• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.253-264
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• 2012

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in the mathematical physics via the (1+1)-dimensional Boussinesq equation by using the following two methods: (i) A further improved ($\frac{G}{G}$) - expansion method, where $G=G({\xi})$ satisfies the auxiliary ordinary differential equation $[G^{\prime}({\xi})]^2=aG^2({\xi})+bG^4({\xi})+cG^6({\xi})$, where ${\xi}=x-Vt$ while $a$, $b$, $c$ and $V$ are constants. (ii) The well known extended tanh-function method. We show that some of the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before which gives more exact solutions than the second method (ii).

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.173-183
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• 2015

A radio k-labeling f of a graph G is a function f from V (G) to $Z^+{\cup}\{0\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}k+1$ for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices $x,y{\in}G$. The span of a radio k-labeling f is denoted by sp(f) and defined as max$\{{\mid}f(x)-f(y){\mid}:x,y{\in}V(G)\}$. The radio k-labeling is a radio labeling when k = diam(G). In other words, a radio labeling is an injective function $f:V(G){\rightarrow}Z^+{\cup}\{0\}$ such that $${\mid}f(x)=f(y){\mid}{\geq}diam(G)+1-d(x,y)$$ for any pair of vertices $x,y{\in}G$. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) - 1, a radio k-labeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function $f:V(G){\rightarrow}\{0,1,2,{\ldots}\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}diam(G)$ holds for all $x,y{\in}G$. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and radio antipodal number for the circulant graphs G(4k + 2; {1, 2}).

• Genomics & Informatics
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• v.16 no.1
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• pp.2-9
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• 2018

Olfactory receptors (ORs) in mammals are generally considered to function as chemosensors in the olfactory organs of animals. They are membrane proteins that traverse the cytoplasmic membrane seven times and work generally by coupling to heterotrimeric G protein. The OR is a G protein-coupled receptor that binds the guanine nucleotide-binding $G{\alpha}_{olf}$ subunit and the $G{\beta}{\gamma}$ dimer to recognize a wide spectrum of organic compounds in accordance with its cognate ligand. Mammalian ORs were originally identified from the olfactory epithelium of rat. However, it has been recently reported that the expression of ORs is not limited to the olfactory organ. In recent decades, they have been found to be expressed in diverse organs or tissues and even tumors in mammals. In this review, the expression and expected function of olfactory receptors that exist throughout an organism's system are discussed.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.459-481
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• 2020

In this paper we introduce relative L-order of a nonconstant entire function f with respect to another nonconstant entire function g. Also we investigate the existence of relative L-proximate order of f with respect to g.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.851-864
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• 2015

In this paper, we study the generalized Littlewood-Paley operators. It is shown that the generalized g-function, Lusin area function and $g^*_{\lambda}$-function on any BMO function are either infinite everywhere, or finite almost everywhere, respectively; and in the latter case, such operators are bounded from BMO($\mathbb{R}^n$) to BLO($\mathbb{R}^n$), which improve and generalize some previous results.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1923-1936
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• 2013

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^*_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BMO functions are also considered.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.241-252
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• 1998

In this paper we try to construct the Green's function and investigate some properties of the Green's function. Also we discuss the variation $\delta$G($\chi$,t) of the Green's function G($\chi$,t) when the interval is varied.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.489-496
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• 2007

Let g be a continuous function on an interval I which is not constant on any subinterval of I, and let ${\mu}$ be a Borel measure on I. In this paper we give a necessary and sufficient conditions guaranteeing, for the strongly measurable function f on I with values in a Banach space X, the existence of a continuous primitive function F on I with respect to g.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.433-444
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• 2023

Given a function f analytic in open disk centred at origin of radius unity and satisfying the condition |f(z)/g(z) - 1| < 1 for a analytic function g with certain prescribed conditions in the unit disk, radii constants R are determined for the values of Rzf'(Rz)/f(Rz) to lie inside the domain enclosed by the curve |w² - 1| = 1 (lemniscate of Bernoulli). This, in turn, provides a partial solution to the conjectures and problems for determination of sharp bounds R for such functions f.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.12B
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• pp.1601-1610
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• 2011

This paper discusses standardization activities, requirements and enabling technologies for 100G Ethernet and 100G OTN. The need of 100Gbps transport capacity has been gaining greater interest from service providers and carrier vendors. Moreover, optical transport networks based on OTN/DWDM are changing their properties to apply Ethernet traffic which is dramatically increasing. We realize and experimentally demonstrate OTU4 framer with commercial FPGA. The key features of the realized OTU4 framer are parallel signal processing function, multi-lane distribution function, GMP function and FEC function. The realized OTU4 framer has the large signal processing capacity of 120Gbps, which allows to transport about 120Gbps client signals such as $12{\times}10G$ Ethernet and $3{\times}40G$ Ethernet. The realized OTU4 framer has the advantages to quickly adjust to changing markets and new technologies by using commercial FPGA instead of ASIC.