• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.761-768
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• 2021

Let I be a nonzero ideal of a prime ring R and m, n are positive integers. If R admits a generalized derivation F satisfying F(x)ⁿF(y)^m - xⁿy^m = 0 for any y, x ∈ I, then F(x) = ax for any x ∈ R and a^m+n = 1, where a ∈ C, the extended centroid of R.

• Korean journal of applied entomology
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• v.45 no.3 s.144
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• pp.333-337
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• 2006

The damage aspects of soybean by common cutworm, Spodoptera litura (Fabricius) (Lepidoptera: Noctuidae) at different larval density and different growth stage of soybean were studied in soybean field. The percent yield reduction(Y) of soybean infested by different densities of S. litura (X, no. of larvae/plant) under outdoor conditions for a three week period were estimated by the following equations: (1) Y = 1.655X - 6.025 ($R^{2}=0.952$) for the R1 (flowering stage); (2) Y = 0.725X - 0.475 ($R^{2}=0.986$) for the R3 (beginning pod stage); and (3) Y = 0.635X - 1.325 ($R^{2}=0.986$) for the R5 (beginning seed stage). Based on the relationships between the densities of S. litura larvae and the yield index of soybean, the number of larvae (2nd-3rd instar) which caused 5% loss of yield (Tolerable injury level) was estimated to as approximately 6.7 for the R1, 7.5 for the R5, and 10.0 per plant for the R5, respectively. Average soybean leaf areas consumed by 1st, 2nd, 3rd, 4th, 5th and 6th larvae of Spodoptera litura during 24 hr at $28^{\circ}C$ was 0.3, 0.7, 2.6, 4.0, 20.1, and $55.8\;cm^{2}$, respectively.

• The Korean Journal of Zoology
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• v.6 no.2
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• pp.11-15
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• 1963

A total of 220 adult male mice (18-20g) of the S.M. strain were divided into ten experimental and control groups. The total-body X-ray irradiation doses used were 50 r, 100r, 200r, 400r, 600r, 800r, 1,000r, 1,200r, 1,400r, and1,600r. The respiratory arrest (mortality) caused by each irradiation doses were observed for 30 days. Relationships between irradiation doses and survival time and percentage of response were examined. From this experiment, a formula was obtained to express the relationship among three factors, which may be presented as follows : {{{{{{{{P= { 10} over { SQRT { 2 pi } } INT _{ - INF }^{ p'} e-{(p'-50)^2 } over {200 }dp···(a) p'=100 LEFT { t^0.3- LEFT ( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } } / LEFT { LEFT ( { 26372.43} over {D-81.86 } RIGHT ) ^{ { 1} over {2.5 } } -( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } ···(b) p= { (D-60) t^0.75-16.9965} over {0.2186 t^0.75 +263.55434 }····(c) }} {{{{P= { 10} over { SQRT { 2 pi } } INT _{ - INF }^{ p'} e-{(p'-50)^2 } over {200 }dp···(a) p'=100 LEFT { t^0.3- LEFT ( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } } / LEFT { LEFT ( { 26372.43} over {D-81.86 } RIGHT ) ^{ { 1} over {2.5 } } -( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } ···(b) p= { (D-60) t^0.75-16.9965} over {0.2186 t^0.75 +263.55434 }····(c)

• The Korean Journal of Zoology
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• v.14 no.4
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• pp.175-180
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• 1971

The effects of X-irradiation on the mitotic activity, the chromosome aberration and the DNA synthetic pattern in synchronized human kidney cells treated with 5-AU were measured in the present experiment. When 5-AU was added, mitotic activity was markedly suppressed. After removal of the cells from the chemical, its activity proceeded synchronouly and reached peaks at hours 10. In 5-AU+100R groups, it was observed the X-ray caused mitotic delay, the irregularity of the time when mitotic peak appeared and the inhibiton of mitotic activity. In the control group, chromosome aerrations per cell was 0.030, whereas 0.147 in 5-AU treated group. In 5-AU+100R and 5-AU+200R groups, chromosome aberrations per cell were 0.583 and 0.669 respectively and the average chromosome aberrations per cell per R was 0.0035. 5-AU increased the frequency of labeled metaphases together with labeling intensity, and this is thought to be due to the accumulation of cells by 5-AU at S stage. On the contrary, X-ray decreased the labeling intensity and the frequency of labeled metaphases.

• East Asian mathematical journal
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• v.30 no.5
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• pp.617-623
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• 2014

Due to Bell, a ring R is usually said to be IFP if ab = 0 implies aRb = 0 for $a,b{\in}R$. It is shown that if f(x)g(x) = 0 for $f(x)=a_0+a_1x$ and $g(x)=b_0+{\cdots}+b_nx^n$ in R[x], then $(f(x)R[x])^{2n+2}g(x)=0$. Motivated by this results, we study the structure of the IFP when proper ideals are taken in place of R, introducing the concept of insertion-of-ideal-factors-property (simply, IIFP) as a generalization of the IFP. A ring R will be called an IIFP ring if ab = 0 (for $a,b{\in}R$) implies aIb = 0 for some proper nonzero ideal I of R, where R is assumed to be non-simple. We in this note study the basic structure of IIFP rings.

• ETRI Journal
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• v.31 no.1
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• pp.68-70
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• 2009

In this letter, a parametric analysis of the Fresnel-field antenna measurement method is performed for a square aperture. As a result, the optimum number of Fresnel fields for one far-field point is guided as $M_{opt}=N_{opt}=D^2/{\lambda}R+5$, where D is the antenna diameter, ${\lambda}$ is the wavelength, and R is the distance between the source antenna and the antenna under test. For the aperture size 5 ${\leq}$ $L_x/{\lambda}$ ${\leq}$ 20, the tolerable distances for gain errors of 0.5 dB and 0.2 dB can be guided as $R_{0.5\;dB}$ ${\approx}$ $1.2Lx/{\lambda}$ and $R_{0.2\;dB}$ ${\approx}$ $2.0L_x/{\lambda}$, where $L_x$ is the lateral length of the square aperture. The tolerable distances for 20 ${\leq}$ $L_x/{\lambda}$ ${\leq}$ 200 are also proposed. This measurement guideline can be fully utilized when performing the Fresnel-field antenna measurement method.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.4 no.1
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• pp.97-101
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• 1968

Effects of weather factors on leaf tobacco yield were studied from the yield data of flue-cured yellow tobacco variety Yellow pryer and weather recordes for 13 years from 1952 to 1964. The results are summarized as follows; 1. Leaf tobacco yield variation was large and larger coefficient of variance was calculated. 2. Yield of leaf tobacco was correlated largely to leaf number, with simple correlation coefficient r=0.736. Leaf number was correlated largely to sunshine hours during May with r=0.745, and multiple correlation coefficient R=0.837 between leaf number and multiple weather factors during May to June. 3. Leaf tobacco yield was largely affected by the sunshine hours (r=0.717) and temperature (r=0.329) in May and precipitation (r=0.421) in June. 4. From the study of partial regression of leaf tobacco yield on weather factors a formulation Y=441.664-31.255$X_1$+1.19$Y_2$-0.031$X_3$ was calculated for the estimation of leaf tobacco yield. Here R=0.8074 d.f.=7 was significant.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1031-1043
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• 2018

Let R be a commutative ring with $1{\neq}0$, I a proper ideal of R, and m and n positive integers. In this paper, we define I to be a weakly (m, n)-closed ideal if $0{\neq}x^m\;{\in}I$ for $x{\in}R$ implies $x^n{\in}I$, and R to be an (m, n)-von Neumann regular ring if for every $x{\in}R$, there is an $r{\in}R$ such that $x^mr=x^n$. A number of results concerning weakly(m, n)-closed ideals and (m, n)-von Neumann regular rings are given.

• Journal of Oral Medicine and Pain
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• v.18 no.1
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• pp.107-117
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• 1993

The author has taken intraoral standard films by the paralleling technique of 6414 teeth in 838 patients ranged from early twenties to early sixties and analysed the change of pulp cavity in the mandibular posterior teeth by ageing. The obtined results were as follows : 1. There was no significant difference between the right and left teeth. 2. The degree of change of pulp cavity in female was higher than that in male. 3. The change of pulp cavity was increased by ageing. 4. The correlation between the degree of change of pulp cavity inmandibular posterior teeth (X) and age (Y) were : Male 1st premolar Y=13.22X3.37+ r=0.79 2nd premolar Y=12.09X+3.65 r=0.79 1st molar Y=11.90X+1.25 r=0.78 2nd molar Y=10.51X+10.43 r=0.83 Female 1st premolar Y=13.66X-2.49 r=0.86 2nd premolar Y=13.63X-2.42 r=0.86 1st molar Y=12.42X-1.44 r=0.79 2nd molar Y=11.42X+5.91 r=0.84