• The Mathematical Education
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• v.50 no.2
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• pp.135-148
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• 2011

We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

• Journal of Plant Biology
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• v.36 no.3
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• pp.281-284
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• 1993

A karyotype of cytotype BB plant in Scilla scilloides Complex was established and the frequency of B-chromosomes were investigated. Chromosome complements of BB genome were composed of five pairs of subtelocentric and four pairs of metacentric chromosomes. Chromosome 1 has satellite with nucleolar organizer. Polymorphism was found in chromosome 2. The karyotype of cytotype BB will be available for analysis of genome composition in various cytotypes of S. scilloides Complex. The frequency of B-chromosome was 78.6%. Numbers of B-chromosome ranged from 1 to 4 and plants with 2B-chromosomes were predominant (57.2%). Two type of B-chromosomes, F and F', were found; F is a large iso-chromosome and F' a small one.

• Journal of international Conference on Electrical Machines and Systems
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• v.1 no.1
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• pp.17-22
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• 2012

This paper presents analyzed results of a permanent magnet motor by using complex E&S modeling. The calculated results are compared with ones from the conventional E&S modeling for verification. Combinations of the numbers of slots and poles are investigated to reduce total iron loss. The results demonstrate that the complex E&S modeling is very useful in design under consideration of rotational magnetic field and magnetic anisotropy.

• Nuclear Engineering and Technology
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• v.49 no.1
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• pp.17-28
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• 2017

The modified power method has been studied by many researchers to calculate the higher eigenmodes and accelerate the convergence of the fundamental mode. Its application to multidimensional problems may be unstable due to degenerated or near-degenerated eigenmodes. Complex eigenmode solutions are occasionally encountered in such cases, and the shapes of the corresponding eigenvectors may change during the simulation. These issues must be addressed for the successful implementation of the modified power method. Complex components are examined and an approximation method to eliminate the usage of the complex numbers is provided. A technique to fix the eigenvector shapes is also provided. The performance of the methods for dealing with those aforementioned problems is demonstrated with two dimensional one group and three dimensional one group homogeneous diffusion problems.

• Journal of Chest Surgery
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• v.19 no.1
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• pp.122-133
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• 1986

Thirteen patients with cyanotic cardiac malformations having more complex intracardiac defects, hemodynamics and operative procedures than ones in Tetralogy of Fallot undertaken total surgical corrections from July 1981 to August 1985. The cases of corrective surgery for complex cardiac malformations were 3.9% of all congenital cardiac malformations and 12.6% of cyanotic cardiac malformations. Six patients died within 30 days after surgery. So operative mortality was 46%; Transposition of the great arteries, two of 4 patients, due to low cardiac output syndrome and tracheal bleeding ; Univentricular heart, one of 3 patients, due to bleeding; Corrected transposition of the great arteries, one of 2 patients, due to acute heart failure; Tricuspid atresia, one of 2 patients, due to low cardiac output syndrome; Double outlet right ventricle, one of single patient, due to respiratory failure. The cases of surgical correction for complex cardiac malformations are progressively increasing in numbers. The more accurate evaluation of anatomical condition and hemodynamics in preoperative diagnosis, studies on applicable surgical procedure and perioperative care of patients are necessary in the improvement of clinical and surgical results.

• Korean Journal of Veterinary Service
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• v.46 no.1
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• pp.29-34
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• 2023

Mycobacterium tuberculosis complex (M. tuberculosis complex) is a causative agent of contagious chronic disease in a wide range of mammalian hosts, mainly cattle, goat, pigs, wildlife, and humans. The definite diagnosis of tuberculosis is made based on culture of M. tuberculosis, but it takes a long time. In the present study, we analyzed whether the detection time of M. tuberculosis could be reduced when cultured in the medium containing the culture-promoting ingredients-107 (CPI-107) using the BacT/Alert 3D system, an automatic culture system. The time to detection (TTD) tended to decrease as the added concentration of CPI-107 increase. In the case of low numbers of M. tuberculosis, it decreased by 21.0% at 1.2 mg/mL of CPI-107 and by 15.9% in the case of high numbers of M. tuberculosis. In the culture using clinically isolated M. tuberculosis strains, the shortening of the culture time by CPI was more evident. In conclusion, the detection time of M. tuberculosis was shortened in the medium added with CPI-107, and this could be used for isolation, culture and drug susceptibility test of M. tuberculosis.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.133-159
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• 2024

In a previous work we studied generalized Stirling numbers of the second kind S^{(a₂,b₂,p₂)}_a1,b1 (p₁, k), where a₁, a₂, b₁, b₂ are given complex numbers, a₁, a₂ ≠ 0, and p₁, p₂ are non-negative integers given. In this work we use these generalized Stirling numbers to define Bernoulli polynomials in two variables B_p1,p2 (x₁, x₂), and Euler polynomials in two variables E_p1p2 (x₁, x₂). By using results for S^{(1,x₂,p₂)}_1,x1 (p₁, k), we obtain generalizations, to the bivariate case, of some well-known properties from the standard case, as addition formulas, difference equations and sums of powers. We obtain some identities for bivariate Bernoulli and Euler polynomials, and some generalizations, to the bivariate case, of several known identities for Bernoulli and Euler numbers and polynomials of the standard case.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.669-674
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• 2000

We define the terminologies for the special type of functions defined on the field $\mathbb{C}$ of complex numbers and consider the solutions of function equations containing such functions in $\mathbb{C}$.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.631-640
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• 2006

In this paper, we prove sufficient conditions of boundedness of maximal operators on the p-adic vector space. We also consider weighted Hardy-Littlewood averages on the p-adic vector space.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.791-800
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• 1998

We present a proof that, among all complex numbers, Duffin-Schaeffer's choice in the Neumann series expansion of the inverse of a frame operator has the best possible convergence rate.