• Title/Summary/Keyword: minimum theorem

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A NEW MINIMUM THEOREM AND ITS APPLICATIONS

  • Kim, Won-Kyu;Rim, Dong-Il;Im, Sung-Mo
    • Journal of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.932-944
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    • 1998
  • In this paper we first prove a new minimum theorem using the upper semicontinuity of minimizing functions, which is comparable to Berge's theorem. Next, as applications, we shall prove the existence of equilibrium in generalized games and the existence theorem of zeros.

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Investigating the substance and acceptability of empirical arguments: The case of maximum-minimum theorem and intermediate value theorem in Korean textbooks

  • Hangil Kim
    • Research in Mathematical Education
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    • v.27 no.1
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    • pp.75-92
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    • 2024
  • Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

Trajectory Optimization Operations for Satellites in Elliptic Orbits

  • Won, Chang-Hee;Mo, Hee-Sook;Kim, In-Jun;Lee, Seong-Pal
    • 제어로봇시스템학회:학술대회논문집
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    • 1999.10a
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    • pp.238-243
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    • 1999
  • Minimum-fuel and -time orbit transfer are two major goals of the satellite trajectory optimization. In this paper, we consider satellites in two coplanar elliptic orbits when the apsidal lines coincide, and analytically find the conditions for the two-impulse minimum-time transfer orbit using Lambert's theorem. The transfer time is a decreasing function of a variable related to the transfer orbit's semimajor axis in the minimum-time case. In the minimum-time case, there is no unique minimum-time solution, but there is a limiting solution. However, there exists a unique solution in the case of minimum-fuel transfer, fur which we find analytically the necessary and sufficient conditions. As a special case, we consider when the transfer angle is one hundred and eighty degrees. In this case, we show that we obtain the classical fuel-optimal Hohmann transfer orbit. We also derive the Hohmann transfer rime and delta-velocity equations from more general equations, which are obtained using Lambert's theorem. We note the tradeoff between minimum-time and - fuel transfer. An optimal coplanar orbit maneuver algorithm to trade off the minimum-time goal against the minimum-fuel goal is proposed. Finally, the numerical simulation results are given to demonstrate the derived theory and the algorithm.

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THE MINIMUM THEOREM FOR THE RELATIVE ROOT NIELSEN NUMBER

  • Yang, Ki-Yeol
    • Communications of the Korean Mathematical Society
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    • v.12 no.3
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    • pp.701-707
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    • 1997
  • In [8], we introduce the relative root Nielsen number N(f;X, A, c) for maps of pairs of spaces $f : (X, A) \to (Y, B)$. From it, we obtain some immediate consequences of the definition and illustrate it by some examples. We consider the question whether there exists a map $g : (X, A) \to (Y, B)$ homotopic to a given map $f : (X, A) \to (Y, B)$ which has precisely N(f;X, A, c) roots, that is, the minimum theorem for N(f;X, A, c).

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A MINIMUM THEOREM FOR THE RELATIVE ROOT NIELSEN NUMBER

  • Yang, Ki-Yeol;Zhao, Xuezhi
    • Communications of the Korean Mathematical Society
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    • v.19 no.1
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    • pp.159-167
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    • 2004
  • In [1], a relative root Nielsen number $N_{rel}(f;\;c)$ is introduced which is a homotopy invariant lower bound for the number of roots at $c\;{\in}\;Y$ for a map of pairs of spaces $f\;:\;(X,\;A)\;{\rightarrow}\;(Y,\;B)$. In this paper, we obtain a minimum theorem for $N_{rel}(f;\;c)$ under some new assumptions on the spaces and maps which are different from those in [1].

DETERMINATION OF MINIMUM LENGTH OF SOME LINEAR CODES

  • Cheon, Eun Ju
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.1
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    • pp.147-159
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    • 2013
  • Hamada ([8]) and Maruta ([17]) proved the minimum length $n_3(6,\;d)=g_3(6,\;d)+1$ for some ternary codes. In this paper we consider such minimum length problem for $q{\geq}4$, and we prove that $n_q(6,\;d)=g_q(6,\;d)+1$ for $d=q^5-q^3-q^2-2q+e$, $1{\leq}e{\leq}q$. Combining this result with Theorem A in [4], we have $n_q(6,\;d)=g-q(6,\;d)+1$ for $q^5-q^3-q^2-2q+1{\leq}d{\leq}q^5-q^3-q^2$ with $q{\geq}4$. Note that $n_q(6,\;d)=g_q(6,\;d)$ for $q^5-q^3-q^2+1{\leq}d{\leq}q^5$ by Theorem 1.2.

Modeling of the Minimum nNise Figure and the Optimum Source Impedance of FETs using the Steady-state Nyquist Theorem for Multi-Terminal Semiconductor Devices (다단자 반도체 소자에서의 steady-state Nyquist 정리를 이용한 FET의 회소 잡음 지수 및 최적 소오스 임피던스 모델링)

  • 이정배;민홍식;박영준
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.32A no.3
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    • pp.110-117
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    • 1995
  • New formulas for the minimum noise figure and the optimum source impedance of microwave FETs are derived using the noise equivalent circuits obtained from the steady-state Nyquist theorem for multi-terminal semiconductor devices. The derived formulas manifest the relationships between the noise sources and the physical parameters of a noise equivalent circuit. Furthermore the formulas can explain the effect of gate leakage current on the minimum noise figure and the optimum source impedance. comparisons with the published experimental data confirm the validity and usability of our formula.

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Stability assessment of tunnel face in a layered soil using upper bound theorem of limit analysis

  • Khezri, Nima;Mohamad, Hisham;Fatahi, Behzad
    • Geomechanics and Engineering
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    • v.11 no.4
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    • pp.471-492
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    • 2016
  • Underground tunnelling is one of the sustainable construction methods which can facilitate the increasing passenger transportation in the urban areas and benefit the community in the long term. Tunnelling in various ground conditions requires careful consideration of the stability factor. This paper investigates three dimensional stability of a shallow circular tunnel in a layered soil. Upper bound theorem of limit analysis was utilised to solve the tunnel face stability problem. A three dimensional kinematic admissible failure mechanism was improved to model a layered soil and limiting assumptions of the previous studies were resolved. The study includes calculation of the minimum support pressure acting on the face of the excavation in closed-face excavations. The effects of the characteristics of the layers on the minimum support pressure were examined. It was found that the ratio of the thickness of cover layers particularly when a weak layer is overlying a stronger layer, has the most significant influence on the minimum tunnel support pressure. Comparisons have been made with the results of the numerical modelling using FLAC3D software. Results of the current study were in a remarkable agreement with those of numerical modelling.