• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.435-445
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• 2015

In this paper, using the fixed point method, we investigate the generalized Hyers-Ulam stability of the system of quintic functional equation $f(x_1+x_2,y)+f(x_1-x_2,y)=2f(x_1,y)+2f(x_2,y)\;f(x,2_{y1}+y_2)+f(x,2_{y1}-y_2)=f(x,y_1-2_{y2})+f(x,y_1+y_2)\;-f(x,y_1-y_2)+15f(x,y_1)+6f(x,y_2)$ in non-Archimedean 2-Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.37-45
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• 2007

Let X, Y be vector spaces. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability problem for a cubic function $f:X{\rightarrow}Y$ satisfies $$r^3f(\frac{\Sigma_{j=1}^{n-1}x_j+2x_n}{r})+r^3f(\frac{\Sigma_{j=1}^{n-1}x_j-2x_n}{r})+8\sum_{j=1}^{n-1}f(x_j)=2f{\sum_{j=1}^{n-1}}x_j)+4{\sum_{j=1}^{n-1}}(f(x_j+x_n)+f(x_j-x_n))$$ for all $x_1,{\cdots},x_n{\in}X$.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.179-190
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• 2017

In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.4 no.1
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• pp.31-71
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• 1968

To clarify the breeding behavior of the hybrids between tropical and temperate area rice varieties, investigations were made on heading days and grain sterility. In this study, crosses were made in half way diallel involving 7 varieties: 2 photoperied sensitive Indicas, 2 less sensitive intermediate Indicas, 1 Ponlai Japonica and 2 high temperature sensitive Japonicas. The parents and $F_1$s were grown under 10 hours and 14 hours daylength controlled conditions at both IRRI(International Rice Research Institute, N$14^{\circ}$17') and Suwon(N$37^{\circ}$16'). F2s with their parents were grown at IRRI in the short day season, and at Suwon under natural conditions. Fa lines with their parents were grown at Suwon under natural conditions. Observations were made for heading days and sterility. The results are summarized as follow; 1. Heading days : 1. For the $F_1$s, earliness showed dominance or overdominance to lateness under the 10 hours condition, and dominance or partial dominance under the 14 hours conditions, at both IRRI and Suwon. 2. For the $F_2$s grown at IRRI during the shortday season earliness appeared to be dominant over lateness and segregation was not distinct and continuous. In the early season culture of $F_2$s at Suwon earliness showed partial dominance or was intermediate. In the proper season culture of $F_2$s lateness showed partial dominance or was intermediate. 3. In the combinations between late parental varieties which do not head at Suwon, transgressive segregants bearing effective panicles were obtained. 4. The crosses of parental varieties having long basic vegetative growth duration showed bigger variance in heading days, and significant correlation was found between of parental varieties and the mean coefficient of variance for parental arrays. 5. The means of heading days of F2 populations were significantly correlated with those of $F_1$ or mid-parents. The means of F 8 lines were also highly correlated with the means of $F_2$s, but, the means of $F_3$ lines grown at Suwon and of their parental $F_2$ individual, grown at IRRI were not correlated. 6. A faint heritability was calculated from the regression of $F_3$ lines grown at Suwon on the $F_2$ individuals grown at IRRI for most combinations, especially in the combinations involving shortday sensitive varieties. This implies low efficiency for the selection of heading days of $F_2$ individuals at IRRI to be grown in lines at Suwon. 7. No significant reciprocal effects were measured for $F_1$ and $F_2$ mean heading days. 8. Partitioning the observed photoperiod sensitivity. into two components, parental array mean md the deviation from this array mean, the parental photoperiod sensitivity contributing to the hybrids was measured in terms of general and specific combining ability for photoperiod sensitivity. 9. The photoperiod sensitivity of $F_1$s was higher than that of the parents, and it decreased as the generation progressed in most combinations of tested varieties. 10. The response of heading days to difference of temperature was weaker for $F_1$ hybrids than for the parents. The differences of temperature responses between the longday and shortday treatments were specific for the variety. 2. Sterility : 1. The $F_1$ sterility was specific for the combinations and not correlated to the parental sterility. The sterility of $F_1$s grown under the 10 hours condition was higher than of those grown under 14 hours. These results were the same at both locations, IRRI and Suwon. 2. The high sterile combinations in $F_1$ showed high sterility in $F_2$. The combinations between a high photoperiod sensitive variety and a high temperature sensitive variety showed high sterility and wider variance. 3. The mean sterility of $F_2$s was lower than of $F_1$s and the mean of $F_3$ lines was lower than of $F_2$s. Sterility decreased as the generation progressed, and the differences of $F_3$ sterility of different combinations were not significant. 4. A faint correlation between grain sterility and pollen sterility was observed in $F_2$ populations. 5. No significant reciprocal effects were measured in $F_1$ and $F_2$ sterility. 6. Following Griffing's method, specific combining ability effects were higher than general combining ability effects, especially in the combinations between highly photoperiod sensitive varieties and highly temperature sensitive varieties. 7. No distinct correlations were found between $F_2$ individual sterility grown at IRRI and $F_3$ line sterility grown at Suwon. 8. No distinct correlations were observed between heading days and sterility of $F_2$ individuals.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.121-140
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• 2010

This study presents one universal mean formula of implicate quantity for speed, temperature, consistency, density, unit cost, and the national income per person in order to avoid the inconvenience of applying different formulas for each one of them. This work is done by using the principle of lever and was led to the formula of two implicate quantity, $M=\frac{x_1f_1+x_2f_2}{f_1+f_2}$, and to help the understanding of relationships in this formula. The value of ratio of fraction cannot be added but it shows that it can be calculated depending on the size of the ratio. It is intended to solve multiple additions with one formula which is the expansion of the mean formula of implicate quantity. $M=\frac{x_1f_1+x_2f_2+{\cdots}+x_nf_n}{N}$, where $f_1+f_2+{\cdots}+f_n=N$. For this reason, this mean formula will be able to help in physics as well as many other different fields in solving complication of structures.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.125-136
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• 2022

For k = 1, 2, let $f_k=h_k+{\bar{g_k}}$ be normalized harmonic right half-plane or vertical strip mappings. We consider the convex combination ${\hat{f}}={\eta}f_1+(1-{\eta})f_2={\eta}h_1+(1-{\eta})h_2+{\overline{\bar{\eta}g_1+(1-\bar{\eta})g_2}}$ and the combination ${\tilde{f}}={\eta}h_1+(1-{\eta})h_2+{\overline{{\eta}g_1+(1-{\eta})g_2}}$. For real 𝜂, the two mappings ${\hat{f}}$ and ${\tilde{f}}$ are the same. We investigate the univalence and directional convexity of ${\hat{f}}$ and ${\tilde{f}}$ for 𝜂 ∈ ℂ. Some sufficient conditions are found for convexity of the combination ${\tilde{f}}$.

• Toxicological Research
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• v.19 no.1
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• pp.51-66
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• 2003

This study was performed to evaluate single and repeated-dose toxicities of Bee Venom Extracts (F1, F3) in Spraque-Dawley. F1 was injected subcutaneously to rat at dose levels of 0, 0.0002, 0.002, 0.02 mg/kg/day for single-dose toxicity study and repeated-dose toxicity study. F3 was injected subcutaneously to rat at dose level of 0, 0.003, 0.03, 0.3 mg/kg/day for single-dose toxicity study and repeated-dose toxicity study. In both studies, there were no dose related changes in mortality, clinical sign, body weight change, food and water consumption, opthalmoscopy, organ weights, urine analysis, biochemical examination, and hematological findings of all animals treated with Bee Venom (F1, F3). Gross and histopathological findings revealed no evidence of specific toxicity related to Bee Venom (F1, F3). These results suggest that the subcutaneous NOEL (No Observed Effect Level) of Bee Venom (F1, F3) may be over F1 -0.02 mg/kg, F3-0.3 mg/kg.

• Asian-Australasian Journal of Animal Sciences
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• v.13 no.6
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• pp.733-738
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• 2000

The objective of this study was to describe the nature of the inheritance of jumping as a behavioral trait and to analyze quantitatively the jumping height as a measure of vigor in two subspecies of mice. Two subspecies of mice, Yonakuni wild mouse (Y) and $CF_{{\sharp}1}$ laboratory mouse (C), were used as the parental types. Reciprocal mating between these two subspecies was made to produce subsequently the first and second generations. The first generation was $F_1$ (YC) resulting from $Y\;male{\times}C\;female$, and $F_1{^\prime}$ (CY) from $C\;male{\times}Y\;female$. The second generation $F_2$ (YCYC) was from mating $F_1{\times}F_1$ and $F_2{^\prime}$ (CYCY) from $F_1{^\prime}{\times}F_1{^\prime}$. Individuals were treated with a set of direct current shock apparatus at six weeks of age to evoke jumping. The results showed that the ratio between jumping and non jumping mice (J: NJ) for C was 0%:100% (0:1), which means that all C did not jump throughout the experiment, whereas Y was 68%:32% (2:1); and the $F_1$ and $F_2$ showed 65%:35% (2:1) and 51%:49% (1:1), respectively. All $F_1{^\prime}$ and $F_2{^\prime}$ individuals jumped as indicated by the ratio 100%:0% (1:0) for both these two genetic groups. Of the jumped mice, average height of the first three jumping observed for pooled sexes in Y, $F_1$, $F_2$, $F_1{^\prime}$ and $F_2{^\prime}$ were 19.3 cm, 19.3 cm, 18.0 cm, 19.9 cm and 16.4 cm, respectively. The distribution of jumping height showed a tendency to be a normal distribution. The jumping activity and jumping height may be affected by some major genes and polygenes, respectively.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.29 no.1
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• pp.84-88
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• 1984

To obtain basic information on the breeding of early maturing, short plant height rapeseed varieties, the following 7 varieties, Isuzu, Miyuki, Norin 25, Rang, Yongdang, Cresus and Tower were used in diallel crosses in 1979. Maturing date, plant height and grain weight per plant for the parents, $F_1$'s and $F_2$'s of the 7 x 7 partial diallel crosses were measured in 1981 for analysis of their genetic behavior. The results obtained are summarized as follows: 1. The days to maturing of $F_1$'s showed complete dominance for early maturing, and both additive and dominance genetic variances were significant. Number of effective factors in $F_1$'s was 3, but in $F_2$'s was 1. The degree of dominance in $F_1$'s was partial, while in $F_2$'s was complete. Both broad and narrow sense herita-bilities in $F_1$'s was high, while in $F_2$'s was low. 2. Yield per plant in $F_2$'s was controlled by additive component of genetic variance only, but $F_1$'s was different. The degree of dominance in $F_1$'s was complete, while in $F_2$'s was partial. The direction of dominance showed almost complete dominance over high yield and three effective factors was estimated. Yield per plant was controlled by recessive genes. 3. The plant height was controlled by both dominance and additive variance. Dominance was directed toward tall plant height. Number of effective factors was 2, and broad and narrow sense heritability were high in the plant height.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.145-153
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• 2016

In this paper, we solve the quadratic ρ-functional inequalities (0.1) ${\parallel}f(x+y)+f(x-y)-2f(x)-2f(y){\parallel}$ $\leq$ ${\parallel}{\rho}(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)){\parallel}$, where $\rho$ is a fixed complex number with $\left|{\rho}\right|$ < 1, and (0.2) ${\parallel}4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y){\parallel}$ $\leq$ ${\parallel}{\rho}(f(x+y)+f(x-y)-2f(x)-2f(y)){\parallel}$, where ρ is a fixed complex number with |ρ| < $\frac{1}{2}$. Furthermore, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.