• Asian-Australasian Journal of Animal Sciences
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• v.33 no.3
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• pp.465-479
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• 2020

Objective: This study performed a meta-analysis of published trials to determine the effects of zinc on the immune response and production performance of broilers. Methods: A database was built from published literature regarding the addition of zinc forms or doses and their relation to the immune response and production performance of broilers. Different doses or forms of zinc were identified in the database. The recorded parameters were related to the immune response and production performance. The database contained a total of 323 data points from 41 studies that met the criteria. Then, the data were processed for a meta-analysis using a mixed model methodology. The doses or different forms of zinc were considered fixed effects, different studies were treated as random effects, and p-values were used as the model statistics. Results: An increase in zinc dose increased (p<0.05) pancreas metallothionein (MT) and zinc concentrations in the plasma, tibia and meat, all in quadratic patterns, but linearly decreased (p<0.05) the heterophil/lymphocyte (H/L) ratio. Regarding the different zinc forms, both inorganic and organic zinc increased (p<0.05) the zinc concentrations in the plasma and tibia, the calcium and phosphorus contents in the tibia, and the antioxidant activity of superoxide dismutase in meat as compared to control. An increase in zinc dose increased average daily gain (ADG) and decreased feed conversion ratio (FCR) following a quadratic pattern (p<0.05). Inorganic and organic zinc decreased (p<0.05) FCR and H/L ratio than that of control, but these two forms were similar for these parameters. Conclusion: Zinc addition has a positive impact on immunity and broiler production. Zinc can suppress stress and inhibit the occurrence of lipid peroxidation in broilers, and it can also improve ADG, FCR, and the quality of broiler carcasses.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.919-920
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• 2011

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that ${\theta}_A(\tau)/{\theta}_B(\tau)$ is a rational function of J, satisfying a certain condition. Where ${\theta}_A(\tau)$ and ${\theta}_B(\tau)$ are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].

• The Journal of the Korea Contents Association
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• v.3 no.3
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• pp.103-109
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• 2003

Functional equations are useful in the expermental science because they play very important to formulate mathematical moods in general terms, through some not very restrictive equations, without postulating the forms of such functions. In this paper n solve one of a generalized quadratic functional equation (equation omitted) and prove the stability of this equation.

• The Journal of the Korea Contents Association
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• v.2 no.4
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• pp.93-98
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• 2002

Functional equations are useful in the experimental science because they play very important role for researchers to formulate mathematical models in general terms, through some not very restrictive equations that only stipulate basic properties of functions showing in these equations, without postulating the exact forms of such functions. Of lots of such functional equations, in this paper we adopt and solve some generalized quadratic functional equation a$^2$f((x+y/a))+b$^2$f((x-y/b)) = 2f(x)+2f(y)

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1249-1268
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• 2011

For imaginary quadratic number fields F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1{\ldots}p_{t-1}})$, where ${\varepsilon}{\in}${-1,-2} and distinct primes $p_i{\equiv}1$ mod 4, we give condition of 8-ranks of class groups C(F) of F equal to 1 or 2 provided that 4-ranks of C(F) are at most equal to 2. Especially for F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1p_2)$, we compute densities of 8-ranks of C(F) equal to 1 or 2 in all such imaginary quadratic fields F. The results are stated in terms of congruence relation of $p_i$ modulo $2^n$, the quartic residue symbol $(\frac{p_1}{p_2})4$ and binary quadratic forms such as $p_2^{h+(2_{p_1})/4}=x^2-2p_1y^2$, where $h+(2p_1)$ is the narrow class number of $\mathbb{Q}(\sqrt{2p_1})$. The results are also very useful for numerical computations.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.81-85
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• 1983

It is the purpose of this paper to give some remarks on finite fields. We shall show that the little theorem of Fermat, Euler's criterion for quadratic residue mod p, and other few theorems in the number theory can be derived from the theorems in theory of finite field K=GF(p), where p is a prime. The forms of some irreducible ploynomials over K-GF(p) will be given explicitly.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.335-339
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• 2022

In this paper, we find the forms of polynomials which generate consecutive prime values. Then, we consider about general form of polynomials and apply on the quadratics and tertiaries.

• International Journal of Ocean System Engineering
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• v.3 no.1
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• pp.1-9
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• 2013

A design procedure for a ship with minimum resistance had been developed using a numerical optimization method called SQP (Sequential Quadratic Programming) combined with computational fluid dynamics (CFD) technique. The frictional resistance coefficient was estimated by the ITTC 1957 model-ship correlation line formula and the wave-making resistance coefficient was evaluated by the potential-flow panel method with the nonlinear free surface boundary conditions. The geometry of the hull surface was represented and modified by B-spline surface modeling technique during the optimization process. The Series 60 ($C_B$=0.60) hull was selected as a parent hull to obtain an optimized hull that produces minimum resistance. The models of the parent and optimized hull forms were tested at calm water condition in order to demonstrate the validity of the proposed methodolgy.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.171-179
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• 2009

In this paper we studied the effective approximations to the distribution of the sum of products of normal variables. Based on the saddlepoint approximations to the quadratic forms, the suggested approximations are very accurate and easy to use. Applications to the FSK (Frequency Shift Keying) communication are also considered.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.479-491
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• 2017

We investigate the zeros of Epstein zeta functions associated with positive definite quadratic forms with rational coefficients in the vertical strip ${\sigma}_1$ < ${\Re}s$ < ${\sigma}_2$, where 1/2 < ${\sigma}_1$ < ${\sigma}_2$ < 1. When the class number h of the quadratic form is bigger than 1, Voronin gave a lower bound and Lee gave an asymptotic formula for the number of zeros. Recently Gonek and Lee improved their results by providing a new upper bound for the error term when h > 3. In this paper, we consider the cases h = 2, 3 and provide an upper bound for the error term, smaller than the one for the case h > 3.