• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.1-7
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• 2022

A mapping T : R → R (not necessarily additive) is called multiplicative left 𝛼-centralizer if T(xy) = T(x)𝛼(y) for all x, y ∈ R. A mapping F : R → R (not necessarily additive) is called multiplicative (generalized)(𝛼, 𝛽)-derivation if there exists a map (neither necessarily additive nor derivation) f : R → R such that F(xy) = F(x)𝛼(y) + 𝛽(x)f(y) for all x, y ∈ R, where 𝛼 and 𝛽 are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (𝛼, 𝛽)-derivations and multiplicative left 𝛼-centralizer on the left ideal of a prime ring R.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.11-15
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• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.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 non-degenerate (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)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) 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 U9R). 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 $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

• Korean Journal of Poultry Science
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• v.34 no.4
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• pp.245-251
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• 2007

This study was conducted to investigate the effects of modification of a herbal recipe(Herb $Mix^{(R)}$) on the growth of pullet and laying performance of hens. The formula of Herb $Mix^{(R)}$, a mixture of Rehmannia glutinosa, Angelica gigas, Discorea japonica, Glycyrrhiza uralensis, Schisandra chinensis and Ligusticum jeholense, was modified in mixing ratio. A total of 1,120 pullets(Hy-Line Brown) of 14 wks old were assigned to seven treatments; control, Herb $Mix^{(R)}$(HM), R. glutinosa fortified HM, A. gigas fortified HM, D. japonica fortified HM, G. uralensis fortified HM, S. chinensis fortified HM, L. jeholense fortified HM and Flavomycin supplemented diet. Each treatment had 8 replicates of 20 birds each housed in 2 birds cages. Body weight at 10% egg production was significantly(P<0.05) influenced by treatments. Birds fed A. gigas fortified HM diet were heaviest followed by L. jeholense fortified HM, HM-original and D. japonica fortified HM, Flavomycin supplemented diet and R. glutinosa while those fed control diet were lightest. Also, age reaching 50% egg production and peak production was earliest in A. gigas fortified HM and latest in the control. Egg production, feed intake, feed conversion and egg weight were significantly influenced by treatments. Significant improvement in egg production and feed intake was shown in A. gigas fortified HM treatment. Feed conversion ratio was lowest in antibiotic(Flavomycin) treatment and egg weight was heaviest in L. jeholense fortified HM treatment. There were no significant differences among treatments in intestinal microflora but cfu of Cl. perfringnes and E. coli tended to be lower in HM treatments than the control. Among the leucocytes of blood, the HM treatments were lower than the control in counts of white blood cell and heterophils. It was concluded that modification of Herb $Mix^{(R)}$ fortifying with A. gigas, D. japonica and L. jeholense significantly influence growth and laying performance of birds.

• Journal of Aquaculture
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• v.10 no.1
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• pp.25-32
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• 1997

Develoment precess and characteristics of eggs of the geoduck clam, Panope japonica are reporting in this study. Eggs and sperm were excised from gonad, artificially fertilized in an aquarium, reared under various temperature regimes, and record and record the larval period and the time need to reach a certain larval stage from ferilization. Unfertilized eggs of P. japonica appeared to be oval with a mean diameter of $70\mu$m and they became spherical after fertilization. The eggs of P. japonica can be classified as demersal. At a constant water temperature of $ 11^{citc}C$, it took 4 hours form fertilization to become four-cell stage, two days to become trochophore larvae, three days to become D-shape larvae, twenty-three days to become umbo stage, and thirty-six days to become fully grown veliger ready form settlement. A negative correlation was observed between the water temperature and the larval period of P. japonica. From fertilization to D-shape larvae, it took five days at 8$^{\circ}C$, while it was only two days to become D-shape larvae at $ 17^{citc}C$. Time required to D-shape larvae from fertilization was proportional to temperature, and the relationships were expressed as follows : To 8-cell stage, 1/t=0.0209 w-0.1167 (r=0.9967) To blastula stage, 1/t=0, 0055 w-0.0192 (r=0.9825) To trochophore stage, 1/t=0.0034 w-0.0155 (r=0.9907) To D-shape larvae stage, 1/t=0.0014 w-0.0023 (r=0.9843) (t, time in hours ; w, water temperature) Bioligical minimum temperature for egg development was calculated as 3.82$^{\circ}C$ in average.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.9 no.1
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• pp.13-18
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• 1976

1) The variation of the reef knot strength $T_r$ and the trawler knot strength $T_\varrho$ with the angle $\varphi$ between the adjacent bars are given by $$T_r=T_{ro}-k_{r\varphi}$$ and $$T_\varrho=T_{{\varrho}o}+k_{\varrho\varphi}$$ where $T_{ro}$ and $T_{{\varrho}o}$ are values of $T_r$ and $T_\varrho$ at $\varphi=0^{\circ}$ respectively, and $k_r$ and $k_\varrho$ constants decided by the fibre materials of netting twines ($\varphi\;is\;0^{\circ}$ when the knot is pulled lengthwise). 2) The variation of the reef knot strength $T_r'$ and the trawler knot strength $T_\varrho'$ with the angle $\varphi'$ between any one bar and the plane made by the other three bars may be expressed by $$T_r'=T_{ro}{'}\varrho^{-c\varphi'}$$ and $$T_\varrho'=T_{{\varrho}o}{'}\varrho^{-c\varphi'}$$ where $T_{ro}{'}$ and $T_{\varrho}o{'}$ are values of $T_r{'}$ and $T_\varrho{'}$ at $\varphi'=0^{\circ}\;{(\varphi=45^{\circ})}$ respectively, and o is the coefficient of attenuation. 3) Knot strength of knotted netting may be expressed by the expression derived in the preyious paper, disregarding its shape and the direction of tensile loads acting on it.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.11-16
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• 2006

In this article we show that if R is a Noetherian ring with the global dimension at most one, then every S-torsion free R-module T has a divisible envelope of the form $T{\hookrightarrow}S^{-1}T$

• Korean Journal of Fisheries and Aquatic Sciences
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• v.31 no.4
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• pp.529-534
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• 1998

Age and growth of the yellow goosefish, Lophius litulon, were studied using samples collected from the southwestern waters of Korea. Vertebrae of the fish had relatively clear annuli on their surface. The opaque zone of vertebrae was formed once a year between March and April. The oldest fish observed in this study was 8 years old for females and 5 years old for males. The relationship between the radius (R) of vertebral centrum and total length (L) was as follows: L=12.7+4.8R for females and L=9.8+5.6R for males. The relationship between total length and body weight (W) was as follows : $W=0.0089L^{3.0311}$ for females and $W=0.0329L^{2.7752}$ for males. Growth in length of the fish was expressed by the von Bertalanffy's equation as $L_t=127.60(1-e^{-0.1228(t+0.3851)})$ for females and $L_t=82.23(1-e^{-0.1832(t+0.6431)})$ for males.

• Research in Community and Public Health Nursing
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• v.1 no.1
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• pp.465-502
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• 1989

The purpose of this study was to find out the general characteristics of school health teachers, the status of school health resources and the degrees of self-confident performance for the 124 school health teachers in Pusan City. Data was collected by means of questionaires from Aug. 1986 to Mar. 1987. The data were analyzed by use of percentage, mean, standard deviation, t-test, ANOVA and Pearson-correlation coefficient. The results of this study were as follows: 1 . General Characteristics of School Health Teachers (SHT) 1) The average of age of the SHT was 32.8 years old and 39.5% of them were from 30 to 34 years old. 2) The average for school nursing experience of the SHT was 7.9 years and 37.9% of them were from 5 to 9 years. 3) The 45.2% of them have not the clinical experience. 4) The 74.2% of them were graduated from the 3 years college of nursing. 2. Status of school health resources and nursing activities. 1) The average of student number was 2497.3 and class number was 45.2. 2) The average of school health budget was 1039000 won and 27.7% of school health budget expended on examination cost. 3) Only 29.0% of all schools have organization for school health. 4) The 84.7% of all schools have health clinic separately and 69.1% of schools have less than $33m^2$ sized. 5) The average of clinic visitor number was 2111.8 for 1 year. 6) Major problem was on digestive system. And other problems were skin, respiratory, musculo-skeletal system and dental problem. 7) The number of literal message was 14.4 times for 1 year. 3. The degree of the school health teachers' self-confidence. The school health teachers' self-confidence was deviced into 6 and the maximum degree was 4. 1) Program planning & evaluation; 2.8 2) Clinic management; 2.9 3) Health education, 3.0 4) Management of school environment; 2.7 5) Health care services; 2.7 6) Operating of school health organization; 2.4 4. Significances to the degree of self-confidence on school health nursing activities. 1) There was significant difference between clinical management and Religion (t=2.15 p<.05) 2) There was significant difference between Operating of school health organization and level of school (F=3.588 p<.05) 3) Program planning & evaluation: expending time for clinical management (r=-0.184 p<.05) expending time for health care services (r=0.273 p<.01) 4) Clinical management: use of separate health clinic (r=0.151 p<.05) 5) Health education: use of separate health clinic (r=0.170 p<0.5) 6) Health care services: No. of student (r=-0.144 p<0.5) No. of class (r=-0.160 p<.05) 5. The degree of the school health teachers' self-discipline. The school health teachers' self-discipline was devided into 2 and the maximum degree was 2. 1) Program planning & evaluation:1.8 2) Clinic management: 1.9 3) Health education: 1.9 4) Management of school environment: 1.7 5) Health care services: 1.8 6) Operating of school health organization.: 1.3 6. Significances to the degree of self-discipline on school health nursing activities 1) Program planning & evaluation; Level of nursing education (F=4.309 p<.01) 2) Clinical management: Level of nursing education (F=3.587 p<.05) 3) Operating of school health organization: School health organization (t=-2.68 p<.01) 4) Health care services: School health organization (t=2,58 p<.05) 5) School health performance: School health organization (t=2.32 p<.05) 6) Program planning & evaluation: School health experience (r=0.239 p<.01) Expending time for program planning & evaluation (r=-0.172 p<.05) 7) Clinic management: School health experience (r=0.249 p<.01) Expending time for dinic management (r=0.181 p<.05) No. of student (r=-0.158 p<.05) Expending time of program planning & evaluation (r=-0.199 p<0.5) 8) Health education: School health experience (r=0.234 p<0.1) Expending time of program planning & evaluation (r=-0.193 p<.05) 9) Management of school environment: Age of school health teacher (r=0.142 p<.05) School health experience (r=0.255 p<.01) 10) Operating of school health organization: Medicine Purchase (r=-0.163 p<.05) 11) Health care services: School health experience (r=0.148 p<.05) Medicine purchase (r=-0.229 p<.01) 12) Total school health performance: School health experience (r=0.200 p<.05) Medicine purchase(r=-0.168 p<.05) Based on the above results, the suggestions are as follows: 1) As the SHT take charge of the reasonable number of student, the students will have benefit of the good health service in quality. 2) It is recommended to use the health clinic separately and to arrange adequate place for good school health service. 3) It is necessary that the SHT participate budget for school health. 4) It is required to enhance self-confidence on school health nursing activities through continuous educational programs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.1
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• pp.188-198
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• 2005

The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Journal of Digital Convergence
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• v.17 no.10
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• pp.349-357
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• 2019

The purpose of this study was to investigate the effects of body mass index(BMI) on insulin. fasting blood sugar(FBS), and hemoglobin A1c(HbA1c). This study analyzed the data of 2015, The Sixth KNHANES, and it was included to 4554 subject over 20 years old. Data were analyzed using descriptive statistics, t-test, ANOVA, Pearson correlation coefficient and stepwise multiple regression analysis(SPSS 25.0). The major findings, BMI was positively correlated with insulin(r=0.397, p<0.001), FBS(r=0.241, p<0.001), and HbA1c(r=0.237, p<0.001). Factors affecting insulin are overweight(${\beta}=.130$, t=8.193, p<0.001), obesity(${\beta}=.390$, t=24.390, p<0.001) and age. the explanatory power is 13.1% (F=53.584, p<0.001). Factors affecting FBS were overweight(${\beta}=.072$, t=4.478, p<0.001), obesity(${\beta}=.186$, t= 11.485, p<0.001), age, the explanatory power was 10.6% (F=42.351, p<0.001). Factors affecting HbA1c were overweight(${\beta}=.059$, t=3.712, p<0.001), obesity(${\beta}=.190$, t=11.895, p<0.001) age and sex, the explanatory power is 14.1% (F=58.134, p<0.001). Based on this study result, diabetes mellitus prevention and management programs should include interventions related to obesity.