• 제목/요약/키워드: discrete mathematics

검색결과 459건 처리시간 0.029초

A Bayesian cure rate model with dispersion induced by discrete frailty

  • Cancho, Vicente G.;Zavaleta, Katherine E.C.;Macera, Marcia A.C.;Suzuki, Adriano K.;Louzada, Francisco
    • Communications for Statistical Applications and Methods
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    • 제25권5호
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    • pp.471-488
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    • 2018
  • In this paper, we propose extending proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured. Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. This proposal also allows for a realistic description of non-risk individuals, since individuals cured due to intrinsic factors (immunes) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. We put the proposed model in a Bayesian framework and use a Markov chain Monte Carlo algorithm for the computation of posterior distribution. A simulation study is conducted to assess the proposed model and the computation algorithm. We also discuss model selection based on pseudo-Bayes factors as well as developing case influence diagnostics for the joint posterior distribution through ${\psi}-divergence$ measures. The motivating cutaneous melanoma data is analyzed for illustration purposes.

MULTIPLE VALUED ITERATIVE DYNAMICS MODELS OF NONLINEAR DISCRETE-TIME CONTROL DYNAMICAL SYSTEMS WITH DISTURBANCE

  • Kahng, Byungik
    • 대한수학회지
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    • 제50권1호
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    • pp.17-39
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    • 2013
  • The study of nonlinear discrete-time control dynamical systems with disturbance is an important topic in control theory. In this paper, we concentrate our efforts to multiple valued iterative dynamical systems, which model the nonlinear discrete-time control dynamical systems with disturbance. After establishing the validity of such modeling, we study the invariant set theory of the multiple valued iterative dynamical systems, including the controllability/reachablity problems of the maximal invariant sets.

THE p-LAPLACIAN OPERATORS WITH POTENTIAL TERMS

  • Chung, Soon-Yeong;Lee, Hee-Soo
    • 대한수학회논문집
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    • 제26권4호
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    • pp.591-601
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    • 2011
  • In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

On Bounds for Moments of Unimodal Distributions

  • Sharma, R.;Bhandaria, R.
    • Communications for Statistical Applications and Methods
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    • 제21권3호
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    • pp.201-212
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    • 2014
  • We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

ERROR ESTIMATES FOR FULLY DISCRETE MIXED DISCONTINUOUS GALERKIN APPROXIMATIONS FOR PARABOLIC PROBLEMS

  • OHM, MI RAY;LEE, HYUN YOUNG;SHIN, JUN YONG
    • East Asian mathematical journal
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    • 제31권5호
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    • pp.685-693
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    • 2015
  • In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

SOME CHARACTERIZATIONS OF DEDEKIND MODULES

  • Kwon, Tae In;Kim, Hwankoo;Kim, Myeong Og
    • 충청수학회지
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    • 제30권1호
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    • pp.53-59
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    • 2017
  • In this article, we generalize the concepts of several classes of domains (which are related to a Dedekind domain) to a torsion-free module and it is shown that for a faithful multiplication module over an integral domain, we characterize Dedekind modules, cyclic submodule modules, and discrete valuation modules in terms of factorable modules and a sort of Euclidean algorithm.

MYRBERG-AGARD DENSITY POINTS AND SCHOTTKY GROUPS

  • Do, Il-Yong;Hong, Sung-Bok
    • 대한수학회지
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    • 제34권1호
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    • pp.77-86
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    • 1997
  • Let $\Gamma$ be a discrete subgroup of hyperbolic isometries acting on the Poincare disc $B^m, m \geq 2$. The discrete group $\Gamma$ acts properly discontinously in $B^m$, and acts on $\partial B^m$ as a group of conformal homemorphisms, but need not act properly discontinously on $\partial B^m$.

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PERIODIC SOLUTIONS OF A DISCRETE-TIME NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH THE BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE

  • Dai, Binxiang;Zou, Jiezhong
    • Journal of applied mathematics & informatics
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    • 제24권1_2호
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    • pp.127-139
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    • 2007
  • In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.

QUEUE RESPONSE APPROXIMATION WITH DISCRETE AUTOREGRESSIVE PROCESSES OF ORDER 1

  • Kim, Yoo-Ra;Hwang, Gang-Uk
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제12권1호
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    • pp.33-39
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    • 2008
  • We consider a queueing system fed by a superposition of multiple discrete autoregressive processes of order 1, and propose an approximation method to estimate the overflow probability of the system. Numerical examples are provided to validate the proposed method.

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