• Korean Journal of Mathematics
• /
• v.14 no.1
• /
• pp.101-112
• /
• 2006

In this paper, we introduce the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and obtain some of their structural properties. We also introduce the concepts of several types of weak quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and investigate some of their properties.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.1049-1061
• /
• 2019

For ${\alpha}{\geq}1$, let $s_{\alpha}(n)={\lceil}{\alpha}n{\rceil}-{\lceil}{\alpha}(n-1){\rceil}$. A continued fraction $C({\alpha})=[0;s_{\alpha}(1),s_{\alpha}(2),{\ldots}]$ is considered and analyzed. Appealing to Diophantine approximation, we investigate the differentiability of $C({\alpha})$, and then show its singularity.

• Korean journal of food and cookery science
• /
• v.14 no.3
• /
• pp.261-265
• /
• 1998

The activity and characteristics of ${\alpha}$-amylase in soy milk as well as in Jeungpyun batters were determined to investigate the enzyme system related to Jeungpyun preparation. ${\alpha}$-Amylase activity was detected in soy milk as well as in Jeungpyun batters. Soy milk had ${\alpha}$-amylase activity of 0.79 units/mg protein for gelatinized starch and 0.036 units/mg protein for raw starch. ${\alpha}$-Amylase in soy milk showed maximum activities at pH 5.92∼6.87 and at 60$^{\circ}C$ for both gelatinized starch and raw starch. ${\alpha}$-Amylase activities of Jeungpyun batters containing soy milk were 25.59 units/mg protein for gelatinized starch and 1.37 units/mg protein for raw starch. Jeungpyun batters without soy milk demonstrated ${\alpha}$-amylase activities of 3.37 units/mg protein for gelatinized starch and 0.49 units/mg protein for raw starch. ${\alpha}$-Amylase of Jeungpyun batters showed an optimal activity at pH 5.25 and at 60$^{\circ}C$ for both gelatinized and raw starch. The results demonstrated that Jeungpyun batters with soy milk showed significantly higher ${\alpha}$-amylase activity than the ones without soy milk.

• Korean Journal of Animal Reproduction
• /
• v.25 no.2
• /
• pp.155-162
• /
• 2001

These experiments were conducted to evaluate the effects of the administration of exogenous PG $F_{2{\alpha}}$ on hormone concentrations and follicular development in early postpartum(pp) Korean native goats. 1. Plasma PG $F_{2{\alpha}}$ concentrations in PG $F_{2{\alpha}}$ treated goals showed a gradual increase from a low on day 2 (GR-1 : 10 day-treatment group: 6.35$\pm$0.5 and GR-2; 4 day-treatment group: 0.22$\pm$0.2 pg/$m\ell$, respectively) to reach a peak of 21.18$\pm$1.6 or 4.21 $\pm$0.4 pg/$m\ell$ on day 4 after treatment of PG $F_{2{\alpha}}$. 2. Plasma PG $F_{2{\alpha}}$ concentrations in GR-1 goats averaged 9.08 $\pm$1.2 pg/$m\ell$ compared with 5.44$\pm$ 1.8 pg/$m\ell$ in GR-2 goats the day before treatment of PG $F_{2{\alpha}}$. Mean PG $F_{2{\alpha}}$ concentrations thereafter remained low during the treatment period but PG $F_{2{\alpha}}$ concentrations did not differ between the two group. 3. Plasma concentrations of estradiol-17 $\beta$ (E,) in PG $F_{2{\alpha}}$ - treated group were decreased gradually until 2 days after PG $F_{2{\alpha}}$ treatment but mean $E_2$ concentrations began to increase on 3 days and were Inaximal on the 4 days after treatment. 4. Plasma lulenizing hormone (LH) concentrations in PG $F_{2{\alpha}}$ - treated goats were slightly higher than in controls but mean LH concentrations did not differ between the two treatment groups. 5. Plasma prolactin (PRL) concentrations were suppressed in both GR-1(10 day-treatment group) and GR-2(4 day-treatment group) goats compared to saline controls but mean PRL concentrations remained lower in PG $F_{2{\alpha}}$ treated animals during post-treatment period. 6. The mean number of small and medium follicles present when PG $F_{2{\alpha}}$ was administrated was similar in all does but the increase in number of large follicles($\geq$4mm) tended to be higher in PG $F_{2{\alpha}}$ treated group than controls. These results suggest that concentrations of PG $F_{2{\alpha}}$ and estradiol-17$\beta$ were positively correlared with follicular diameter. We conclude that PG $F_{2{\alpha}}$ treatment stimulates follicular development similarly in both GR-1 and GR-2 group.

• Korean Journal of Food Science and Technology
• /
• v.15 no.2
• /
• pp.160-163
• /
• 1983

Alpha-barleys prepared by boiling had the highest water absorption and those prepared by autoclaving showed the lowest water absorption among all the treatments, but all of ${\alpha}-barleys$ were higher than untreated barleys. The values of hardness on cooked ${\alpha}-barleys$ decreased as the degree of polishing increased, and untreated burleys showed the higher values than ${\alpha}-barleys$. There were no significant difference in total scores of sensory evaluation between ${\alpha}-barley-rice$ mixtures and untreated barley-rice mixtures after cooking.

• Honam Mathematical Journal
• /
• v.32 no.3
• /
• pp.413-439
• /
• 2010

W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.

• Kyungpook Mathematical Journal
• /
• v.49 no.3
• /
• pp.457-471
• /
• 2009

Let S = {a, b, c, ...} and ${\Gamma}$ = {${\alpha}$, ${\beta}$, ${\gamma}$, ...} be two nonempty sets. S is called a ${\Gamma}$-semigroup if $a{\alpha}b{\in}S$, for all ${\alpha}{\in}{\Gamma}$ and a, b ${\in}$ S and $(a{\alpha}b){\beta}c=a{\alpha}(b{\beta}c)$, for all a, b, c ${\in}$ S and for all ${\alpha}$, ${\beta}$ ${\in}$ ${\Gamma}$. An element $e{\in}S$ is said to be an ${\alpha}$-idempotent for some ${\alpha}{\in}{\Gamma}$ if $e{\alpha}e$ = e. A ${\Gamma}$-semigroup S is called an E-inversive ${\Gamma}$-semigroup if for each $a{\in}S$ there exist $x{\in}S$ and ${\alpha}{\in}{\Gamma}$ such that a${\alpha}$x is a ${\beta}$-idempotent for some ${\beta}{\in}{\Gamma}$. A ${\Gamma}$-semigroup is called a right E-${\Gamma}$-semigroup if for each ${\alpha}$-idempotent e and ${\beta}$-idempotent f, $e{\alpha}$ is a ${\beta}$-idempotent. In this paper we investigate different properties of E-inversive ${\Gamma}$-semigroup and right E-${\Gamma}$-semigroup.

• Journal of the Korean Mathematical Society
• /
• v.41 no.6
• /
• pp.945-955
• /
• 2004

In this paper, we establish a number system in $R^n$ which arises from a Haar wavelet basis in connection with decompositions of certain Cuntz algebra representations on $L^2$( $R^n$). Number systems in $R^n$ are also of independent interest [9]. We study radix-representations of $\chi$ $\in$ $R^n$: $\chi$:$\alpha$$_{ι}$ $\alpha$$_{ι-1}$…$\alpha$$_1$$\alpha$$_{0}$ ㆍ$\alpha$$_{-1}$ $\alpha$$_{-2}$ … as $\chi$= $M^{ι}$$\alpha$$_{ι}$ $\alpha$＋…M$\alpha$$_1$＋$\alpha$$_{0}$ ＋ $M^{-1}$ $\alpha$$_{-1}$ ＋ $M^{-2}$ $\alpha$$_{-2}$ ＋… where each $\alpha$$_{k}$ $\in$ D, and D is some specified digit set. Our analysis uses iteration techniques of a number-theoretic flavor. The view-point is a dual one which we term fractals in the large vs. fractals in the small,illustrating the number theory of integral lattice points vs. fractions.s vs. fractions.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.119-132
• /
• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for $a,b{\in}R$. In this paper, we study an extension of a reversible ring with its endomorphism. An endomorphism ${\alpha}$ of a ring R is called strong right (resp., left) reversible if whenever $a{\alpha}(b)=0$ (resp., ${\alpha}(a)b=0$) for $a,b{\in}R$, ba = 0. A ring R is called strong right (resp., left) ${\alpha}$-reversible if there exists a strong right (resp., left) reversible endomorphism ${\alpha}$ of R, and the ring R is called strong ${\alpha}$-reversible if R is both strong left and right ${\alpha}$-reversible. We investigate characterizations of strong ${\alpha}$-reversible rings and their related properties including extensions. In particular, we show that every semiprime and strong ${\alpha}$-reversible ring is ${\alpha}$-rigid and that for an ${\alpha}$-skew Armendariz ring R, the ring R is reversible and strong ${\alpha}$-reversible if and only if the skew polynomial ring $R[x;{\alpha}]$ of R is reversible.

• Korean Journal of Microbiology
• /
• v.37 no.2
• /
• pp.164-169
• /
• 2001

The conversion of cephalosporin C to 7$\alpha$-hydroxycephalosporin C was examined with the cell-free extract of several cephamycin producing strains. Streptomyces clavuligerus ATCC 27064 was the most potent strain for the activity of cephalosporin 7$\alpha$-hydroxylase. Partially purified and immobilized cephalosporin 7$\alpha$-hydroxylase with resins were used to synthesize 7$\alpha$-hydroxycephalosporin C from the substrate, cephalosporin C. The molecular weight of the product isolated from the reaction mixture were determined to be 431 by ESI-Mass. $^1H$ NMR also support the conversion of cephalosporin C to 7$\alpha$-hydroxycephalosporin C by immobilized enzyme.