• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.515-536
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• 2012

This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing Razumikhin-type theorems aim at only the moment stability. By virtue of the $M$-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

• Journal for History of Mathematics
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• v.31 no.3
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• pp.151-166
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• 2018

The rule of the game of Chomp is simple and the existence of a winning strategy can easily be proved. However, the existence tells us nothing about what strategies are winning in reality. Like in Chess or Baduk, many researchers studied the winning moves using computer programs, but no general patterns for the winning actions have not been found. In the paper, we aim to construct practical winning strategies based on backward induction. To do this we develop how to analyze Chomp and prove and find the winning strategies of the simple games of Chomp.

• The Journal of Economics, Marketing and Management
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• v.10 no.5
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• pp.1-6
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• 2022

Purpose: To overcome the question that depends too much on expert's subjective judgment in traditional risk identification, this paper structure the multilevel generalized fuzzy comprehensive evaluation mathematics model of the risk identification of project, to research the risk identification of the project. Research design, data and methodology: This paper constructs the multilevel generalized fuzzy comprehensive evaluation mathematics model. Through iterative algorithm of AHP analysis, make sure the important degree of the sub project in risk analysis, then combine expert's subjective judgment with objective quantitative analysis, and distinguish the risk through identification models. Meanwhile, the concrete method of multilevel generalized fuzzy comprehensive evaluation is probed. Using the index weights to analyse project risks is discussed in detail. Results: The improved fuzzy comprehensive evaluation algorithm is proposed in the paper, at first the method of fuzzy sets core is used to optimize the fuzzy relation matrix. It improves the capability of the algorithm. Then, the method of entropy weight is used to establish weight vectors. This makes the computation process fair and open. And thereby, the uncertainty of the evaluation result brought by the subjectivity can be avoided effectively and the evaluation result becomes more objective and more reasonable. Conclusions: In this paper, we use an improved fuzzy comprehensive evaluation method to evaluate a railroad engineering project risk. It can give a more reliable result for a reference of decision making.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.235-249
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• 2012

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1773-1778
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• 2017

We give an alternative proof of a recent result by B. Pasquier stating that for a generalized flag variety X = G/P and an effective ${\mathbb{Q}}-divisor$ D stable with respect to a Borel subgroup the pair (X, D) is Kawamata log terminal if and only if ${\lfloor}D{\rfloor}=0$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1549-1566
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• 2016

Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.198-212
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• 1995

This study provides a nonparametric procedure for the statistical inference of the parameters in stationary autoregressive processes. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both underthe null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.397-405
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• 2022

In this article we investigate the transfer of multiplication-like properties to homomorphic images, direct products and amalgamated duplication of a ring along an ideal. Our aim is to provide examples of new classes of commutative rings satisfying the above-mentioned properties.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.665-732
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• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.799-813
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• 2008

This paper deals with the properties of the fuzzy least squares estimators for fuzzy linear regression model. Especially fuzzy triangular input-output model including error term is proposed. The error term is considered as a fuzzy random variable. The asymptotic unbiasedness and the consistency of the estimators are proved using a suitable metric.