• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• International Journal of Highway Engineering
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• v.8 no.4 s.30
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• pp.63-74
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• 2006

It's essential to meet the expectations of drivers through reasonable road design, which makes the drivers to recognize the conditions of road sufficiently. In this case, we could say that because the roads are consistently designed, drivers can make a safe and comfortable drive. There are so many studies about the alignment design consistency methods which are previously mentioned. In this study, Firstly we categorize the studies which are concerned with the estimation of the alignment design consistency methods and then apply the method which fits for the actual condition into the practice. And we'll make a realistic method by using the data which aye collected from the National Road. The developed model in this study is the predicting model including speed($V_t$) as the variable on the upper stream 100m of the curve. This model was developed which divided to two cases in the all directions of two lanes; One case is the $R{\leq}200m$ and another case is the R>200m. In the section of the $R{\leq}200m$, this case was influenced on the road alignment(R) and($V_t$) and another section was found that is affected to the speed($V_t$) on the upper stream loom rather than the effect of road alignment(R). In the case of all directions of four lanes, however, this study is predicted divided to two sections on the 400m of R, these section have more influenced to($V_t$) than the road alignment factors. This result of the four lanes was represented to different result with the two lanes. This study will further need development of the predicting model with the higher confidence through collecting data with more the exact data, the various road alignment data and speed of the several sections on the upper stream on the curve.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.671-682
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• 1999

Using a base-point free version of the infinite symmetric product we define a fibrewise infinite symmetric product for any fibration $E\;\longrightarrow\;B$. The construction works for any commutative ring R with unit and is denoted by $R_f(E)\;l\ongrightarrow\;B$. For any pointed space B let $G_I(B)\;\longrightarrow\;B$ be the i-th Ganea fibration. Defining $M_R-cat(B):= inf{i\midR_f(G_i(B))\longrihghtarrow\;B$ admits a section} we obtain an approximation to the Lusternik-Schnirelmann category of B which satisfies .g.a product formula. In particular, if B is a 1-connected rational space of finite rational type, then $M_Q$-cat(B) coincides with the well-known (purely algebraically defined) M-category of B which in fact is equal to cat (B) by a result of K.Hess. All the constructions more generally apply to the Ganea category of maps.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1139-1161
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• 2012

Let $p$ be an odd prime number and let F be a finite field with $p^m$ elements. We study representations and strict representations of polynomials $M{\in}F$[T] by sums of ($p^r$ + 1)-th powers. A representation $$M=M_1^k+{\cdots}+M_s^k$$ of $M{\in}F$[T] as a sum of $k$-th powers of polynomials is strict if $k$ deg $M_i<k$ + degM.

• The Pure and Applied Mathematics
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• v.13 no.2 s.32
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• pp.113-120
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• 2006

In this paper, we introduce the concept of P(r,m) $\Gamma$-near-ring and obtain some characterization of P(r,m) $\Gamma$-near-rings through regularity conditions.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.559-571
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• 2017

We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.28 no.3
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• pp.373-381
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• 1995

Oxygen consumption of marine fishes according to different water temperatures, fish population densities and body weights was measured in the respiratory chamber for the following six species: the olive flounder Paralichthys olivaceus, the tiger puffer Takifugu rubripes, the rockfish Sebastes schlegeli, the sea bass Lateolabrax Japonicus, the red seabream Pagrus major and the black seabream Acanthopagrus schlegeli. Also the lethal concentration of dissolved oxygen in them was determined. Oxygen consumption in each fish species increased as the water temperature increased. The relationship between the oxygen consumption rate $(Oc,\;ml/kg{\cdot}\;hr)$ and the water temperature (T,$^{\circ}C$) for each species appeared as the following equations demonstrate; olive flounder: Oc=34.0515T-339.5987 $(r^2=0.9730)$, tiger puffer: Oc=34.4941T-479.8732 $(r^2=0.9483),$ rockfish: Oc=44.7970T-634.2627 $(r^2=0.9718),$ sea bass: Oc=26.1488T-318.0633 $(r^2=0.9316),$ red seabream: Oc=61.1020T-722.8926 $(r^2= 0.9805),$ black seabream: Oc=75.1460T-947.9370 $(r^2=0.9392).$ The of gen consumption of fish with different population densities decreased as the number of fish increased. As the body weight of the olive flounder increased, the mass-specific oxygen consumption decreased. The relationship between oxygen consumption and body weight (W; g) was expressed as Oc=2532.0268W-0.6565 $(r^2=0.9229)$. The levels of lethal dissolved oxygen in the olive flounder, rockfish, tiger puffer and red seabream were 0.66, 0.79, 0.75 and 1.36 m1/1, respectively.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.517-529
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• 2012

In this paper, the existence theorem of two positive solutions is established for nonlinear m-point boundary value problem by using an inequality for the following third-order differential equations $$({\phi}(u^{\prime\prime}))^{\prime}+a(t)f(t,u(t))=0,\;t{\in}(0,1)$$, $${\phi}(u^{\prime\prime}(0))=\sum^{m-2}_{i=1}a_i{\phi}(u^{\prime\prime}({\xi}_i)),\;u^{\prime}(1)=0,\;u(0)=\sum^{m-2}_{i=1}b_iu({\xi}_i)$$, where ${\phi}:R{\rightarrow}R$ is an increasing homeomorphism and homomorphism and $\phi(0)=0$. The nonlinear term f may change sign, as an application, an example to demonstrate our results is given.

• YAKHAK HOEJI
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• v.42 no.3
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• pp.296-301
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• 1998

To investigate the effects of ginsenosides from Panax ginseng on mitogenic responses in macrophages and splenocytes from murine, we examined the effects of representative protopanaxadiol and protopanaxatriol ginsenosides ($Rb_1,\;Rb_2,\;Re\;and\;Rg_1$) on tumor necrosis factor-${\alpha}$ (TNF-(${\alpha}$) production in murine macrophage cell line (RAW264.7 cells) stimulated by lipopolysaccharide (LPS) and T cell proliferation in splenocytes stimulated by concanavalin A (Con A). Among the ginsenosides tested, protopanaxadiol ginsenosides ($Rb_1\;and\;Rb_2$) significantly inhibited TNF-${\alpha}$ production in a dose-dependent manner. However, protoppanaxatriol ginsenosides (Re and $Rg_1$) showed little inhibitory activity. The molar concentrations of $Rb_1\;and\;Rb_2$ producing 50% inhibition ($IC_{50}$) of TNF-${\alpha}$ production were $55.8{\mu}g/ml\;(48.0{\mu}M)\;and\;31.8{\mu}g/ml (27.9{\mu}M)$, respectively. As a positive control, prednisolone also exhibited inhibitory activity with an $IC_{50}$ value of $21.7{\mu}M$. In T cell proliferation, $Rg_1$, was not effective but $Rb_1$ and Re or $Rb_2$ significantly increased or inhibited at high concentration, 75 and $100{\mu}g/ml$. In contrast, prednisolone showed potent inhibitory activity with an $IC_{50}$ value of 6.1nM. These results suggest that ginsenosides may take part in the mitogen-induced signaling pathway for TNF-${\alpha}$ production and T cell proliferation from macrophages and splenocytes.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.867-871
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• 2009

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.