• BMB Reports
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• 제44권1호
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• pp.11-21
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• 2011

During the last decade small regulatory RNA (srRNA) emerged as central players in the regulation of gene expression in all kingdoms of life. Multiple pathways for srRNA biogenesis and diverse mechanisms of gene regulation may indicate that srRNA regulation evolved independently multiple times. However, small RNA pathways share numerous properties, including the ability of a single srRNA to regulate multiple targets. Some of the mechanisms of gene regulation by srRNAs have significant effect on the abundance of free srRNAs that are ready to interact with new targets. This results in indirect interactions among seemingly unrelated genes, as well as in a crosstalk between different srRNA pathways. Here we briefly review and compare the major srRNA pathways, and argue that the impact of srRNA is always at the system level. We demonstrate how a simple mathematical model can ease the discussion of governing principles. To demonstrate these points we review a few examples from bacteria and animals.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.227-245
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• 2014

Suppose G is a simple graph. The ${\ell}$-eigenvalues ${\delta}_1$, ${\delta}_2$,..., ${\delta}_n$ of G are the eigenvalues of its normalized Laplacian ${\ell}$. The normalized Laplacian Estrada index of the graph G is dened as ${\ell}EE$ = ${\ell}EE$(G) = ${\sum}^n_{i=1}e^{{\delta}_i}$. In this paper the basic properties of ${\ell}EE$ are investigated. Moreover, some lower and upper bounds for the normalized Laplacian Estrada index in terms of the number of vertices, edges and the Randic index are obtained. In addition, some relations between ${\ell}EE$ and graph energy $E_{\ell}$(G) are presented.

• 대한수학회보
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• 제39권2호
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• pp.309-315
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• 2002

Let I be an open interval and X a complex Banach space. Let$\varepsilon\geq0\;and\;\lambda$ a non-zero complex number with Re $\lambda\neq0$. If $\varphi$ is a strongly differentiable map from I to X with $\parallel\varphi^'(t)-\lambda\varphi(t)\parallel\leq\varepsilon\;for\;all\;t\in\;I$, then we show that the distance between $\varphi$ and the set of all solutions to the differential equation y'=$\lambda$y is at most $\varepsilon/$\mid$Re\lambda$\mid$$.

• 대한수학회보
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• 제49권4호
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• pp.787-797
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• 2012

In this paper the authors study the $L^p$ boundedness for parabolic Littlewood-Paley operator $${\mu}{\Phi},{\Omega}(f)(x)=\({\int}_{0}^{\infty}{\mid}F_{\Phi,t}(x){\mid}^2\frac{dt}{t^3}\)^{1/2}$$, where $$F_{\Phi,t}(x)={\int}_{p(y){\leq}t}\frac{\Omega(y)}{\rho(y)^{{\alpha}-1}}f(x-{\Phi}(y))dy$$ and ${\Omega}$ satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.

• 대한수학회지
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• 제47권4호
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• pp.691-704
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• 2010

Over a ring R, let $P_R$ be a finitely generated projective right R-module. Then we define the G-injector (G-projector) if $P_R$ preservers Gorenstein injective modules (Gorenstein projective modules), the Gflator if $P_R$ preservers Gorenstein flat modules. G-injector (G-flator) and G-injector are characterized focus primarily on the cases where R is a Gorenstein ring, and under this condition we also study the relations between the injector (projector, flator) and the G-injector (G-projector, G-flator). Over any ring we also give the characteristics of G-injector (G-flator) by the Gorenstein injective (Gorenstein flat) dimensions of modules.

• 대한수학회지
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• 제57권5호
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• pp.1187-1237
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• 2020

Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic 2, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the Clebsch-Gordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.

• 대한수학회보
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• 제48권6호
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• pp.1195-1205
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• 2011

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

• 대한수학회논문집
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• 제35권2호
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• pp.613-623
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• 2020

The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3-dimensional almost Kenmotsu Einstein manifold M is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• 대한수학회지
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• 제41권6호
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• pp.995-1005
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• 2004

The aim of this paper is to prove the stability in the sense of Hyers-Ulam- Rassias of the Banach space valued differentialequation y' = λy, where λ is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y' = λy, then there exists an exact solution of the equation near to f.