• Title, Summary, Keyword: difference operators

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q-Analogue of Exponential Operators and Difference Equations

  • Asif, Mohammad
    • Kyungpook Mathematical Journal
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    • v.53 no.3
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    • pp.349-369
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    • 2013
  • The present paper envisages the $q$-analogue of the exponential operators, determined by G. Dattoli and his collaborators for translation and diffusive operators which were utilized to establish analytical solutions of difference and integral equations. The generalization of their technique is expected to cover wide range of such utilization.

RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES WITH THEIR DIFFERENCE OPERATORS

  • LI, XIAO-MIN;YI, HONG-XUN;KANG, CONG-YUN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1401-1422
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    • 2015
  • Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in [6] for a finite-order meromorphic function and its shift operator.

Derivations of moments for discrete probability distributions using backward difference operators (후진 미분 연산자를 이용한 이산확률분포의 적률 유도)

  • Cho, Kil-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.3
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    • pp.505-513
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    • 2011
  • In this paper, we obtain the derivations of moments of discrete probability distributions by using the backward difference operators. Also, we presents such derivations for several well-known distributions; they are the binomial, Poisson, geometric, hypergeometric and negative hypergeometric distributions.

FRACTIONAL DYNAMICAL SYSTEMS FOR VARIATIONAL INCLUSIONS INVOLVING DIFFERENCE OF OPERATORS

  • Khan, Awais Gul;Noor, Muhammad Aslam;Noor, Khalida Inayat
    • Honam Mathematical Journal
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    • v.41 no.1
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    • pp.207-225
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    • 2019
  • In the present paper, we propose some new fractional dynamical systems. These dynamical systems are associated with the variational inclusions involving difference of operators problem. The equivalence between the variational inclusion problems and the fixed point problems and as well as the resolvent equations are used to suggest fractional resolvent dynamical systems and fractional resolvent equation dynamical systems, respectively. We show that these dynamical systems converge ${\alpha}$-exponentially to the unique solution of variational inclusion problems under fewer restrictions imposed on operators and parameters. Several special cases also discussed.

Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient

  • Nyamwala, Fredrick Oluoch;Ambogo, David Otieno;Ngala, Joyce Mukhwana
    • Kyungpook Mathematical Journal
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    • v.60 no.2
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    • pp.297-305
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    • 2020
  • We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.

A Dispersion Analysis for Minimum Grids in the Frequency Domain Acoustic Wave Equation (주파수영역 음향 파동방정식에서 최소 격자수 결정을 위한 격자분산 분석)

  • Jang Seong-Hyung;Shin Chang-Soo;Yoon Kwang-Jin;Suh Sang-Young;Shin Sung-Ryul
    • Geophysics and Geophysical Exploration
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    • v.3 no.2
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    • pp.39-47
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    • 2000
  • A great deal of computing time and a large computer memory are needed to solve wave equation in a large complex subsurface layers using the finite difference method. The computing time and memory can be reduced by decreasing the number of grid points per minimum wave length. However, the decrease of grids may cause numerical dispersion and poor accuracy. In this study we performed the grid dispersion analysis for several rotated finite difference operators, which was commonly used to reduce grids per wavelength with accuracy in order to determine the solution for the acoustic wave equation in frequency domain. The rotated finite difference operators were to be extended to 81, 121 and 169 difference stars and studied whether the minimum grids could be reduced to 2 or not. To obtain accuracy (numerical errors less than $1\%$) the following was required: more than 13 grids for conventional 5 point difference stars, 9 grids for 9 difference stars, 3 grids for 25 difference stars, and 2.7 grids for 49 difference stars. After grid dispersion analysis for the new rotated finite difference operators, more than 2.5 grids for 81 difference stars, 2.3 grids for 121 difference stars and 2.1 grids for 169 difference stars were needed. However, in the 169 difference stars, there was no solution because of oscillation of the dispersion curves in the group velocity curves. This indicated that the grids couldn't be reduced to 2 in the frequency acoustic wave equation. According to grid dispersion analysis for the determination of grid points, the more rotated finite difference operators, the fewer grid points. However, the more rotated finite difference operators that are used, the more complex the difference equation terms.

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MEROMORPHIC FUNCTIONS SHARING FOUR VALUES WITH THEIR DIFFERENCE OPERATORS OR SHIFTS

  • Li, Xiao-Min;Yi, Hong-Xun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1213-1235
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    • 2016
  • We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from [12], where the meromorphic functions and the entire functions are of hyper order less than 1. An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.

Analysis of Collision Risk Perceived by Ship Operators in Ship Collision Risk Situation (선박충돌 위기상황에서 선박운항자가 지각한 충돌위험도 분석)

  • Kim, Dae Sik;Yim, Jeong Bin
    • Journal of the Ergonomics Society of Korea
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    • v.36 no.5
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    • pp.447-458
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    • 2017
  • Objective: The purpose of this study is to present the basic guidelines for preventing human error by measuring and analyzing the risk of collision perceived by the ship operator in the collision risk situation by using Korea Coast Guard patrol ships. Background: In the last 5 years, 97.5% of the causes of ship collision occurred at the sea was caused by human factors. However, the rate of marine accidents due to human error has not been reduced yet. Experiments and researches on the ship operators using the ships in actual operation are rarely performed. Method: Using two K.C.G Ships on the sea, the ship measured by 30 persons who are the subject of the ship (ship operator) when both ships approach and the relative distance gradually decreases in four encounter situations, perceived ship collision risk (PSCR) data were analyzed by statistical analysis. Results: The age and boarding career of the ship operator in the situation of ship collision risks encountered a negative impact on perceived collision risk in all four opposing encounter situations S1 ($000^{\circ}$), S2 ($045^{\circ}$), S3 ($090^{\circ}$) and S4 ($135^{\circ}$) respectively. That is, the higher the age of the ship operator, the lower the perceived risk of collision and the lower the age, the higher the risk of collision. Also, there was a difference between the average of group A (20~30 years) and group B (40~50 years) according to age of the ship operators at $000^{\circ}$, $045^{\circ}$ and $090^{\circ}$ and there was no difference at $135^{\circ}$. The mean difference of the experience of boarding career was also significantly different between group A (less than 4 years) and group B (more than 5 years), but there was no significant difference at $135^{\circ}$. Conclusion: The results showed that age and boarding career of the ship operators had negative impact on perceived collision risk and there was a difference in perceived risk of collision according to age and abundance of boarding career. As a result, by focusing on the ship operators who are in the age group of 20~30 years old and have less than 4 years of experience in boarding the ship. It is expected that the effect of prevention of marine accidents can be expected by avoiding collision avoidance. Application: The results of this study can be used as policy data of related organizations to prevent human error of ship operators and as training data of training institutes.