• The Pure and Applied Mathematics
• /
• v.31 no.2
• /
• pp.119-130
• /
• 2024

In this paper we discuss on the growth properties of composite entire and meromorphic functions on the basis of generalized (α, β, γ) order and generalized (α, β, γ) type comparing to their corresponding left and right factors.

• Journal of Animal Science and Technology
• /
• v.59 no.2
• /
• pp.3.1-3.7
• /
• 2017

Background: The modelling of lactation curve provides guidelines in formulating farm managerial practices in dairy cows. The aim of the present study was to determine the suitable non-linear model which most accurately fitted to lactation curves of five lactations in 134 Gir crossbred cows reared in Research-CumDevelopment Project (RCDP) on Cattle farm, MPKV (Maharashtra). Four models viz. gamma-type function, quadratic model, mixed log function and Wilmink model were fitted to each lactation separately and then compared on the basis of goodness of fit measures viz. adjusted $R^2$, root mean square error (RMSE), Akaike's Informaion Criteria (AIC) and Bayesian Information Criteria (BIC). Results: In general, highest milk yield was observed in fourth lactation whereas it was lowest in first lactation. Among the models investigated, mixed log function and gamma-type function provided best fit of the lactation curve of first and remaining lactations, respectively. Quadratic model gave least fit to lactation curve in almost all lactations. Peak yield was observed as highest and lowest in fourth and first lactation, respectively. Further, first lactation showed highest persistency but relatively higher time to achieve peak yield than other lactations. Conclusion: Lactation curve modelling using gamma-type function may be helpful to setting the management strategies at farm level, however, modelling must be optimized regularly before implementing them to enhance productivity in Gir crossbred cows.

• Communications of the Korean Mathematical Society
• /
• v.20 no.1
• /
• pp.93-106
• /
• 2005

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

• Water for future
• /
• v.26 no.4
• /
• pp.73-83
• /
• 1993

This study focuses on the separation effect analysis of rainfall data for 2-parameter log-normal, 3-parameter log-normal, type-extreme value, 2-parameter gamma, 3-parameter gamma, log-Pearson type-III, and general extreme value distribution functions. Difference in the relationship between the mean and standard deviation of skewness for historical data and relations derived from 7 distribution functions are analyzed suing the Monte Carlo experiment. The results show that rainfall data has the separation effect for 6 distribution functions except 3-parameter gamma distribution function.

• The Plant Pathology Journal
• /
• v.19 no.6
• /
• pp.301-304
• /
• 2003

Gamma-ray irradiation is known to induce various mutations in plants caused by chromosome alterations. This study investigated disease responses of selected gamma-ray induced rice mutants generated from seven Japonica-type rice cultivars against three plant diseases. Among the tested 22 mutants, three gain-of-function mutants and six loss-of-function mutants against rice blast were obtained, as well as three loss-of-function mutants against bacterial leaf blight (BLB). Two of the loss-of-function mutants were susceptible to both rice blast and BLB. Gain-of-function mutation has not been frequently observed in rice plants, thus, the mutants can be used to identify loci of novel genes for the regulation of disease resistant response.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.429-445
• /
• 2004

In this paper we investigate the generalized Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(x,y)){\;}={\;}\phi(x,y)f(x,y)$, where x, y lie in the set S. As a consequence we obtain stability in the sense of Hyers, Ulam, Rassias, Gavruta, for some well-known equations such as the gamma, beta and G-function type equations.

• Communications of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.75-84
• /
• 2017

In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.575-598
• /
• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• The Journal of Internal Korean Medicine
• /
• v.28 no.4
• /
• pp.902-910
• /
• 2007

Objective : Peroxisome proliferator-activated receptor (PPAR)-gamma, a transcription factor in adipocyte differentiation, has important effects on insulin sensitivity, atherosclerosis, endothelial cell function and inflammation. Through these effects, PPAR-gamma2 might be involved with type 2 diabetes and vascular disease, including diabetic complications. Recently, it has been reported that the C161T polymorphism in the exon 6 of PPAR-gamma is associated with type 2 diabetes interacting with uncoupling protein 2 (UCP2) gene, and is associated with acute myocardial infarction. We studied the association of this polymorphism with type 2 diabetes and its complications, such as retinopathy, ischemic stroke, nephropathy and neuropathy in Korean non-diabetic and type 2 diabetic populations. Methods : Three hundred and thirty eight type 2 diabetic patients (retinopathy: 64, ischemic stroke: 67, nephropathy: 39 and neuropathy: 76) and 152 healthy matched control subjects were evaluated. The PPAR-gamma C161T polymorphism was analyzed by PCR-RFLP. Results : PPAR-gamma C161T genotype and allele frequency did not show significant differences between type 2 diabetic patients and healthy controls (T allele: 17.0 vs. 14.5, OR= 1.21, P=0.3188). In the analysis for diabetic complications, T allele in diabetic nephropathy was significantly higher than controls (P=0.0358). T allele in the ischemic stroke patients was also higher than healthy controls, although it had no significance (P=0.1375). Conclusions : These results suggest that the C161T polymorphism of the PPAR-gamma gene might be associated with diabetic nephropathy in type 2 diabetes.

• Proceedings of the KWS Conference
• /
• 2002.10a
• /
• pp.803-808
• /
• 2002

A computer-aided alloy-designing technique to develop the insert metal for transient liquid phase (TLP) bonding was applied to high aluminum Ni-base superalloys. The main procedure of a mathematical programming method was to obtain the optimal chemical composition through rationally compromising the plural objective performances of insert metal by a grid-search which involved data estimation from the limited experimental data using interpolation method. The objective function Z which was introduced as an index of bonding performance of insert metal involved the melting point, hardness (strength), formability of brittle phases and void ratio (bonding defects) in bond layer as the evaluating factors. The contour maps of objective function Z were also obtained applying the interpolation method. The compositions of Ni-3.0%Cr-4.0%B-0.5%Ce (for ${\gamma}$/${\gamma}$/${\beta}$ type alloy) and Ni3.5%Cr-3.5%B-3%Ti (for ${\gamma}$/${\gamma}$ type alloy) which optimized the objective function were determined as insert metal. SEM observations revealed that the microstructure in bond layers using the newly developed insert metals indicated quite sound morphologies without forming microconstituents and voids. The creep rupture properties of both joints were much improved compared to a commercial insert metal of MBF-80 (Ni-15.5%Cr-3.7%B), and were fairly comparable to those of base metals.