• Title/Summary/Keyword: mathematical errors

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A study on the Analysis and the Correction of third-year Middle School Students Error Related to Graph of Quadratic Function (이차함수 그래프에 관련된 중학교 3학년 학생들이 범하는 오류와 교정)

  • Gu, Young Hwa;Kang, Young Yug;Ryu, Hyunah
    • East Asian mathematical journal
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    • v.30 no.4
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    • pp.451-474
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    • 2014
  • The purpose of this study is to analyze error patterns third-year middle school students make on quadratic function graph problems and to examine about the possible correct them by providing supplementary tutoring. To exam the error patterns that occur during problem solving processes, to 82 students, We provided 25 quadratic function graph problems in the preliminary-test. The 5 types of errors was conceptual errors, false intuition errors, incorrect use of conditions in problems, technical errors, and errors from slips or carelessness. Statistical analysis of the preliminary-test and post-test shows that achievement level was higher in the post-test, after supplementary tutoring, and the t-test proves this to be meaningful data. According to the per subject analyses, the achievement level in the interest of symmetry, parallel translation, and general graph, respectively, were all higher in the post-test than the preliminary-test and this is meaningful data as well. However, no meaningful relation could be found between the preliminary-test and the post-test on other subjects such as graph remodeling and relations positions of the parabola. For the correction of errors, try the appropriate feedback and various teaching and learning methods.

THE CONVERGENCE THEOREMS FOR COMMON FIXED POINTS OF UNIFORMLY L-LIPSCHITZIAN ASYMPTOTICALLY Φ-PSEUDOCONTRACTIVE MAPPINGS

  • Xue, Zhiqun
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.295-305
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    • 2010
  • In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Finally, we obtain the convergence theorems of Ishikawa iterative sequence and the modified Ishikawa iterative process with errors.

ERROR ANALYSIS ASSOCIATED WITH UNIFORM HERMITE INTERPOLATIONS OF BANDLIMITED FUNCTIONS

  • Annaby, Mahmoud H.;Asharabi, Rashad M.
    • Journal of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1299-1316
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    • 2010
  • We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

NEW ITERATIVE PROCESS FOR THE EQUATION INVOLVING STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

  • Zeng, Ling-Yan;Li, Jun;Kim, Jong-Kyu
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.861-870
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    • 2007
  • In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.

REPEATED LOW-DENSITY BURST ERROR DETECTING CODES

  • Dass, Bal Kishan;Verma, Rashmi
    • Journal of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.475-486
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    • 2011
  • The paper deals with repeated low-density burst error detecting codes with a specied weight or less. Linear codes capable of detecting such errors have been studied. Further codes capable of correcting and simultaneously detecting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided.

ITERATIVE ALGORITHMS WITH ERRORS FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Jung, Jong-Soo
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.771-790
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    • 2006
  • The iterative algorithms with errors for nonexpansive mappings are investigated in Banach spaces. Strong convergence theorems for these algorithms are obtained. Our results improve the corresponding results in [5, 13-15, 23, 27-29, 32] as well as those in [1, 16, 19, 26] in framework of a Hilbert space.

A-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGN WITH CORRELATED ERRORS

  • Ceranka, Bronislaw;Graczyk, Malgorzata
    • Journal of applied mathematics & informatics
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    • v.16 no.1_2
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    • pp.143-150
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    • 2004
  • In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound of tr$(X'G^{-1}X)^{-1}$ is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design.

ITERATIVE SOLUTIONS TO NONLINEAR EQUATIONS OF THE ACCRETIVE TYPE IN BANACH SPACES

  • Liu, Zeqing;Zhang, Lili;Kang, Shin-Min
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.265-273
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    • 2001
  • In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

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CONVERGENCE TO COMMON FIXED POINTS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Saluja, G.S.
    • East Asian mathematical journal
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    • v.29 no.1
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    • pp.23-37
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    • 2013
  • The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.

AN UPPER BOUND ON THE NUMBER OF PARITY CHECKS FOR BURST ERROR DETECTION AND CORRECTION IN EUCLIDEAN CODES

  • Jain, Sapna;Lee, Ki-Suk
    • Journal of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.967-977
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    • 2009
  • There are three standard weight functions on a linear code viz. Hamming weight, Lee weight, and Euclidean weight. Euclidean weight function is useful in connection with the lattice constructions [2] where the minimum norm of vectors in the lattice is related to the minimum Euclidean weight of the code. In this paper, we obtain an upper bound over the number of parity check digits for Euclidean weight codes detecting and correcting burst errors.