• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.63-71
• /
• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.

• Proceedings of the Botanical Society of Korea Conference
• /
• 1985.08b
• /
• pp.73-81
• /
• 1985

We have previously isolated OsMADS4 gene that is a member of the class B MADS box genes from rice. In this study, another member of the class B MADS box genes was isolated from rice flower by the yeast two-hybrid screening method using OsMADS4 as bait. RNA blot analyses revealed that the clone, OsMADS16, was expressed in the second and third whorls, whereas the OsMADS4 transcripts were present in the second, third, and fourth whorls. These expression patterns of the OsMADS16 and OsMADS4 genes are very similar with those of AP3 and PI, the class B genes of Arabidopsis, respectively. In the yeast two-hybrid system, OsMADS4 interacted only with OsMADS16 among several rice MADS genes investigated, suggesting that OsMADS4 and OsMADS16 function as a heterodimer in specifying sepal and petal identities. We have also isolated OsMADS6 gene using OsMADS1 as a probe. Both are members of the AGL2 MADS family. Various MADS genes that encode for protein-protein interaction partners of the OsMADS6 protein were isolated by the yeast two-hybrid screening method. A majority of these genes belong to the AGL2 family. Sequence Homology, expression pattern, and ectopic expression phenotypes indicated that one of the interaction partners, OsMADS14, appears to be homologous to API, the class A MADS gene of Arabidopsis.

• The KIPS Transactions:PartB
• /
• v.11B no.5
• /
• pp.611-618
• /
• 2004

This paper addresses the design and implementation of class distribution in distributed object-oriented databases. The proposed strategy of distribution consists of two-step design of fragments. One is class fragmentation and the other is allocation of fragments. In step of class fragmentation, we have defined partitioning algorithms to reflect the characteristics of object-oriented databases such as method, inheritance and composite-object. In step of allocation, we have defined the objective function for allocation considering system operating cost including storage, query processing and communication and implemented it using Genetic Algorithm.

• Journal of Plant Biology
• /
• v.9 no.1_2
• /
• pp.7-16
• /
• 1966

In order to determine the factors related to site quality, 13 areas of Larch growing in the Kwangung and its vicinity forest as sample plots, were examined. Sample plots included various site classes as well as age classes. Three were divided into two groups (major and minor trees). Average height of dominant trees was determined through messurement of 5 to 6 dominant tree in each sample plots. Average height of dominant 30 year-old trees was the basis for site index. A Standard Yield Table for the larch produced in Kwangnung forest was made by various data, which included age class 5, ranging from 10 to 45 years. The relationship of the height of the trees, the site conditions, and ground vegetation are investigated in this paper. The site indexes of 40 forest class age in 28-B and 28-G forest classes of the larch associations for ground vegetation had comparatively rarge differences due to the sampled areas. The relation of the direction of forest communities to the height and the diameter of the tree shwoed that its communiteis of northest and northwest parts appeared higher valueof the height and the diameter. The diameter and the height of trees were closely realted to each other. The samller the occupied area per tree and the smaller the average distance among trees, the more density was increased. The larger the density was the lower height of the trees. In the ground vegetation of the larch communities, there seems to be a definite correlation between the height of trees and the occupied area per tree or the average distance among the trees. The height of trees and site index of two larch communities were as follow: 28-B forest class site index 20.8, height 24.0m, 28-G forest class site index 18.4, height 20.9m. The ground layer was analyzed by the method of Quadrat(20/20sq. cm) with an interval of 1M. It set up 40 Quadrats of the larch communiteis. The community structure of the ground vegetation of two larch was analyzed, and important value was calculated and then evaluated. The ground vegetation under the larch had developed Burmannii Beauv stratal society below the 28-B and 28-G the forest class. Accordingly, the first important value of Burmannii Beauv was found in two ground vegetation below the larch. Therefore, this species could be quantitatively considered as the forest indicator species. Common species of each community appeared 18 species out of 34 species in the ground vegetation under two larch communities. The ground vegetation of the 28-B forest class showed more than that of the 28-G forest class. the similarity of the ground vegetation was measrued by the Frequency Index Community Coefficient. The differences between the associations were lcearly manifested by the ground vegetation tested by Gleason's Frequency Index of Community Coefficient for the analysis of each stratal society of all associations. According to F.I.C.C. the ground vegetation under two larch(28-B and 28-G) forest classes showed higher value. An investigation into the relationship of physical and chemical properties of soil and site was considered the next step to be taken in the study of the larch site classification.

• The Pure and Applied Mathematics
• /
• v.7 no.1
• /
• pp.27-32
• /
• 2000

The quadratic fields generated by $x^2$=ax+1($\alpha\geq$1) are studied. The regulators are relatively small and are known at one. The class numbers are relatively large and easy to compute. We shall find all the values of p, where p=$\alpha^2$+4 is a prime in $\mathbb{Z}$, such that $\mathbb{Q}(\sprt{p})$ has class numbers 1, 3 and 5.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.107-119
• /
• 2009

In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.

• The Pure and Applied Mathematics
• /
• v.12 no.1
• /
• pp.57-63
• /
• 2005

Let ∑(p)(p ∈ N) be the class of functions f(z) = z/sup -p/ + α/sub 1-p/ z/sup 1-p/ + α/sub 2-p/z/sup 2-p/ + ... analytic in 0 < ｜z｜ < 1 and let M(p, λ, μ)(0 < λ≤ 2 and 2λ(λ - 1) ≤ μ ≤ λ²) denote the class of functions f(z) ∈ ∑(p) which satisfy (equation omitted). The object of the present paper is to derive some properties of functions in the class M(p, λ, μ).

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1149-1161
• /
• 2021

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.23-32
• /
• 2023

Let 𝓢 be a Serre class in the category of modules and 𝖆 an ideal of a commutative Noetherian ring R. We study the containment of Tor modules, Koszul homology and local homology in 𝓢 from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when Tor^R_𝓼+t(R/𝖆, X) ≅ Tor^R_𝓼(R/𝖆, H^𝖆_t(X)).

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.315-323
• /
• 2023

First, we recall the results for prime-producing polynomials related to class number one problem of quadratic fields. Next, we give the relation between prime-producing cubic polynomials and class number one problem of the simplest cubic fields and then present the conjecture for the relations. Finally, we numerically compare the ratios producing prime values for several polynomials in some interval.