• Animal Bioscience
• /
• v.37 no.8
• /
• pp.1355-1366
• /
• 2024

Objective: The analysis of runs of homozygosity (ROH) has been applied to assess the level of inbreeding and identify selection signatures in various livestock species. The objectives of this study were to characterize the ROH pattern, estimate the rate of inbreeding, and identify signatures of selection in the red-brown Korean native chickens. Methods: The Illumina 60K single nucleotide polymorphism chip data of 651 chickens was used in the analysis. Runs of homozygosity were analysed using the PLINK v1.9 software. Inbreeding coefficients were estimated using the GCTA software and their correlations were examined. Genomic regions with high levels of ROH were explored to identify selection signatures. Results: A total of 32,176 ROH segments were detected in this study. The majority of the ROH segments were shorter than 4 Mb. The average ROH inbreeding coefficients (F_ROH) varied with the length of ROH segments. The means of inbreeding coefficients calculated from different methods were also variable. The correlations between different inbreeding coefficients were positive and highly variable (r = 0.18-1). Five ROH islands harbouring important quantitative trait loci were identified. Conclusion: This study assessed the level of inbreeding and patterns of homozygosity in Red-brown native Korean chickens. The results of this study suggest that the level of recent inbreeding is low which indicates substantial progress in the conservation of red-brown Korean native chickens. Additionally, Candidate genomic regions associated with important production traits were detected in homozygous regions.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.105-116
• /
• 2013

In this paper, we consider the positive solution to a Cauchy problem in $\mathbb{B}^N$ of the fast diffusive equation: ${\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}$ < $p$ < 2, $q$ > 1 and 0 < $m{\leq}n$ < $qm+N(q-1)$. We prove that $q_c=p-1{\frac{p+n}{N+m}}$ is the critical Fujita exponent. That is, if 1 < $q{\leq}q_c$, then every positive solution blows up in finite time, but for $q$ > $q_c$, there exist both global and non-global solutions to the problem.

• Journal of applied mathematics & informatics
• /
• v.31 no.1_2
• /
• pp.165-177
• /
• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.1
• /
• pp.43-55
• /
• 2011

We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate (does not depend on the initial value) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.

• Journal of applied mathematics & informatics
• /
• v.30 no.5_6
• /
• pp.1031-1049
• /
• 2012

In this paper, a class of impulsive fuzzy bi-directional associative memory (BAM) neural networks with distributed delays and variable coefficients are considered. Using Lyapunov functional method and fixed point theorem, we derived some sufficient conditions for the existence and globally exponential stability of unique periodic solution of the networks. The results obtained are new and extend the previous known results. In addition, an example is given to show the effectiveness of our results obtained.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.627-645
• /
• 2007

We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by $L_vu\;:=-{\Delta}u+a(x,\;y)u_x+b(x,\;y)u_y+d(x,\;y)u$, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator $L_cu$ is constructed by using the leading term of $L_vu$ plus the constant reaction term such that $L_cu\;:=-{\Delta}u+d_cu$. Using the field of values arguments, we show that the eigenvalues of the preconditioned matrix are clustered at some number. Some numerical evidences are also provided.

• International Journal of Control, Automation, and Systems
• /
• v.2 no.3
• /
• pp.319-332
• /
• 2004

This paper proposes some further improvements on N.K. Bose's 2D stability test for polynomials with real coefficients by revealing symmetric properties of the polynomials, resultants occurring in the test and by generalizing Sturm's method. The improved test can be fulfilled by a totally algebraic algorithm with a finite number of steps and the computational complexity is largely reduced as it involves only certain real variable polynomials with degrees not exceeding half of their previous complex variable counterparts. Nontrivial examples for 2D polynomials having both numerical and literal coefficients are also shown to illustrate the computational advantage of the proposed method.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.30B no.7
• /
• pp.14-23
• /
• 1993

This paper proposes an algorithm to reduce the bitrate for transmission of MCP(motion compensated prediction) error signals. Many digital image coders have recently employed hybrid coding schemes which perform motion compensation, DCT transform, quantization, and variable length coding. The variable length coding compresses the quantized DCT coefficient data by removing their statistical redundancy. But some DCT blocks have the interblock statistical redundancy as well as the intrablock one. To utilize both of them, the DCT blocks are classified into the interleaving group and the non-interleaving group. And then each DCT blocks in the interleaving group are is encoded independently, and the DCT blocks in the interleaving group are encoded after interleaving the DCT coefficients. Through the simulations, it is shown that the proposed method outperforms the conventional method in which each DCT block is encoded independently.

• Structural Engineering and Mechanics
• /
• v.45 no.2
• /
• pp.259-275
• /
• 2013

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

• Journal of the Korean Institute of Telematics and Electronics C
• /
• v.36C no.5
• /
• pp.67-75
• /
• 1999

This paper presents a production method to GRM coefficients which are consist of $P^n$ polarities to n variables over GF(p). In general production method to GRM coefficients is derived from RM coefficients to polarity 0 using RM expansion and extended to GRM coefficients. The procedure of proposed production method to GRM coefficients is consists of 2 steps. First, obtain the optimal polarity which is contains a minimal operation to single variable and then apply the same process to all generation process of GRM coefficients using cyclic property of the polarity. Proposed method simplify the generation procedure and reduces a number of operators because of the cyclic property of polarity.