• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.355-361
• /
• 2000

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.409-420
• /
• 2006

In this paper we consider the set of all n + 1-tuples of real numbers, not necessarily all distinct, in the decreasing order from the unit interval under the usual ordering of real numbers, always including 1. Such n + 1-tuples inherently arise as the membership values of fuzzy subsets and are called keychains. An natural equivalence relation is introduced on this set and the equivalence classes of keychains are studied here. The number of such keychains is finite and the set of all keychains is a lattice under the coordinate-wise ordering. Thus keychains are subchains of a finite chain of real numbers in the unit interval. We study some of their properties and give some applications to counting fuzzy subsets of finite sets.

• Kyungpook Mathematical Journal
• /
• v.56 no.4
• /
• pp.1103-1113
• /
• 2016

In this paper, we study a directed simple graph ${\Gamma}_S(N)$ for a near-ring N, where the set $V^*(N)$ of vertices is the set of all left N-subsets of N with nonzero left annihilators and for any two distinct vertices $I,J{\in}V^*(N)$, I is adjacent to J if and only if IJ = 0. Here, we deal with the diameter, girth and coloring of the graph ${\Gamma}_S(N)$. Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring N in the left annihilator of some vertex in the strong zero-divisor graph ${\Gamma}_S(N)$.

• Journal of Korea Society of Digital Industry and Information Management
• /
• v.9 no.3
• /
• pp.21-30
• /
• 2013

Powell-Miller theory is a good method to express or treat incorrect information. But it has limitation that requires too much time to apply to actual situation because computational complexity increases in exponential and functional way. Accordingly, there have been several attempts to reduce computational complexity but side effect followed - certainty factor fell. This study suggested expanded Approximation Algorithm. Expanded Approximation Algorithm is a method to consider both smallest supersets and largest subsets to expand basic space into a space including inverse set and to reduce Approximation error. By using expanded Approximation Algorithm suggested in the study, basic probability assignment function value of subsets was alloted and added to basic probability assignment function value of sets related to the subsets. This made subsets newly created become Approximation more efficiently. As a result, it could be known that certain function value which is based on basic probability assignment function is closely near actual optimal result. And certainty in correctness can be obtained while computational complexity could be reduced. by using Algorithm suggested in the study, exact information necessary for a system can be obtained.

• Journal of Gastric Cancer
• /
• v.5 no.2
• /
• pp.106-112
• /
• 2005

Purpose: Considering that nutritional state correlates to immunity, we performed this study to evaluate the correlation by assessing the numerical changes of the levels of serum albumin and lymphocyte subsets. Materials and Methods: The study was performed on patients who were diagnosed as having gastric cancer and who underwent curative surgery from August 1998 to August 2004 in the Gyeongsang National University Hospital and whose peripheral blood lymphocyte subsets were tested prior to surgery. The study population was a total of 150 cases. Results: The change in the lymphocyte subsets in relation to the change in the level of serum albumin in all patients with gastric cancer was determined, and was compared to disease stages. When patients were classified by using the level of serum albumin with 3.2 mg/dl as the cut-off point (low group: serum albumin <3.2 mg/dl, normal group = serum albumin $\geq$ 3.2 mg/dl), the number of peripheral blood lymphocytes, CD3+ cells, CD4+ cells, CD8+ cells, and CD16+ 56 cells were, significantly lower in the group with the level of serum albumin below 3.2 mg/dl (low group) than it was in the group with a serum albumin level above 3.2 mg/dl (normal group) (P<0.05). In stage I (n=59), CD16+56 cells were significantly lower in the low group. In stage II (n=29), the number of CD16+56 cells was lower and the ratio of CD4+/CD8+ was higher in the low group than in the normal group significantly. In stage IV (n=33), except for CD19+ cells, the number of all lymphocyte subsets was significantly lower and the ratio of CD4+/CD8+ was significantly higher in the low group. Conclusion: The group with a low level of serum albumin had a low absolute number of lymphocyte subsets. Based on this, we reconfirmed that the nutritional state is closely related with the immune state in patients with gastric cancer.

• East Asian mathematical journal
• /
• v.19 no.2
• /
• pp.317-335
• /
• 2003

In this paper, we characterize SL(2, $\mathbb{C}$)-representations of an n-periodic link $\tilde{L}$ in terms of SL(2, $\mathbb{C}$)-representations of its quotient link L and express the SL(2, $\mathbb{C}$)-representation variety R($\tilde{L}$) of $\tilde{L}$ as the union of n affine algebraic subsets which have the same dimension. Also, we show that the dimension of R($\tilde{L}$) is bounded by the dimensions of affine algebraic subsets of the SL(2, $\mathbb{C}$)-representation variety R(L) of its quotient link L.

• The Korean Journal of Applied Statistics
• /
• v.25 no.4
• /
• pp.661-668
• /
• 2012

For displaying multivariate numerical data on a 2D plane by the projection, principal components biplot and the GGobi are two main tools of data visualization. The biplot is very useful for capturing the global shape of the dataset, by representing $n$ observations and $p$ variables simultaneously on a single graph. The GGobi shows a dynamic movie of the images of $n$ observations projected onto a sequence of unit vectors floating on the $p$-dimensional sphere. Even though these two methods are certainly very valuable, there are drawbacks. The biplot is too condensed to describe the detailed parts of the data, and the GGobi is too burdensome for ordinary data analyses. In this paper, "the local projective display(LPD)" is proposed for visualizing multivariate numerical data. Main steps of the LDP are 1) $k$-means clustering of the data into $k$ subsets, 2) drawing $k$ principal components biplots of individual subsets, and 3) sequencing $k$ plots by Hurley's (2004) endlink algorithm for cognitive continuity.

• The Pure and Applied Mathematics
• /
• v.8 no.2
• /
• pp.145-152
• /
• 2001

Posner [Proc. Amer. Math. Soc. 8 (1957), 1093-1100] defined a derivation on prime rings and Herstein [Canad, Math. Bull. 21 (1978), 369-370] derived commutative property of prime ring with derivations. Recently, Bergen [Canad. Math. Bull. 26 (1983), 267-227], Bell and Daif [Acta. Math. Hunger. 66 (1995), 337-343] studied derivations in primes and semiprime rings. Also, in near-ring theory, Bell and Mason [Near-Rungs and Near-Fields (pp. 31-35), Proceedings of the conference held at the University of Tubingen, 1985. Noth-Holland, Amsterdam, 1987; Math. J. Okayama Univ. 34 (1992), 135-144] and Cho [Pusan Kyongnam Math. J. 12 (1996), no. 1, 63-69] researched derivations in prime and semiprime near-rings. In this paper, Posner, Bell and Mason＇s results are extended in prime near-rings with some conditions.

• Korean Journal of Biological Psychiatry
• /
• v.25 no.1
• /
• pp.9-15
• /
• 2018

Objectives This study intended to identify the deficits of cognitive control among patients with bipolar I disorder and their first-degree relatives, and identify the possibility of cognitive control as an endophenotype of bipolar disorder. Methods The study included three groups: euthymic states patients with bipolar I disorder (n = 55), unaffected first-degree relatives of probands with bipolar I disorder (n = 30), and a healthy control group (n = 51), that was matched on age, sex, and years of education. The AX version of the continuous performance test (CPT) was used to examine cognitive control. Error rate, correct response times of each subsets (AX, BX, AY, BY), and d' as an indication of accuracy sensitivity index were calculated. Psychopathology, intelligence, and psychomotor speed were also assessed. Results Patients with bipolar I disorder showed significantly worse error rates in the AX (p = 0.01) and BX (p = 0.02) subsets and d' (p = 0.05) than the others. They also showed more delayed correct response times than the healthy control group and first-degree relatives in all subsets (p < 0.01). But first-degree relatives showed neither high error rates nor delayed correct response times than healthy control group. Conclusions These findings suggest that cognitive control is impaired in bipolar I disorder but less likely to be an endophynotype of bipolar I disorder.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.865-872
• /
• 2020

Let X ⊂ ℙ^r be an integral and non-degenerate variety. Set n := dim(X). Let 𝜌(X)" be the maximal integer such that every zero-dimensional scheme Z ⊂ X smoothable in X is linearly independent. We prove that X is linearly normal if 𝜌(X)" ≥ 2⌈(r + 2)/2⌉ and that 𝜌(X)" < 2⌈(r + 1)/(n + 1)⌉, unless either n = r or X is a rational normal curve.