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

• Journal of Yeungnam Medical Science
• /
• v.4 no.1
• /
• pp.1-15
• /
• 1987

Magnetic Resonance (M.R.) is rapidly emerging technique that provides high quality images and potentially provides much more diagnostic information than do conventional imaging modalities. M.R.I. is conceptually quite different from currently used imaging methods. The complex nature of M.R.I. allows a great deal of flexibility in image product ion and available information, and key points are as follows. 1. M.R.I. offers a non-invasive technique with which to gene rate in vivo human images without ionizing radiation and with no known adverse biological effects. 2. Imaging mechanism of M.R.I. is quite different from conventional imaging modality and for more accurate diagnostic application, It is necessary for physician to understand imaging mechanism of M.R.I. 3. M.R. makes available basic chemical parameters that may provide to be useful for diagnostic medical imaging and more specific pathophysiologic information which are not available by alternate techniques. 4. M.R. can be produced by number of different methods. This flexibility allows the imaging technique to be applicated for particular clinical purpose. Multiplanar and three dimensional imaging may extend the imaging process beyond the single section available with current CT. 5. Future directions include efforts to; a. Further development of hard ware b. More fasternning scan time c. Respiratory and cardiac gated imaging d. Imaging of additional nuclei except hydrogen e. Further development of contrast media f. M.R. in vivo spectroscopy g. Real time M.R. imaging.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.13 no.4
• /
• pp.239-250
• /
• 1993

The dynamic resilient modulus tests to determine the $M_R$ of the soils require expensive equipments and well trained personnels to obtain reliable test results. These problems inherent in the dynamic resilient modulus testing have been realized as major negative factors to hinder the $M_R$ test from being practically implemented as a routine test. In this regard. it is highly desirable to develop a simpler alternative testing method incorporating inexpensive equipments and easy-to-perform testing procedures. Developed in this study is an alternative $M_R$ test method based on statically repeated loading scheme utilizing the standard static triaxial test equipments. Applicability and limitations of the developed static $M_R$ testing method are investigated for typical subgrade soils in Korea.

• International Journal of Highway Engineering
• /
• v.2 no.2
• /
• pp.149-161
• /
• 2000

The stiffness of the subbase materials is represented by the resilient modulus, $M_R$, which are very important properties in the mechanistic design of flexible pavement system. However, the cyclic $M_R$ testing method is too complex, expensive, and time consuming to be applicable on a production basis. In this study, the alternative $M_R$ testing technique for subbase materials was developed using a free-free resonant column (FF-RC) test considering deformational characteristics of subbase materials. To estimate the deformational characteristics of subbase materials, effects of strain amplitude and mean effective stress on modulus of subbase materials were investigated. The $M_R$ values determined by alternative testing procedures matched well with those determined by standard $M_R$ test, showing the capability of the proposed methods being used in determining $M_R$ values.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.295-306
• /
• 2012

Let (R, $m_R$, k) be a local maximal commutative subalgebra of $M_n$(k) with nilpotent maximal ideal $m_R$. In this paper, we will construct a maximal commutative subalgebra $R^{ST}$ which is isomorphic to R and study some interesting properties related to $R^{ST}$. Moreover, we will introduce a method to construct an algebra in $MC_n$(k) with i($m_R$) = n and dim(R) = n.

• Kyungpook Mathematical Journal
• /
• v.62 no.4
• /
• pp.769-772
• /
• 2022

Given a prime number p and a natural number m not divisible by p, we propose the problem of finding the smallest number r₀ such that for r ≥ r₀, every group G of order p^rm has a non-trivial normal p-subgroup. We prove that we can explicitly calculate the number r₀ in the case where every group of order p^rm is solvable for all r, and we obtain the value of r₀ for a case where m is a product of two primes.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.885-898
• /
• 2012

Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.

• Journal of the Korean Society of Radiology
• /
• v.5 no.3
• /
• pp.155-159
• /
• 2011

The purposed of this study were measured the radiation exposure of patients and workers by generators, and the protection state for radiation facilities. The subject of the study by X-ray generators in university hospitals of capital area, we measured the maximum irradiation condition of 80 kVp, 200 mA, 0.1 second in the control entrance, control room window, entrance of radiography, adjacent site. The leakage dose per week was which the control entrance was 0.11 mR/week, control room window was 0.15 mR/week, entrance of radiography was 0.12 mR/week and adjacent site was 0.06 mR/week with X-ray unit the mean And the leakage mean dose was 0.11 mR/week. Diagnostic X-ray tubes must ensure that the leakage radiation in the maximum leakage dose in week emitted by the tube outside the useful beam does not exceed certain levels provided by standards.

• Honam Mathematical Journal
• /
• v.31 no.4
• /
• pp.515-527
• /
• 2009

Let R be a commutative ring with identity. Then we prove $M_n(R)=GL_n(R)$ ${\cup}${$A{\in}M_n(R)\;{\mid}\;detA{\neq}0$ and det $A{\neq}U(R)$}${\cup}Z(M-n(R))$ where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring $M_n(F)$ over a field F is the disjoint union of the general linear group $GL_n(F)$ of degree n over the field F and the set $Z(M_n(F))$ of all zero-divisors of $M_n(F)$. Using the result and universal mapping property we prove that $M_n(F)$ is its total ring of fractions.

• Journal of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.87-98
• /
• 2014

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say ${\Gamma}(M)$, such that when M = R, ${\Gamma}(M)$ is exactly the classic zero-divisor graph. Many well-known results by D. F. Anderson and P. S. Livingston, in [5], and by D. F. Anderson and S. B. Mulay, in [6], have been generalized for ${\Gamma}(M)$ in the present article. We show that ${\Gamma}(M)$ is connected with $diam({\Gamma}(M)){\leq}3$. We also show that for a reduced module M with $Z(M)^*{\neq}M{\backslash}\{0\}$, $gr({\Gamma}(M))={\infty}$ if and only if ${\Gamma}(M)$ is a star graph. Furthermore, we show that for a finitely generated semisimple R-module M such that its homogeneous components are simple, $x,y{\in}M{\backslash}\{0\}$ are adjacent if and only if $xR{\cap}yR=(0)$. Among other things, it is also observed that ${\Gamma}(M)={\emptyset}$ if and only if M is uniform, ann(M) is a radical ideal, and $Z(M)^*{\neq}M{\backslash}\{0\}$, if and only if ann(M) is prime and $Z(M)^*{\neq}M{\backslash}\{0\}$.