation method is applied to synthesize the cathode material Li[L $i_{x}$M $n_{1-x-y}$C $r_{y}$ ] $O_2$ for lithium rechargeable batteries at $650^{\circ}C$ (CR650) and 8$50^{\circ}C$ (CR850), respectively. Rietveld indices indicate that $R_{wp}$ with respect to $R_{exp}$ ( $R_{wp}$/ $R_{exp}$) are 9.2%/10.1% for CR650 and 15.9%/9.76% for CR850, respectively. $R_{B}$ and S (GofF) shows 10.9%, 8.54% and 1.9, 1.6, respectively. Rietveld structure refinement reveals that layer structure of LiMn $O_2$ (R3m) coexists with lower symmetry of Li[L $i_{1}$3/M $n_{2}$3/] $O_2$ (C2/c) due to superlattice ordering of Li and Mn in metal-transition containing layers. Unit-cell parameters are calculated as a=2.8520(2)$\AA$, c=14.248(2)$\AA$, V=100.40(l)$\AA^3$ for CR650, and a=2.8504(1)$\AA$, c=14.2371(7)$\AA$, V=100.179(8)$\AA^3$ for CR850. Final chemistry is obtained as Li[L $i_{0.35}$M $n_{0.56}$C $r_{0.09}$] $O_2$ (CR650) and Li[L $i_{0.27}$M $n_{0.61}$C $r_{0.13}$] $O_2$ (CR850), respectively.y...y..vely.y...y..

• Journal of Sensor Science and Technology
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• v.24 no.1
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• pp.47-53
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• 2015

Fall-related injuries in elderly people are a major health care problem. This paper introduces determination of fall direction before impact using support vector machine (SVM). Once a falling phase is detected, dynamic characteristic parameters measured by the accelerometer and gyroscope and then processed by a Kalman filter are used in the SVM to determine the fall directions, i.e., forward (F), backward (B), rightward (R), and leftward (L). This paper compares the determination sensitivities according to the selected parameters for the SVM (velocities, tilt angles, vs. accelerations) and sensor attachment locations (waist vs. chest) with regards to the binary classification (i.e., F vs. B and R vs. L) and the multi-class classification (i.e., F, B, R, vs. L). Based on the velocity of waist which was superior to other parameters, the SVM in the binary case achieved 100% sensitivities for both F vs. B and R vs. L, while the SVM in the multi-class case achieved the sensitivities of F 93.8%, B 91.3%, R 62.3%, and L 63.6%.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.22 no.4
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• pp.201-213
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• 1989

This study is just to be carried out to grasp the efficiency of jet stream excavating for the ground. Changing the dynamic pressure, nozzle diameter, distance off the ground, we measured the impulse, the excavated depth, the excavated width. According as each dynamic pressure increases from 100 to $500gf/cm^2$, the impulse of the jet stream increases from 43 to 114gf, from 52 to 227gf, from 114 to 506gf, from 137 to 768gf, in 4, 6, 8, 10mm nozzles respectively, but it makes no difference in the value of distance within 50cm off ground. The excavated depth increases at the invariable rate in accordance with nozzle diameter, dynamic pressure, nozzle distance. We obtain the equations relevant to the ground I, II as follows: $$L_I=[0.01(H/r-100) -0.43\cdot\iota+11.78]{\cdot}D/4$$ $$L_{II}=[0.03(H/r-100) -0.34\cdot\iota+6.39]{\cdot}D/4$$ where, $L_I,\;L_{II}$ are respectively the excavated depths of the ground I, II, cm; H is the dynamic pressure, $gf/cm^2\;:\;\iota$ is the distance off the ground, cm; D is Nozzle diameter, mm; r is the specific weight, $1gf/cm^2$.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.731-751
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• 2023

If p(z) is a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1, then for any complex number α with |α| ≥ k, and r ≥ 1, Aziz [1] proved $$\left{{\int}_{0}^{2{\pi}}\,{\left|1+k^ne^{i{\theta}}\right|^r}\,d{\theta}\right}^{\frac{1}{r}}\;{\max\limits_{{\mid}z{\mid}=1}}\,{\mid}p^{\prime}(z){\mid}\,{\geq}\,n\,\left{{\int}_{0}^{2{\pi}}\,{\left|p(e^{i{\theta}})\right|^r\,d{\theta}\right}^{\frac{1}{r}}.$$ In this paper, we obtain an improved extension of the above inequality into polar derivative. Further, we also extend an inequality on polar derivative recently proved by Rather et al. [20] into L^r-norm. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.