• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.373-381
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• 2010

In this paper we determine all elements in the root lattice of symmetrizable generalized Kac-Moody algebras whose reflections preserve the root systems. Also we discuss elements in the root lattices whose reflection preserve the root lattices.

• 충청수학회지
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• 제23권4호
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• pp.625-628
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• 2010

The purpose of this paper is to show that there exists a unit whose p-th root generates the first layer of anti-cyclotomic ${\mathbb{Z}}_p$-extension of certain imaginary quadratic number fields.

• 대한수학회보
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• 제53권1호
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• pp.21-28
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• 2016

It is known that no two of the roots of the polynomial equation (1) $$\prod\limits_{l=1}^{n}(x-r_l)+\prod\limits_{l=1}^{n}(x+r_l)=0$$, where 0 < $r_1{\leq}r_2{\leq}{\cdots}{\leq}r_n$, can be equal and all of its roots lie on the imaginary axis. In this paper we show that for 0 < h < $r_k$, the roots of $$(x-r_k+h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x-r_l)+(x+r_k-h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x+r_l)=0$$ and the roots of (1) in the upper half-plane lie alternatively on the imaginary axis.

• 대한수학회보
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• 제50권4호
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• pp.1243-1259
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• 2013

In this paper, we study the root system of rank 2 hyperbolic Kac-Moody algebras. We give some sufficient conditions for the existence of imaginary roots of square length $-2k(k{\in}\mathbb{Z}_{>0}$. We also give several relations between the integral points on the hyperbola $\mathfrak{h}$ to show that the value of the symmetric bilinear form of any two integral points depends only on the number of integral points between them. We also give some generalizations of Binet formula and Catalan's identity.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.107-113
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• 2010

In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the sufficient conditions for existence of imaginary roots of square length -2k ($k\;{\in}\;\mathbb{Z}$>0). We also give several relations between the roots on g(A).

• 제어로봇시스템학회논문지
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• 제16권3호
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• pp.222-226
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• 2010

In this paper we study the consensus problem of SISO (Single-Input Single-Output) linear multi-agent systems under a fixed weighted undirected network communication. The dynamics of each agent can be of any order, while it is constrained to be neutrally stable. Based on a simple root locus argument, we show that the problem at hand is always solvable if the gain and zeros of the dynamic compensator, of which dimension is the same as the number of plant poles on the imaginary axis, are chosen suitably, finally the result is successfully verified by an example.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.587-595
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• 2015

In this article, we will examine the Diophantine equation $ax^6+by^3+cz^2=0$, for arbitrary rational integers a, b, and c in Gaussian integers and find all the solutions of this equation for many different values of a, b, and c. Moreover, two equations of the type $x^6{\pm}iy^3+z^2=0$, and $x^6+y^3{\pm}wz^2=0$ are also discussed, where i is the imaginary unit and w is a third root of unity.

• Journal of electromagnetic engineering and science
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• 제10권4호
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• pp.231-236
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• 2010

This study proposes a temperature compensation method of the complex permittivities of biological tissues and organs. The method is based on the temperature dependence of the Debye model of water, which has been thoroughly investigated. This method was applied to measured data at room temperature for whole blood, kidney cortex, bile, liver, and heart muscle. It is shown that our method can compensate for the Cole-Cole model using measured data at 20 $^{\circ}C$, given the Cole-Cole model based on measured data at 35 $^{\circ}C$, with a root-mean-squared deviation of 3~11 % and 2~6 % for the real and imaginary parts of the complex permittivities, respectively, among the measured tissues.

• Journal of Periodontal and Implant Science
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• 제39권2호
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• pp.111-118
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• 2009

Purpose: The integrity of interproximal hard/soft tissue has been widely accepted as the key determinant for success or degree of root coverage following the connective tissue graft. However, we reason that the gingival biotype of an individual, defined as the distance from the interproximal papilla to gingiva margin, may be the key determinant that influence the extent of root coverage regardless of traditional classification of gingival recession. Hence, the present study was performed with an aim to verify that individual gingival scalloping pattern inherent from biotype influence the level of gingival margin following the connective tissue graft for root coverage. Methods: Test group consisted of 43 single-rooted teeth from 21 patients (5 male and 16 female patients, mean age: 36.6 years) with varying degrees of gingival recession requiring connective tissue graft; 20 teeth of Miller class I and 23 teeth of Miller class III gingival recession, respectively. The control group consisted of contralateral teeth which did not demonstrate apparent gingival recession, and thus not requiring root coverage. For a biotype determination, an imaginary line connecting two adjacent papillae of a test tooth was drawn. The distance from this line to gingival margin at mid-buccal point and this distance (P-M distance) was designated as "gingival biotype" for a given individual. The distance was measured at baseline and 3 to 6 months examinations postoperatively both in test and control groups. The differences in the distance between Miller class I and III were subject to statistical analysis by using Student.s t-test while those between the test and control groups within a given patient were by using paired t-test. Results: The P-M distance at 3 to 6 months postoperatively was not significantly different between Miller class I and Miller class III. It was not significantly different between the test and control group in a given patient, either, both in Miller class I and III. Conclusions: The amount of root coverage following the connective tissue graft was not dependent on Miller's classification, but rather was dependent on P-M distance, strongly implying that the gingival biotype of a given patient may play a critical impact on the level of gingival margin following connective tissue graft.

• Journal of the Optical Society of Korea
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• 제20권1호
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• pp.70-77
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• 2016

This paper proposes an optical system for complex holographic display that enhances the quality of the reconstructed three-dimensional image. This work focuses on a new design for an optical system and the evaluation of the complex holographic display, using a single spatial light modulator (SLM) and a circular grating. The optical system is based on a 4-f system in which the imaginary and real information of the hologram is displayed on concentric rectangular areas of the SLM and circular grating. Thus, this method overcomes the lack of accuracy in the pixel positions between two window holograms in previous studies, and achieves a higher intensity of the real object points of the reconstructed hologram than the original phase-reconstructed hologram. The proposed method provides approximately 30% less NMRS (Normal Root Mean Square) error, compared to previous systems, which is verified by both simulation and optical experiment.