• Title, Summary, Keyword: inverse functions

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A FURTHER INVESTIGATION OF GENERATING FUNCTIONS RELATED TO PAIRS OF INVERSE FUNCTIONS WITH APPLICATIONS TO GENERALIZED DEGENERATE BERNOULLI POLYNOMIALS

  • Gaboury, Sebastien;Tremblay, Richard
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.831-845
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    • 2014
  • In this paper, we obtain new generating functions involving families of pairs of inverse functions by using a generalization of the Srivastava's theorem [H. M. Srivastava, Some generalizations of Carlitz's theorem, Pacific J. Math. 85 (1979), 471-477] obtained by Tremblay and Fug$\grave{e}$ere [Generating functions related to pairs of inverse functions, Transform methods and special functions, Varna '96, Bulgarian Acad. Sci., Sofia (1998), 484-495]. Special cases are given. These can be seen as generalizations of the generalized Bernoulli polynomials and the generalized degenerate Bernoulli polynomials.

EXPANSIVITY ON ORBITAL INVERSE LIMIT SYSTEMS

  • Chu, Hahng-Yun;Lee, Nankyung
    • Journal of the Chungcheong Mathematical Society
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    • v.32 no.1
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    • pp.157-164
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    • 2019
  • In this article, we study expansiveness of the shift maps on orbital inverse limit spaces which consist of two cross bonding mappings. On orbital inverse limit systems, horizontal directions express inverse limit systems and vertical directions mean orbits based on horizontal axes. We characterize the c-expansiveness of functions on orbital spaces. We also prove that the c-expansiveness of the functions is equivalent to the expansiveness of the shift maps on orbital inverse limit spaces.

Maximal Algebraic Degree of the Inverse of Linearized Polynomial (선형 다항식의 역원의 maximal 대수적 차수)

  • Lee, Dong-Hoon
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.15 no.6
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    • pp.105-110
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    • 2005
  • The linearized polynomial fan be regarded as a generalization of the identity function so that the inverse of the linearized polynomial is a generalization of e inverse function. Since the inverse function has so many good cryptographic properties, the inverse of the linearized polynomial is also a candidate of good Boolean functions. In particular, a construction method of vector resilient functions with high algebraic degree was proposed at Crypto 2001. But the analysis about the algebraic degree of the inverse of the linearized Polynomial. Hence we correct the inexact result and give the exact maximal algebraic degree.

COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

  • Panigrahi, Trailokya
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1531-1538
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    • 2013
  • In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions $w=f(z)$ defined on $\tilde{\Delta}:=\{z{\in}\mathbb{C}:1<{\mid}z{\mid}<{\infty}\}$ whose inverse $f^{-1}(w)$ is also univalent meromorphic in $\tilde{\Delta}$. Estimates for the initial coefficients are obtained for the functions in these new subclasses.

Variable Selection in Sliced Inverse Regression Using Generalized Eigenvalue Problem with Penalties

  • Park, Chong-Sun
    • Communications for Statistical Applications and Methods
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    • v.14 no.1
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    • pp.215-227
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    • 2007
  • Variable selection algorithm for Sliced Inverse Regression using penalty function is proposed. We noted SIR models can be expressed as generalized eigenvalue decompositions and incorporated penalty functions on them. We found from small simulation that the HARD penalty function seems to be the best in preserving original directions compared with other well-known penalty functions. Also it turned out to be effective in forcing coefficient estimates zero for irrelevant predictors in regression analysis. Results from illustrative examples of simulated and real data sets will be provided.

Performance Improvement of the Inverse Modeling using Adaptive Line Enhancer (적응 선형 증진기를 이용한 인버스 모델링의 성능향상)

  • Kim, Heung-Sub;Hong, Jin-Seok;Son, Dong-Gu;Shin, Jun;Oh, Jae-Eung
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.267-271
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    • 1996
  • In this study, performance improvement of the inverse modeling as the on-line control method for the estimation, control experiment is performed. As the modeling errors is occurred in duct system arbitrarily, a case using the filtered-x LMS algorithm only as the control method, a case using tile inverse modeling method only and a case using the inverse modeling with the adaptive line enhancer are compared. The estimation errors between real secondary path transfer functions and the estimated and the control performances of primary noises with these estimated transfer functions are compared.

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An Unified Method of Finding the Inverse of a Matrix with Entries of a Linear Combination of Piecewise Constant Functions (각 항들이 구간 일정 함수의 선형 결합으로 표현된 행렬의 역을 구하는 방법)

  • ;Zeung Nam Bien
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.25 no.6
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    • pp.606-613
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    • 1988
  • This paper presents an unified method of obtaining the inverse of a matrix whose elements are a linear combination of piecewise constant functions. We show that the inverse of such a matrix can be obtained by solving a set of linear algebraic equations.

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Application of Inverse Pole Figure to Rietveld Refinement: II. Rietveld Refinement of Tungsten Liner using Neutron Diffraction Data

  • Kim, Yong-Il;Lee, Jeong-Soo;Jung, Maeng-Joon;Kim, Kwang-Ho
    • The Korean Journal of Ceramics
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    • v.6 no.3
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    • pp.240-244
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    • 2000
  • The three-dimensional orientation distribution function of a conical shaped tungsten liner prepared by the thermo-mechanical forming process was analyzed by 1.525$\AA$ neutrons to carry out the Rietveld refinement. The pole figure data of three reflections, (110)(220) and (211) were measured. The orientation distribution functions for the normal and radial directions were calculated by the WIMV method. The inverse pole figures of the normal and radial directions were obtained from their orientation distribution functions. The Rietveld refinement was performed with the RIETAN program that was slightly modified for the description of preferred orientation effect. We could successfully do the Rietveld refinement of the strongly textured tungsten liner by applying the pole density of each reflection obtained from the inverse pole figure to the calculated diffraction pattern. The correction method of preferred orientation effect based on the inverse pole figures showed a good improvement over the semi-empirical texture correction based on the direct usage of simple empirical functions.

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DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.745-758
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    • 2011
  • Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.

The Inverse Laplace Transform of a Wide Class of Special Functions

  • Soni, Ramesh Chandra;Singh, Deepika
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.49-56
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    • 2006
  • The aim of the present work is to obtain the inverse Laplace transform of the product of the factors of the type $s^{-\rho}\prod\limit_{i=1}^{\tau}(s^{li}+{\alpha}_i)^{-{\sigma}i}$, a general class of polynomials an the multivariable H-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in nature. On account of the general nature of our main findings, the inverse Laplace transform of the product of a large variety of polynomials and numerous simple special functions involving one or more variables can be obtained as simple special cases of our main result. We give here exact references to the results of seven research papers that follow as simple special cases of our main result.

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