• Korean Journal of Mathematics
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• v.20 no.4
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• pp.415-422
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• 2012

In this paper, we define the weak property (${\beta}_{\kappa}$) and get the following strict implications. $$(UC){\Rightarrow}w-({\beta}_1){\Rightarrow}w-({\beta}_2){\Rightarrow}\;{\cdots}\;{\Rightarrow}w-({\beta}_{\infty}){\Rightarrow}(BS)$$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.505-511
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• 2015

In this paper, we investigate relationships among property ($k-{\beta}$), weak property (${\beta}_k$), k-nearly uniformly convexity and property ($A_k$).

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.463-469
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• 2014

In this paper, we investigate relationship between superreflexivity and weak property (${\beta}_k$). Indeed, we get the following diagram.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.359-367
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• 2005

Let A be a Banach algebra, we say that A has the strongly double limit property (SDLP) if for each bounded net $(a_\alpha)$ in A and each bounded net $(a^{\ast}\;_\beta)\;in\;A^{\ast},\;lim_\alpha\;lim_\beta=lim_\beta\;lim_\alpha$ whenever both iterated limits exist. In this paper among other results we show that if A has the SDLP and $A^{\ast\ast}$ is (n - 2)-weakly amenable, then A is n-weakly amenable. In particular, it is shown that if $A^{\ast\ast}$ is weakly amenable and A has the SDLP, then A is weakly amenable.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• Korean Journal of Materials Research
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• v.24 no.4
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• pp.201-206
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• 2014

TiC-21 mol% Mo solid solution (${\delta}$-phase) and TiC-99 mol% Mo solid solution (${\beta}$-phase), and TiC-(80~90) mol% Mo hypo-eutectic composite were deformed by compression in a temperature range from room to 2300 K and in a strain rate range from $4.9{\times}10^{-5}$ to $6.9{\times}10^{-3}/s$. The deformation behaviors of the composites were analyzed from the strengths of the ${\delta}$- and ${\beta}$-phases. It was found that the high strength of the eutectic composite is due primarily to solution hardening of TiC by Mo, and that the ${\delta}$-phase undergoes an appreciable plastic deformation at and above 1420 K even at 0.2% plastic strain of the composite. The yield strength of the three kinds of phase up to 1420 K is quantitatively explained by the rule of mixture, where internal stresses introduced by plastic deformation are taken into account. Above 1420 K, however, the calculated yield strength was considerably larger than the measured strength. The yield stress of ${\beta}$-phase was much larger than that of pure TiC. A good linear relationship was held between the yield stress and the plastic strain rate in a double-logarithmic plot. The deformation behavior in ${\delta}$-phase was different among the three temperature ranges tested, i.e., low, intermediate and high. At an intermediate temperature, no yield drop occurred, and from the beginning the work hardening level was high. At the tested temperature, a good linear relationship was held in the double logarithmic plot of the yield stress against the plastic strain rate. The strain rate dependence of the yield stress was very weak up to 1273 K in the hypo-eutectic composite, but it became stronger as the temperature rose.

• Korean Journal of Food Science and Technology
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• v.32 no.3
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• pp.590-597
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• 2000

The rheological properties of ${\beta}-glucans$ isolated from non-waxy and waxy barley were investigated. ${\beta}-Glucan$ solutions showed pseudoplastic properties and their behaviors were explained by applying Power law model in the range of concentrations$(1{\sim}4%)$ and temperatures$(20{\sim}65^{\circ}C)$. The effects of temperature and concentration on the apparent viscosity at $700\;s^{-1}$ shear rate were examined by applying Arrhenius equation and power law equation, and their effect was more pronounced in waxy ${\beta}-glucan$ solutions. The activation energy for flow of ${\beta}-glucan$ solutions decreased with the increase of concentration, and the concentration-dependent constant A increased with the increase of temperature. The intrinsic viscosity of waxy ${\beta}-glucan$ was higher than that of non-waxy ${\beta}-glucan$. The transition from dilute to concentrate region occurred at a critical coil overlap parameter $C^*[{\eta}]=0.02.$ The slopes of non-waxy and waxy ${\beta}-glucan$ at $C[{\eta}] were similar, but the slope of waxy ${\beta}-glucan$ at $C[{\eta}]>C^*[{\eta}]$ was higher than that of non-waxy ${\beta}-glucan$. Dynamic viscoelasticity measurement showed that cross-over happened, and storage modulus was higher than loss modulus at frequency range above cross-over. ${\beta}-Glucan$ solutions formed weak gels after stored for 24 hr.

• Korean Journal of Soil Science and Fertilizer
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• v.41 no.3
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• pp.206-213
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• 2008

We observed the physical and chemical properties of a soil on pine mushroom picking areas where were located in the most upper and lower parts showing a comparative climatic characteristics in Korea. The slope gradients within the investigation areas which were divided into 100 quadrates of $1m^2$ ranged from $5.7{\sim}8.6{\beta}$ to $24{\sim}22.7{\beta}$ (left to right) and $4.5{\sim}6.8{\beta}$ to $13.5{\sim}17.8{\beta}$ (top to bottom) for Ponghwa and Gansung, respectively. The amount of clay and thickness of organic matter were significantly decreased with increasing slope gradient, resulting in decrease of the soil moisture content around a fairly ring-colony of Tricholoma matsutake which was observed under the relatively thicker organic matter layer beyond 3 cm depth. Soil pHswere weak acid and average EC was $0.44dS\;m^{-1}$ in both areas. The cations were in the order of Fe K > Na > Mg > Ca and Fe > K > Na > Ca > Mg for the upper(Gansung) and the lower (Ponghwa) part. And the amount of Fe was approximately $80dS\;m^{-1}$ or greater in the pine mushroom picking soil. From this, we could assume that the growth of the pine mushroom was closely related not only with iron but also soil moisture content.