• 대한수학회보
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• 제46권5호
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• pp.999-1011
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• 2009

In this paper, we are concerned with the following eigenvalue problems of m-point boundary value problem for p-Laplacian dynamic equation on time scales $(\varphi_p(u^{\Delta}(t)))^\nabla+{\lambda}h(t)f(u(t))=0,\;t\in(0,T)$, $u(0)=0,\varphi_p(u^{\Delta}(T))=\sum\limits_{i=1}^{m-2}a_i\varphi_p(u^{\Delta}(\xi_i))$, where $\varphi_p(u)=|u|^{p-2}$u, p > 1 and $\lambda$ > 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solution and nonexistence are obtained for $\lambda$ evaluated in different intervals. Our work develop and improve many known results in the literature even for the continual case. In doing so the usual restriction that $f_0=lim_{u{\rightarrow}0}+f(u)/\varphi_p(u)$ and $f_\infty = lim_{u{\rightarrow}{\infty}}f(u)/\varphi_p({u})$ exist is removed. As an applications, an example is given to illustrate the main results obtained.

• 한국독어학회지:독어학
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• 제6집
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• pp.123-154
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• 2002

Im Mittelpunkt der vorliegenden Arbeit steht die Untersuchung der Dynamik im System des deutschen Passivs mit dem $R\"{u}ckblick$ auf das Genuanische. Dabei steht es vorrangig im Zusammenhang mit der Grammatikalisierung der $Verbalf\"{u}gungen$ 'werden + PP' und 'sein + PP'. Und im heutigen deutschen Passivsystem ist zwar die $F\"{u}gung$ 'werden + PP' unmarkiert, aber im Genuanischen $\"{u}berwiegt\;die\;F\"{u}gung$ 'sein + PP'. Das Partizip der Kombination 'werden/sein + PP' wird im Gotischen $ausschlie{\ss}lich$ und im Althochdeutschen noch stellenweise flektiert. Hieraus darf geschlossen werden, dass im $Fr\"{u}hdeutschen$ das Verb finita und das Partizip als relativ $unabh\"{a}ngige$ Glieder einander $gegen\"{u}ber$ stehen und in einer Konstruktion verkettet werden, die einfach den Status der neuhochdeutschen periphrastischen Konstruktion aufweist. Die aspektuelle Bedeutung der $Passivf\"{u}gungen\;l\"{a}sst$ sich da als $bin\"{a}re$ Opposition von kategoriellen Merkmalen 'mutativ' (= Zustandswechel) und 'statal' (= Zustand), verteilt auf die F\"{u}gungen$ 'werden + PP' und 'sein + pp', beschreiben. Diese Merkmale kommt jeweils aus dem inchoativen bzw. durativen Verbalaspekt der Verba 'werden' bzw. 'sein' heraus. Diese Opposition unterscheidet sich von der neuhochdeutschen $Gegen\"{u}berstellung$ vom Vorgangspassiv und Zustandspassiv. Die Eigenbedeutung der Verben 'werden' und 'sein' $l\"{o}st$ sich nun, insbesondere im $Sp\"{a}talthochdeutschen$ in der Semantik der ganzen $F\"{u}gungen$ weitgehend auf, was seinerseits den Verlust der aspektualen Markiertheit der Passiv-Periphrasen mit den Verben finiten verursacht und ihre Entwicklung in Richtung auf die Paradigmatisierung der beiden $F\"{u}gungen\;erm\"{o}glicht$. Die weiter Entwicklung von $Passivf\"{u}gungen$ zeichnet sich durch eine zunehmende Expansion der $F\"{u}gung$ 'werden+PP' in die ursprungliche aspektuale $Sph\"{a}re$ der sein-Konstruktion aus. Dieser Prozess, der zur Auxilialisierung des Verbums finitum $f\"{u}hrt$, setzt schon im $Sp\"{a}talthochdeutschen$ ein und gelangt im Mittelhochdeutschen zur vollen $Auspr\"{a}gung$. Die Konkurrenz der beiden Passivkonstruktionen $f\"{u}hrt$ nun zur $allm\"{a}hlichen$ Verengung des aspektualen Bereichs der $F\"{u}gung$ '.sein+PP', $f\"{u}r$ die nun nur das Resultivum $\"{u}brig$ bleibt.

• Journal of Advanced Marine Engineering and Technology
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• 제24권6호
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• pp.24-33
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• 2000

This paper investigates the relationship between J-integral and crack tip opening displacement, ${\delta}_t$ using Gordens results of numerical analysis. Estimation were carried out for several strength levels such as ultimate, flow, yield, ultimate-flow, flow-yield stress to determine the influence of strain hardening and the ratio of crack length to width on the $J-{\delta}_t$ relationship. It was found that for SE(B) specimens, the $J-{\delta}_t$ relationship can be applied to relate J to ${\delta}_t$ as follows $J=m_j{\times}{\sigma}_i{\times}{\delta}_t$ where $m_j=1.27773+0.8307({\alpha}/W)$, ${\sigma}_i:{\sigma}_U$, ${\sigma}_{U-F}={\frac{1}{2}} ({\sigma}_U+{\sigma}_F$), ${\sigma}_F$, ${\sigma}_F}$ $Y=({\sigma}_F+{\sigma}_Y)$, ${\sigma}_Y$

• 충청수학회지
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• 제23권4호
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• pp.773-784
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• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• 대한수학회보
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• 제54권6호
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• pp.2091-2106
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• 2017

The authors investigate f-biharmonic maps u : (M, g) ${\rightarrow}$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature, and derive that if $\int_{M}f^p{\mid}{\tau}(u){\mid}^pdv_g$ < ${\infty}$, $\int_{M}{\mid}{\tau}(u){\mid}^2dv_g$ < ${\infty}$ and $\int_{M}{\mid}du{\mid}^2dv_g$ < ${\infty}$, then u is harmonic. When u is an isometric immersion, the authors also get that if u satisfies some integral conditions, then it is minimal. These results give an affirmative partial answer to conjecture 4 (generalized Chen's conjecture for f-biharmonic submanifolds).

• Korean Journal of Mathematics
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• 제23권4호
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• pp.607-618
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• 2015

An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such that ${\mid}f(u)-f(v){\mid}{\geq}2$ if d(u, v) = 1 and ${\mid}f(u)-f(v){\mid}{\geq}1$ if d(u, v) = 2. The ${\lambda}$-number of G, denoted ${\lambda}(G)$, is the smallest number k such that G admits an L(2, 1)-labeling with $k=\max\{f(u){\mid}u{\in}V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its ${\lambda}$-number. In addition, we also completely determine its edge span.

• 대한수학회논문집
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• 제21권2호
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• 대한수학회논문집
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• 제31권1호
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• pp.131-138
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• 2016

We determine the general solutions $f:\mathbb{R}^2{\rightarrow}\mathbb{R}$ of the functional equation f(ux-vy, uy+v(x+y)) = f(x, y)f(u, v) for all x, y, u, $v{\in}\mathbb{R}$. We also investigate both bounded and unbounded solutions of the functional inequality ${\mid}f(ux-vy,uy+v(x+y))-f(x,y)f(u,v){\mid}{\leq}{\phi}(u,v)$ for all x, y, u, $v{\in}\mathbb{R}$, where ${\ph}:\mathbb{R}^2{\rightarrow}\mathbb{R}_+$ is a given function.

• 대한수학회논문집
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• 제31권3호
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• pp.495-505
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• 2016

Let $f:{\mathbb{R}}^3{\rightarrow}{\mathbb{R}}$. In this paper we prove the stability of functional inequalities ${\mid}f(ux+vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$, ${\mid}f(ux-vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$ for all $x,y,z,u,v,w{\in}{\mathbb{R}}$. Furthermore, we give refined descriptions of bounded functions satisfying the inequalities as in Albert and Baker [1].