• Title/Summary/Keyword: quadratic equation

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Digital Watermarking using a Quadratic Equation Embedding Method in Wavelet Transform Domain (웨이블릿 변환영역에서 이차방정식 삽입 방법을 이용한 디지털 워터마킹)

  • 신용달
    • Journal of Korea Multimedia Society
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    • v.6 no.5
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    • pp.870-875
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    • 2003
  • We Present digital watermarking using a quadratic equation embedding method in wavelet transform domain in order to improve the invisibility. Generally, embedding watermark used a simple equation form, but we extended a quadratic equation form in this paper. We performed a computer simulation in order to compare proposed method to other methods using LENA, GOLDHILL, BARBARA, and MAN images By computer experiments, invisibility of the proposed method better than the conventional methods at 100 % normalized similarity.

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A Study on Application of Mathematics History of Chosun Dynasty to a Quadratic Equation of Middle School (중학교 이차방정식 단원에서 조선시대(朝鮮時代) 수학사(數學史)의 활용에 대한 연구)

  • Shim, Sang-Kil
    • Journal for History of Mathematics
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    • v.22 no.2
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    • pp.117-130
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    • 2009
  • This study shows how to use effectively construction and solution of the quadratic equation developed by mathematicians such as Gyung Sun-jing, Hong Jung-ha, Hong Dae-yong, Lee Sang-hyuk, and Nam Byung-gil through mathematics history of Chosun Dynasty. Mathematics history of Chosun Dynasty can be used in order to enhance comprehension and increase interest in an introduction to the quadratic equation. It also can be used to help motivate middle school students to solve the quadratic equation with much interest during the development phase, and develope conceptual thinking and reflective thinking in the practical phase.

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ON THE STABILITY OF A GENERAL QUADRATIC FUNCTIONAL EQUATION AND ITS APPLICATIONS

  • Jun, Kil-Woung;Kim, Hark-Mahn
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.1
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    • pp.57-75
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    • 2004
  • The aim of this paper is to solve the general solution of a quadratic functional equation f(x + 2y) + 2f(x - y) = f(x - 2y) + 2f(x + y) in the class of functions between real vector spaces and to obtain the generalized Hyers-Ulam stability problem for the equation.

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ON THE HYERS-ULAM STABILITY OF A GENERALIZED QUADRATIC AND ADDITIVE FUNCTIONAL EQUATION

  • JUN, KIL-WOUNG;KIM, HARK-MAHN
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.133-148
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    • 2005
  • In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a $\neq$ -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.

A QUADRATIC INTEGRAL EQUATION IN THE SPACE OF FUNCTIONS WITH TEMPERED MODULI OF CONTINUITY

  • PENG, SHAN;WANG, JINRONG;CHEN, FULAI
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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    • pp.351-363
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    • 2015
  • In this paper, we investigate existence of solutions to a class of quadratic integral equation of Fredholm type in the space of functions with tempered moduli of continuity. Two numerical examples are given to illustrate our results.