• Journal for History of Mathematics
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• v.26 no.4
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• pp.301-320
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• 2013

Although many people have recognized the importance of history of mathematics in mathematics education, there are few studies that history and mathematics educations are connected. In this paper, we present and discuss the ways of introducing the instruction with mathematics machines. This instruction use the history of mathematics as part of a class not as a tool to stimulate students' interest but as a goal that it can be targeted mathematical itself. To do this, we first analyze the characteristics of applying history of mathematics in mathematical education, second, describe the meaning and the educational value of mathematical machines, and finally explained the way of applying history of mathematics with mathematics machines. The Instruction of history of mathematics with mathematics machines has advantages that practice (manipulation and experiment) and theory (elaboration of definition, production of conjectures and constructions of proofs) are interlaced within a historic-cultural perspective.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1407-1433
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• 2020

Parts I-IV showed that the number of ways to place q nonattacking queens or similar chess pieces on an n × n chessboard is a quasipolynomial function of n whose coefficients are essentially polynomials in q. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds for the periods of those quasipolynomials by calculating explicit denominators of vertices of the inside-out polytope. Here we discover more about the counting quasipolynomials for partial queens, both familiar and strange, and the nightrider and its subpieces, and we compare our results to the empirical formulas found by Kotššovec. We prove some of Kotššovec's formulas and conjectures about the quasipolynomials and their high-order coefficients, and in some instances go beyond them.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.933-943
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• 2020

Let M be a Fano manifold, and H^🟉(M; ℂ) be the quantum cohomology ring of M with the quantum product 🟉. For 𝜎 ∈ H^🟉(M; ℂ), denote by [𝜎] the quantum multiplication operator 𝜎🟉 on H^🟉(M; ℂ). It was conjectured several years ago [7,8] and has been proved for many Fano manifolds [1,2,10,14], including our cases, that the operator [c₁(M)] has a real valued eigenvalue 𝛿₀ which is maximal among eigenvalues of [c₁(M)]. Galkin's lower bound conjecture [6] states that for a Fano manifold M, 𝛿₀ ≥ dim M + 1, and the equality holds if and only if M is the projective space ℙⁿ. In this note, we show that Galkin's lower bound conjecture holds for Lagrangian and orthogonal Grassmannians, modulo some exceptions for the equality.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1989.06a
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• pp.114-117
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• 1989

An infrasonic wide band transducer fabricated by polytetrafluoroethylene(PTFE)is studied experimentally. The sensitivity of the transducer depends largely on the surface charge of the Electret and is typically between-50 and -62[dBV] for a sound-pressure level of 1[ubar]. The sensitivity of the transducer does not decay over periods of the order of years at room temperature. The frequency response is within 1.5[dB] from 1 to 6,000[Hz] and within 12[dB] from 0.05[Hz] to 1[Hz] respectively. The resonance frequency of the element is 510 [Hz]. We conjectures that the element is applicable to accustics, communication system, seismological observation and other similar filed.

• Journal of the Korean School Mathematics Society
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• v.5 no.1
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• pp.13-19
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• 2002

In this experiment we emphasized the cooperative small group learning and the members of my group worked together to succeed and communicate their mathematics ideas freely. The researcher(teacher) became an observer and facilitator of small group interaction, paying attention to the ongoing learning process, Sometimes the researcher suggested some investigation approach(or discovery)being written by computer software or papers. In this experiment we provided 6 activities as follows : (1) changing the conditions in given problem. (2) operating the meaningful heuristics with the problem sets. (3) creating the problem situations related to understanding (4) creating the Modeling situations. (5) creating the problem related to combinatorial thinking in real world. (6) posing some real problem from real world. we could observed several conjectures First, Attitude and chility to interpret the problem setting is highly important to pose the problem effectively. Second, Generating the understanding can be a great tool to pose the problem effectively. Third, Sometimes inquiry approach represented by software or programmed book could be some motivation to enhance the posing activities. Forth, The various posing activities relate to one concept could give the students some opportunity to be adaptable and flexible in the their approach to unfamiliar problem sets.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.4
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• pp.315-324
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• 2011

This paper presents a historical study on the derivation of the differential equation of motion for the single-degree-of-freedom m-k system with the harmonic excitation. It was Euler for the first time in the history of vibration theory who tackled the equation of motion for that system analytically, then gave the solution of the free vibration and described the resonance phenomena of the forced vibration in his famous paper E126 of 1739. As a result of the chronological progress in mechanics like pendulum condition from Galileo to Euler, the author asserts two conjectures that Euler could apply to obtain the equation of motion at that time.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.437-454
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• 2000

Let C be a smooth k-gonal curve of genus g. We study the number of pencils of degree k on C. In case $g\geqk(k-a)/2$ we state a conjecture based on a discussion on plane models for C. From previous work it is known that if C possesses a large number of pencils then C has a special plane model. From this observation the conjectures are split up in two cases : the existence of some types of plane curves should imply the existence of curves C with a given number of pencils; the non-existence of plane curves should imply the non-existence of curves C with some given large number of pencils. The non-existence part only occurs in the range $k(k-1)/2\leqg\leqk(k-1)/2] if k\geq7$. In this range we prove the existence part of the conjecture and we also prove some non-existence statements. Those result imply the conjecture in that range for $k\leq10$. The cases $k\leq6$ are handled separately.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.295-303
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• 2007

In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form $$x_{n+1}=\frac{a_0+{{\sum}^k_{j=1}}a_jx_{n-j+1}}{b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}},\;\;n=0,\;1,...$$ where $k{\in}N,\;and\;a_j,b_j,\;j=0,\;1,...,\;k $, are nonnegative numbers such that $b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}>0$ for every $n{\in}N{\cup}\{0\}$. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations(part 6), J. Differ. Equations Appl. 11(8)(2005), 759-777.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.749-755
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• 2009

In this paper, we investigate the invariant interval, periodic character, semicycle and global attractivity of all positive solutions of the equation $Y_{n+1}\;=\;\frac{p+qy_{n-k}}{1+y_n+ry_{n-k}}$, n = 0, 1, ..., where the parameters p, q, r and the initial conditions $y_{-k}$, ..., $y_{-1}$, $y_0$ are positive real numbers, k $\in$ {1, 2, 3, ...}. It is worth to mention that our results solve the open problem proposed by Kulenvic and Ladas in their monograph [Dynamics of Second Order Rational Difference Equations: with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002]

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.361-372
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• 2006

This study was extended as one of the properties of isosceles triangles to polygons(n-angles) by conjectures-proofs-reputations-reformations and developed teaching-learning materials which can be used in high-level classes for middle and high school students.