• Journal of the Korean Mathematical Society
• /
• 제45권4호
• /
• pp.923-952
• /
• 2008

In this paper several continuities and homeomorphisms in computer topology are studied and their applications are investigated in relation to the classification of subs paces of Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$. Precisely, the notions of K-$(k_0,\;k_1)$-,$(k_0,\;k_1)$-,KD-$(k_0,\;k_1)$-continuities, and Khalimsky continuity as well as those of K-$(k_0,\;k_1)$-, $(k_0,\;k_1)$-, KD-$(k_0,\;k_1)$-homeomorphisms, and Khalimsky homeomorphism are studied and further, their applications are investigated.

• Journal of the Korean Mathematical Society
• /
• 제44권6호
• /
• pp.1479-1503
• /
• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• Journal of applied mathematics & informatics
• /
• 제28권5_6호
• /
• pp.1439-1443
• /
• 2010

For a positive integer k $\geq$ 2, the k-bonacci sequence {$g^{(k)}_n$} is defined as: $g^{(k)}_1=\cdots=g^{(k)}_{k-2}=0$, $g^{(k)}_{k-1}=g^{(k)}_k=1$ and for n > k $\geq$ 2, $g^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n-2}+{\cdots}+g^{(k)}_{n-k}$. And the k-Lucas sequence {$l^{(k)}_n$} is defined as $l^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n+k-1}$ for $n{\geq}1$. In this paper, we give a representation of nth k-Lucas $l^{(k)}_n$ by using determinant.

• KOREAN JOURNAL OF CROP SCIENCE
• /
• 제50권3호
• /
• pp.151-155
• /
• 2005

This study was carried out to get information for diversifying of resistant genes to bacterial blight (BB) in Japonica cultivar breeding programs. TWo hundred nine rice varieties were tested for qualitive resistance to four races of BB; HB9101 isolate for race K1, HB9102 isolate for race K2, HB9103 isolate for race K3, and HB01001 isolate for race K3a. Two hundred nine rice varieties were divided into five groups according to their race reaction. Fourteen Tongil-type varieties and ninetyseven Japonica varieties showed susceptible reaction to four races; Kl, K2, K3 and K3a. Thirteen Tongil-type varieties and thirty-one Japonica varieties were resistant to only one race; K1. Nine Tongil-type varieties and one Japonica variety were resistant to two races; K1 and K2. One Tongil-type variety and twenty-eight Japonica varieties were resistant to the three races; K1, K2, and K3. Fourteen Tongil-type varieties and one Japonica variety were resistant to four races; K1, K2, K3, and K3a. A number of Tongil-type varieties showed broad spectrum resistance to four races, while a number of Japonica varieties showed broad spectrum resistance to three races; K1, K2, and K3.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• 제40권3호
• /
• pp.491-496
• /
• 2015

In this paper, we introduce two classes of optimal codes, [$2^k-1$, k, $2^{k-1}$] simplex codes and [$2^k-1+k$, k, $2^{k-1}+1$] codes, attaining Griesmer bound with equality. We further present and compare the locality of them. The [$2^k-1+k$, k, $2^{k-1}+1$] codes have good locality property as well as optimal code length with given code dimension and minimum distance. Therefore, we expect that [$2^k-1+k$, k, $2^{k-1}+1$] codes can be applied to various distributed storage systems.

• Honam Mathematical Journal
• /
• 제25권1호
• /
• pp.43-52
• /
• 2003

The fuzzification of positive implicative hyper K-ideals in hyper K-algebras is considered, Relations between fuzzy positive implicative hyper K-ideal and fuzzy hyper K-ideal are given. Characterizations of fuzzy positive implicative hyper K-ideals are provided. Using a family of positive implicative hyper K-ideals we make a fuzzy positive implicative hyper K-ideal. Using the notion of a fuzzy positive implicative hyper K-ideal, a weak hyper K-ideal is established.

• Journal of Mushroom
• /
• 제11권1호
• /
• pp.1-8
• /
• 2013

In this study, twelve of Lepista nuda were collected from various localities in Korea. Also thirteen exotic L. nuda species were collected from Japan, France, Switzerland and Portugal. Spores were isolated under optical microscope. These spores were placed on the surface of YM medium for inducing to germination. Eleven mating-groups were selected by morphological characters of fruit body such as size, color and stipe patterns. Intra-isolate crosses were made between two single-spore isolates derived from mating-groups. Also, dikaryotic crossing using the isolates from L. nuda were carried out to evaluated tetrakaryon formation. Cross-mating compatibility tests also verified its dikaryotic state by microscopic or molecular genetic observation of clamp connection and Random Amplified Polymorphic DNA (RAPD) band pattern. To analyze the growth rate of hybrids and parents mycelium in dikaryons obtained from compatible mating groups were placed on PDA medium. Intra-isolate crosses determined eleven mating-groups within L. nuda. The typical clamp connection were mostly observed in mating-groups of Korean L. nuda in $K1{\times}K2$, $K1{\times}K3$, $K1{\times}K4$, $K1{\times}K6$, $K1{\times}K5$, $K2{\times}K4$, $K2{\times}K3$, $K2{\times}K6$, $K3{\times}K4$, $K4{\times}K5$, and $K4{\times}K6$. Korean L. nuda type of dikaryon, shown to cross-incompatibility with L. sordida, it seemed that mating induce more rapidly than wild types in a view of growth rate. In conclusion, it would be useful to improve mass production with better morphological characteristics through a special mating of L. nuda.

• Parasites, Hosts and Diseases
• /
• 제35권4호
• /
• pp.251-258
• /
• 1997

Tachyzoite antigens of Toxoplosnc gondii (RH) were partially purified by immunoaffinity chromatography. The cultivated ToxopLusmc in uiuo (mouse) and in nitro (Hep-2 cell) and peritoneal fluid of T. Bondii infected mice were collected for antigen analy- sis. Tachyzoite antigens collected from infected mouse showed positive bands of 76 kDa, 70 kDa,64 kDa, 53 kDa, 46 kDa, 44 kDa, 41 kDa, 35 kDa, 25 kDa, 18 kDa, and 13 kDa on immunoblot with anti-Toxoplcsmn rabbit sera, and those from infected Hep-2 cells revealed reactive bands of 70 kDa,64 kDa,53 kDa,35 kDa,28 kDa, and 13-10 kDa. After applying to an IgG-Sepharose column, two elusion peaks, E-1 and I-2 fractions, were obtained from both soluble antigen of T. gondii and the peritoneal fluid of infected mice, respectively. Immunoblots of soluble antigen with immunized rabbit sera revealed positive bands of 97 kDa, 63 kDa, 53 kDa and 35 kDa from I-1 fraction and 53 kDa and 35 kDa from I-2. In the case of the eluted peaks from mice peritoneal fluid, E-1 showed protein bands of 84 kDa,76 kDa,53 kDa and 29 kDa bands and 53 kDa and 45 kDa from I-2 on immunoblots. Serum IgG antibody titer of mice immunized with T gonnii tachyzoites was increased on 1 week after booster immunization when analysed by ELISA using crude antigen, while it was elevated on 3 weeks after booster immunization by ELISA using puri- fied antigen.

• Journal of applied mathematics & informatics
• /
• 제27권1_2호
• /
• pp.89-96
• /
• 2009

In this article, we show a generalization of Clement's theorem on the pair of primes. For any integers n and k, integers n and n + 2k are a pair of primes if and only if 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) whenever (n, (2k)!) = (n + 2k, (2k)!) = 1. Especially, n or n + 2k is a composite number, a pair (n, n + 2k), for which 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) is called a pair of pseudoprimes for any positive integer k. We have pairs of pseudorimes (n, n + 2k) with $n{\leq}5{\times}10^4$ for each positive integer $k(4{\leq}k{\leq}10)$.

• Journal of the Korean Mathematical Society
• /
• 제46권1호
• /
• pp.187-213
• /
• 2009

For a positive integer k and an arbitrary integer h, the classical Dedekind sums s(h,k) is defined by $$S(h,\;k)=\sum\limits_{j=1}^k\(\(\frac{j}{k}\)\)\(\(\frac{hj}{k}\)\),$$ where $$((x))=\{{x-[x]-\frac{1}{2},\;if\;x\;is\;not\;an\;integer; \atop \;0,\;\;\;\;\;\;\;\;\;\;if\;x\;is\;an\;integer.}\$$ J. B. Conrey et al proved that $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^{2m}(h,\;k)=fm(k)\;\(\frac{k}{12}\)^{2m}+O\(\(k^{\frac{9}{5}}+k^{{2m-1}+\frac{1}{m+1}}\)\;\log^3k\).$$ For $m\;{\geq}\;2$, C. Jia reduced the error terms to $O(k^{2m-1})$. While for m = 1, W. Zhang showed $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^2(h,\;k)=\frac{5}{144}k{\phi}(k)\prod_{p^{\alpha}{\parallel}k}\[\frac{\(1+\frac{1}{p}\)^2-\frac{1}{p^{3\alpha+1}}}{1+\frac{1}{p}+\frac{1}{p^2}}\]\;+\;O\(k\;{\exp}\;\(\frac{4{\log}k}{\log\log{k}}\)\).$$. In this paper we give some formulae on the mean value of the Dedekind sums and and Hardy sums, and generalize the above results.