• Asian-Australasian Journal of Animal Sciences
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• v.15 no.6
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• pp.890-894
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• 2002

The accuracy of the gamma function to describe lactation curve of Yankasa ewes was investigated using milk production data obtained from 168 ewes with either complete or incomplete 84 day lactation records. Ewes were daily hand milked after over-night separation from lamb and thorough disinfection of the udder. The daily milk yield on the average was estimated from the weekly total yield. The effect of type of birth, parity, season of birth and lactation length on the components of lactation curve (a, b, c and s) were analysed by least-square procedures. All factors except parity significantly (p<0.01) influenced the curve parameters. The goodness of fit of the function did not differ between the two classes of varying duration of lactation; incomplete lactation however, showed a lower persistency and as expected lower level of production. Correlations ($r_p$) between lamb weight gain and milk yield using the weight records from lamb weighed at weekly intervals indicated a high and positive relationship in the early lactation that decreased in intensity as the lactation advanced.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1183-1210
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• 2016

During the past four decades or so, due mainly to a wide range of applications from natural sciences to social sciences, the so-called fractional calculus has attracted an enormous attention of a large number of researchers. Many fractional calculus operators, especially, involving various special functions, have been extensively investigated and widely applied. Here, in this paper, in a systematic manner, we aim to establish certain image formulas of various fractional integral operators involving diverse types of generalized hypergeometric functions, which are mainly expressed in terms of Hadamard product. Some interesting special cases of our main results are also considered and relevant connections of some results presented here with those earlier ones are also pointed out.

• International Journal of Contents
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• v.3 no.1
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. Although, multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of the distributions. The computation methods we adopted are exact and no interpolations are involved.

• Asian-Australasian Journal of Animal Sciences
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• v.8 no.4
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• pp.365-368
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• 1995

Lactation curves of dairy cows were generated using three models, namely; incomplete gamma function (model 1), polynomial inverse function (model 2) and non-linear regression (model 3). Secondary milk yield data of 27 cows which had completed 6 lactations were used in this study. Milk yield records (once a week) throughout the lactation and from the first three months of lactation were fitted to the models. Estimation of total milk yield by model 3 using the data once a week throughout the lactation resulted in smaller % bias and standard error than those generated from model 1 and 2. But, model 2 was more accurate in predicting the 305-day milk yield equivalent closer to actual yields with smaller bias % and error using partial records up to 3 months. Also, model 2 was able to estimate the time to reach peak yield close to the actual data using partial records and model 2 could be used as a tool to advise farmers on appropriate feeding and management practices to be adopted.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.109-124
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• 2017

In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator $\mathcal{L}^{\alpha}_{a,{\lambda}}$ is applied for defining and studying some new subclasses of analytic functions in the unit disk E. Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.1
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• pp.99-108
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• 1990

A Synthetic Unit Hydrograph Method was investigated for representation of the effective rainfall-direct runoff hydrograph by using a Geomorphologic Instantaneous Unit Hydrograpb(GIUH) proposed by Gupta et al(1980). The response function of the basin was assumed to be the two-parameter gamma probability density function. The physical parameters of the response function(Nash Model) was determined by using the regression eqs. were parameterized in terms of Horton order ratios and the relations between the basin lag time and time-scale parameter. The capability of the Synthetic Unit Hydrograph to the real basin was tested for the Pyungchang river basin and Wi Stream basin, and its capability to reproduce the hydrologic response was investigate and compared with the Moment Method and the Least Square Method used incomplete gamma function. The representation of the peak flow, the time to peak and the hydrographs the derived Synthetic Unit Hydrograph were tested on some obseved flood data and showed promising, and it was approved to be used for prediction of the ungaged basins.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.1
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• pp.63-72
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• 1994

The objective of the study is to develop weather generators for daily rainfall and small pan evaporation and to test the applicability with recorded data. Daily rainfall forecasting model(DRFM) was developed that uses a first order Markov chain to describe rainfall seque- nces and applies an incomplete Gamma function to predict the amount of precipitation. Daily evaporation forecasting model(DEFM) that adopts a normal distribution function to generate the evaporation for dry and wet days was also formulated. DRFM and DEFM were tested with twenty year weather data from eleven stations using Chi-square and Kolmogorov and Smirnov goodness of fit tests. The test results showed that the generated sequences of rainfall occurrence, amount of rainfall, and pan evaporation were statistically fit to recorded data from eleven, seven, and seven stations at the 5% level of significance. Generated rainfall data from DRFM were very close in frequency distri- bution patterns to records for stations all over the country. Pan evaporation for rainy days generated were less accurate than that for dry days. And the proposed models may be used as tools to provide many mathematical models with long-term daily rainfall and small pan evaporation data. An example is an irrigation scheduling model, which will be further detailed in the paper.

• Asian-Australasian Journal of Animal Sciences
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• v.26 no.9
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• pp.1237-1246
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• 2013

The objective of this study was to estimate variance components and genetic parameters for lactation milk yield (LY), lactation length (LL), average milk yield per day (YD), initial milk yield (IY), peak milk yield (PY), days to peak (DP) and parameters (ln(a) and c) of the modified incomplete gamma function (MIG) in an Ethiopian multibreed dairy cattle population. The dataset was composed of 5,507 lactation records collected from 1,639 cows in three locations (Bako, Debre Zeit and Holetta) in Ethiopia from 1977 to 2010. Parameters for MIG were obtained from regression analysis of monthly test-day milk data on days in milk. The cows were purebred (Bos indicus) Boran (B) and Horro (H) and their crosses with different fractions of Friesian (F), Jersey (J) and Simmental (S). There were 23 breed groups (B, H, and their crossbreds with F, J, and S) in the population. Fixed and mixed models were used to analyse the data. The fixed model considered herd-year-season, parity and breed group as fixed effects, and residual as random. The single and two-traits mixed animal repeatability models, considered the fixed effects of herd-year-season and parity subclasses, breed as a function of cow H, F, J, and S breed fractions and general heterosis as a function of heterozygosity, and the random additive animal, permanent environment, and residual effects. For the analysis of LY, LL was added as a fixed covariate to all models. Variance components and genetic parameters were estimated using average information restricted maximum likelihood procedures. The results indicated that all traits were affected (p<0.001) by the considered fixed effects. High grade $B{\times}F$ cows (3/16B 13/16F) had the highest least squares means (LSM) for LY ($2,490{\pm}178.9kg$), IY ($10.5{\pm}0.8kg$), PY ($12.7{\pm}0.9kg$), YD ($7.6{\pm}0.55kg$) and LL ($361.4{\pm}31.2d$), while B cows had the lowest LSM values for these traits. The LSM of LY, IY, YD, and PY tended to increase from the first to the fifth parity. Single-trait analyses yielded low heritability ($0.03{\pm}0.03$ and $0.08{\pm}0.02$) and repeatability ($0.14{\pm}0.01$ to $0.24{\pm}0.02$) estimates for LL, DP and parameter c. Medium heritability ($0.21{\pm}0.03$ to $0.33{\pm}0.04$) and repeatability ($0.27{\pm}0.02$ to $0.53{\pm}0.01$) estimates were obtained for LY, IY, PY, YD and ln(a). Genetic correlations between LY, IY, PY, YD, ln(a), and LL ranged from 0.59 to 0.99. Spearman's rank correlations between sire estimated breeding values for LY, LL, IY, PY, YD, ln(a) and c were positive (0.67 to 0.99, p<0.001). These results suggested that selection for IY, PY, YD, or LY would genetically improve lactation milk yield in this Ethiopian dairy cattle population.