• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.25-37
• /
• 2019

Let G be a bipartite graph with (X, Y ) as its bipartition. Let B be a complete bipartite graph with a bipartition ($V_1$, $V_2$) such that $X{\subseteq}V_1$ and $Y{\subseteq}V_2$. A bi-packing of G in B is an injection ${\sigma}:V(G){\rightarrow}V(B)$ such that ${\sigma}(X){\subseteq}V_1$, ${\sigma}(Y){\subseteq}V_2$ and $E(G){\cap}E({\sigma}(G))={\emptyset}$. In this paper, we show that if G is a bipartite graph of order n with girth at least 12, then there is a complete bipartite graph B of order n + 1 such that there is a bi-packing of G in B. We conjecture that the same conclusion holds if the girth of G is at least 8.

• Korean Journal of Fisheries and Aquatic Sciences
• /
• v.36 no.4
• /
• pp.402-408
• /
• 2003

A quantitative method was suggested for estimating damages in fishery production due to the diffusion and deposition of suspended silt and clay by various construction processes in tidal flat fishing grounds. Marine populations are maintained through the process of spawning, growth, recruitment, natural death and death by fishing each year. All of the year classes of the population in a fishery ground could be affected when damages occur by human activities such as land filling or reclamation. The propose of this study is to calculate damages in terms of fishery production using a quantitative population dynamic method. If the maximum age in the population is $X_\lambda,$ the starting year of damage is $t_s,$ and the ending year of damage is $t_e,$ the number of year classes damaged is $t_{s-n\lambda}-t_e,$ Many year classes present in the year $t_s,$ and so if damages occur, they Influence all the year classes which are present in the population. Damaged year classes in year $t_e$ would still be in the population until the year $t_{e+n\lambda}$, where $n_{\lambda}$ is the oldest age class. If the expected yield of a year class is constant, the total yield from year classes in the fishing ground during the construction periods can be calculated as follows: $Y_\Phi=[(t_e-t_s+1)+n_c]{\cdot}Y_E+\sum\limits^{n_\lambda-n_c}_{l=1}\;\sum\limits^{n_\lambda-n_c}_{l=i}\;Y_{n_c+i}$ This method was applied for damage estimation in the production of Ruditapes philippinarum in a tidal flat fishing ground.

• Animal Bioscience
• /
• v.34 no.4
• /
• pp.751-758
• /
• 2021

Objective: The objectives of this study were to investigate the relationship between the mRNA expression of adipocyte type fatty acid binding protein (A-FABP) and heart type FABP (H-FABP) in Thai native chicken crossbreeds and evaluate the level of exotic inclusion in native chicken that will improve growth while maintaining its relatively low carcass fat. Methods: The fat deposition traits and mRNA expression of A-FABP and H-FABP were evaluated at 6, 8, 10, and 12 weeks of age in 4 chicken breeds (n = 8/breed/wk) (100% Chee breed [CH] [100% Thai native chicken background], CH male and broiler female [Kaimook e-san1; KM1] [50% CH background], broiler male and KM1 female [Kaimook e-san2; KM2] [25% CH background], and broiler [BR]) using abdominal fat (ABF) and muscular tissues. Results: The BR breed was only evaluated at 6 weeks of age. At week 6, the CH breed had a significantly lower A-FABP expression in ABF and intramuscular fat (IF) compared with the other breeds. At 8 to 12 weeks, the KM2 groups showed significant upregulation (p<0.05) of A-FABP in both ABF and IF compared to the CH and KM1 groups. The expression of H-FABP did not follow any consistent pattern in both ABF and IF across the different ages. Conclusion: Some level of crossbreeding CH chickens can be done to improve growth rate while maintaining their low ABF and IF. The expression level of A-FABP correlate with most fat traits. There was no consistency of H-FABP expression across breed. A-FABPs is involved in fat deposition, genetic markers in these genes could be used in marker assisted studies to select against excessive fat accumulation.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.1
• /
• pp.1-5
• /
• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• Journal of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.657-673
• /
• 2009

The fixed point algebra $C^*(E)^{\gamma}$ of a gauge action $\gamma$ on a graph $C^*$-algebra $C^*(E)$ and its AF subalgebras $C^*(E)^{\gamma}_{\upsilon}$ associated to each vertex v do play an important role for the study of dynamical properties of $C^*(E)$. In this paper, we consider the stability of $C^*(E)^{\gamma}$ (an AF algebra is either stable or equipped with a (nonzero bounded) trace). It is known that $C^*(E)^{\gamma}$ is stably isomorphic to a graph $C^*$-algebra $C^*(E_{\mathbb{Z}}\;{\times}\;E)$ which we observe being stable. We first give an explicit isomorphism from $C^*(E)^{\gamma}$ to a full hereditary $C^*$-subalgebra of $C^*(E_{\mathbb{N}}\;{\times}\;E)({\subset}\;C^*(E_{\mathbb{Z}}\;{\times}\;E))$ and then show that $C^*(E_{\mathbb{N}}\;{\times}\;E)$ is stable whenever $C^*(E)^{\gamma}$ is so. Thus $C^*(E)^{\gamma}$ cannot be stable if $C^*(E_{\mathbb{N}}\;{\times}\;E)$ admits a trace. It is shown that this is the case if the vertex matrix of E has an eigenvector with an eigenvalue $\lambda$ > 1. The AF algebras $C^*(E)^{\gamma}_{\upsilon}$ are shown to be nonstable whenever E is irreducible. Several examples are discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.211-214
• /
• 1995

Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.1-13
• /
• 1999

The purpose of this paper is to show that if the Fatou set F(f) of a CF-meromorphic function f has two completely invariant components, then they are the only components of F(f) and that the Julia set of the entire transcendental function $E_{\lambda}(z)={\lambda}e^z$ for 0 < ${\lambda}$ < $\frac{1}{e}$ contains a Cantor bouquet by employing the Devaney and Tangerman's theorem[10].

• The Pure and Applied Mathematics
• /
• v.13 no.3 s.33
• /
• pp.189-195
• /
• 2006

Let R be a prime ring with characteristics not 2 and ${\sigma},\;{\tau},\;{\alpha},\;{\beta}$ be auto-morphisms of R. Suppose that $d_1$ is a (${\sigma},\;{\tau}$)-derivation and $d_2$ is a (${\alpha},\;{\beta}$)-derivation on R such that $d_{2}{\alpha}\;=\;{\alpha}d_2,\;d_2{\beta}\;=\;{\beta}d_2$. In this note it is shown that; (1) If $d_1d_2$(R) = 0 then $d_1$ = 0 or $d_2$ = 0. (2) If [$d_1(R),d_2(R)$] = 0 then R is commutative. (3) If($d_1(R),d_2(R)$) = 0 then R is commutative. (4) If $[d_1(R),d_2(R)]_{\sigma,\tau}$ = 0 then R is commutative.

• Bulletin of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.171-174
• /
• 1988

Let M be an n-dimensional compact connected and oriented Riemannian manifold isometrically immersed in an (n+2)-dimensional Euclidean space $R^{n+2}$. Moore [5] proved that if M is of positive curvature, then M is a homotopy sphere. This result is generalized by Baldin and Mercuri [2], Baik and Shin [1] to the case of non-negative curvature, which is stated as follows: If M of non-negative curvature, then M is either a homotopy sphere or diffeomorphic to a product of two spheres. In particular, if there is a point at which the curvature operator is positive, then M is homeomorphic to a sphere.e.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.1101-1113
• /
• 2014

We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle E of rank r and degree d with gcd(r, d) = 1 is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.