• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1079-1089
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• 2009

In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.383-388
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• 2007

A (g, f)-factor F of a graph G is Called a Hamiltonian (g, f)-factor if F contains a Hamiltonian cycle. The binding number of G is defined by $bind(G)\;=\;{min}\;\{\;{\frac{{\mid}N_GX{\mid}}{{\mid}X{\mid}}}\;{\mid}\;{\emptyset}\;{\neq}\;X\;{\subset}\;V(G)},\;{N_G(X)\;{\neq}\;V(G)}\;\}$. Let G be a connected graph, and let a and b be integers such that $4\;{\leq}\;a\;<\;b$. Let g, f be positive integer-valued functions defined on V(G) such that $a\;{\leq}\;g(x)\;<\;f(x)\;{\leq}\;b$ for every $x\;{\in}\;V(G)$. In this paper, it is proved that if $bind(G)\;{\geq}\;{\frac{(a+b-5)(n-1)}{(a-2)n-3(a+b-5)},}\;{\nu}(G)\;{\geq}\;{\frac{(a+b-5)^2}{a-2}}$ and for any nonempty independent subset X of V(G), ${\mid}\;N_{G}(X)\;{\mid}\;{\geq}\;{\frac{(b-3)n+(2a+2b-9){\mid}X{\mid}}{a+b-5}}$, then G has a Hamiltonian (g, f)-factor.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.55-65
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• 2014

A graph G is called a fractional (g, f, n)-critical graph if any n vertices are removed from G, then the resulting graph admits a fractional (g, f)-factor. In this paper, we determine the new toughness condition for fractional (g, f, n)-critical graphs. It is proved that G is fractional (g, f, n)-critical if $t(G){\geq}\frac{b^2-1+bn}{a}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.779-789
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• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.37 no.4
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• pp.305-312
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• 1992

This experiment was carried out to investigate seed set, variation in chromosome number, and agronomic characteristics of the progeny in the cross between hexaploid triticale variety, Sinkihomil(P$_1$) and tetraploid rye variety, Dooroohomil(P$_2$). Seed set rate obtained was 30.5% in the cross of Sinkihomil with Dooroohomil, whereas 3.26% in reciprocal cross using Dooroohomil as female. Alsoseed set was 8.75% in F$_1$/P$_1$, 7.20% in F$_1$/P$_2$, and 1.53% in F$_2$(=F$_1$ /F$_1$, respectively. Germination rate of crossed seed was 37% in cross of P$_1$ with P$_2$, 39.0% in F$_1$/P$_1$(BC$_1$), 50% in F$_1$/P$_2$(BC$_2$) and 43.0% in F$_1$/F$_1$(F$_2$), and 1,000 grain wight was 20.7g in the cross of P$_1$ with P$_2$, which have 41.9g and 47.7g, respectively, 24.5g in F$_1$/P$_1$, 23.6g in F$_1$/P$_2$, and 24.5g in F$_1$/F$_1$, respectively. In pollen fertility of F$_1$ plant, 69.8% turned out to be abnormal or sterile pollen grains, whereas 30.2% was fertile or normal. In meiosis of pollen mother cell of F$_1$ plant, 13.5 univalents, 8.89 bivalent and 1.24 trivalent were appeared. Somatic chromosome number of 35 in F$_1$, both 32 to 33 and 35 to 36 in F$_2$, 35 to 39 in BC$_1$ and 28 to 36 in BC$_2$ which mean producing female gamate was 14 to 18 chromosome in PMC of F$_1$ plant. Rate of fertile plant turned out to be 100% in F$_1$, 4.5% in F$_2$, 42.9% in BC$_1$, and 50.0% in BC$_2$, respectively. Number of seed set per spike appeared to be 1.17 in F$_1$ plant, 13.3 in F$_2$, 2.36 in BC$_1$, and 3.75 in BC$_2$, respectively. Days to heading of F$_1$ was intermediate, but F$_2$ was later than both parents. Plant height of F$_1$ , BC$_1$ ,and BC$_2$ was shorter than both parent, but F$_2$, longer than both parents.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.609-618
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• 1994

F. Rhodes [2] introduced the fundamental group $\sigma(X, x_0, G)$ of a transformation group (X,G) as a generalization of the fundamental group $\pi_1(X, x_0)$ of a topological space X and showed a sufficient condition for $\sigma(X, x_0, G)$ to be isomorphic to $\pi_1(X, x_0) \times G$, that is, if (G,G) admits a family of preferred paths at e, $\sigma(X, x_0, G)$ is isomorphic to $\pi_1(X, x_0) \times G$. B.J.Jiang [1] introduced the Jiang subgroup $J(f, x_0)$ of the fundamental group of X which depends on f and showed a condition to be $J(f, x_0)$ = Z(f_\pi(\pi_1(X, x_0)), \pi_1(X, f(x_0)))$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.109-116
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• 2004

In this paper, we study the uniqueness of entire functions and prove the following result: Let f(z) and g(z) be two nonconstant entire functions, $n\;{\geq}\;7$ a positive integer, and let a be a nonzero finite complex number. If $f^{n}(z)(f(z)\;-\;1)f'(z)\;and\;g^{n}(z)(g(z)\;-\;1)g'(z)$ share a CM, then $f(z)\;{\equiv}\;g(z)$. The result improves the theorem due to ref. [3].

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• KSBB Journal
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• v.22 no.5
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• pp.345-350
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• 2007

Phosphosugars are found in all living organisms and are commercially valuable compounds with possible applications in the development of a wide range of specialty chemicals and medicines. In carbohydrate metabolism, fructose 6-phosphate (F6P) is an essential intermediate formed by phosphorylation of 6' position of fructose in glycolysis, gluconeogenesis, pentose phosphate pathway and Calvin cycle. In glycolysis, F6P lies within the glycolysis metabolic pathway and is produced by isomerisation of glucose 6-phosphate. For large-scale production, F6P could be produced from starch using many enzymes such as pullulanase, starch phosphorylase, isomerase and mutase. In enzymatic reactions carried out at high temperatures, the solubility of starch is increased and microbial contamination is minimized. Thus, thermophile-derived enzymes are preferred over mesophile-derived enzymes for industrial applications using starch. Recently, we reported the production of glucose 1-phosphate (G1P) from starch by Thermus caldophilus GK24 enzymes. Here we report the production of F6P from starch through three steps; from starch to glucose 1-phosphate (glucan phosphorylase, GP), then glucose 6-phosphate (phosphoglucomutase, GM) and then F6P (phosphoglucoisomerase, GI). Using 200 L of 1.2% soluble starch solution in potassium phosphate buffer, 1,253 g of G1P were produced. Then, 30% yields of F6P were attained at the optimum reaction conditions of GM : G1 (1 : 2.3), 63.5$^{\circ}C$, and pH 6.85. The optimum conditions were found by response surface methodology and the theoretical values were confirmed by the experiments. The optimum starch concentrations were 20 g/L under the given conditions.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.101-110
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• 2015

A Total Mean Cordial labeling of a graph G = (V, E) is a function $f:V(G){\rightarrow}\{0,1,2\}$ such that $f(xy)={\Large\lceil}\frac{f(x)+f(y)}{2}{\Large\rceil}$ where $x,y{\in}V(G)$, $xy{\in}E(G)$, and the total number of 0, 1 and 2 are balanced. That is ${\mid}ev_f(i)-ev_f(j){\mid}{\leq}1$, $i,j{\in}\{0,1,2\}$ where $ev_f(x)$ denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). If there is a total mean cordial labeling on a graph G, then we will call G is Total Mean Cordial. Here, We investigate the Total Mean Cordial labeling behaviour of prism, gear, helms.