• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.935-946
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• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.225-231
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• 1995

An eventual uniform equicontinuity condition is investigated in the context of the uniform central limit theorem (UCLT) for continuous martingales. We assume the usual intergrability condition on metric entropy. We establish an exponential inequality for a martingales. Then we use the chaining lemma of Pollard (1984) to prove an eventual uniform equicontinuity which is a sufficient condition of UCLT. We apply the result to approximate a stochastic integral with respect to a martingale to that of a Brownian motion.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.2
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• pp.166-172
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• 2001

We construct several supercategories of ACHY (of approach Cauchy spaces) and AULim (of approach uniform limit spaces) and investigate the relation among them.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1043-1055
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• 2023

In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.539-559
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• 2014

We derive the exact distribution of summation for random samples from uniform distribution and then compare the exact distribution with the approximated normal distribution obtained by the central limit theorem. To check the similarity between two distributions, we consider five existing normality tests based on the difference between the target normal distribution and empirical distribution: Anderson-Darling test, Kolmogorov-Smirnov test, Cramer-von Mises test, Shapiro-Wilk test and Shaprio-Francia test. For the purpose of comparison, those normality tests are applied to the simulated data. It can sometimes be difficult to derive an exact distribution. Thus, we try two different transformations to find out which transform is easier to get the exact distribution in terms of calculation complexity. We compare two transformations and comment on the advantages and disadvantages for each transformation.

• Advances in materials Research
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• v.9 no.2
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• pp.115-131
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• 2020

Limit elastic speed analysis of Al/SiC-based functionally graded annular disk of uniform thickness has been carried out for two cases, namely: metal-rich and ceramic rich. In the present study, the unknown field variable for radial displacement is solved using variational method wherein the solution was obtained by Galerkin's error minimization principle. One of the objectives was to identify the variation of induced stress in a functionally graded disk of uniform thickness at limit elastic speed using modified rule of mixture by comparing the induced von-Mises stress with the yield stress along the disk radius, thereby locating the yield initiation. Furthermore, limit elastic speed has been reported for a combination of varying grading index (n) and aspect ratios (a/b).Results indicate, limit elastic speed increases with an increase in grading indices. In case of an increase in aspect ratio, limit elastic speed increases up to a critical value beyond which it recedes. Also, the objective was to look at the variation of yield stress corresponding to volume fraction variation within the disk which later helps in material tailoring. The study reveals the qualitative variation of yield stress for FG disk with volume fraction, resulting in the possibility of material tailoring from the processing standpoint, in practice.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.689-699
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• 2010

We discuss in this paper the notions of extended negative quadrant dependence and its properties. We study a class of bivariate uniform distributions having extended negative quadrant dependence, which is derived by generalizing the uniform representation of a well-known Farlie-Gumbel-Morgenstern distribution. Finally, we also study the limit behavior on the extended negative quadrant dependence.

• Steel and Composite Structures
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• v.42 no.3
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• pp.375-388
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• 2022

In this work, limit elastic speed analysis of functionally graded porous rotating disks has been reported. The work proposes an effective approach for modeling the mechanical properties of a porous functionally graded rotating disk. Four different types of porosity models namely: uniform, symmetric, inner maximum, and outer maximum distribution are considered. The approach used is the variational principle, and the solution has been achieved using Galerkin's error minimization theory. The study aims to investigate the effect of grading indices, aspect ratio, porosity volume fraction, and porosity types on limit angular speed for uniform and variable disk geometries of constant mass. To validate the current study, finite element analysis has been used, and there is good agreement between the two methods. The study yielded a decrease in limit speed as grading indices and aspect ratio increase. The porosity volume fraction is found to be more significant than the aspect ratio effect. The research demonstrates a range of operable speeds for porous and non-porous disk profiles that can be used in industries as design data. The results show a significant increase in limit speed for an exponential disk when compared to other disk profiles, and thus, the study demonstrates a range of FG-based structures for applications in industries that will not only save material (lightweight structures) but also improve overall performance.

• Nuclear Engineering and Technology
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• v.55 no.3
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• pp.1105-1117
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• 2023

In this study, the pressure drop behavior of single- and two-phase flows of air and water through the porous beds filled with uniform and non-uniform sized spherical particles was examined. The pressure drop data in the single-phase flow experiments for the uniform particle beds agreed well with the original Ergun correlation. The results from the two-phase flow experiments were analyzed using numerical results based on three types of previous models. In the experiments for the uniform particle beds, the data on the two-phase pressure drop clearly showed the effect of the flow regime transition with a variation in the gas flow rate under stagnant liquid condition. The numerical analyses indicated that the predictability of the previous models for the experimental data relied mainly on the sub-models of the flow regime transitions and interfacial drag. In the experiments for the non-uniform particle beds, the two-phase pressure loss could be predicted well with numerical calculations based on the effective particle diameter. However, the previous models failed to accurately predict the counter-current flooding limit observed in the experiments. Finally, we propose a relation of falling liquid velocity into the particle bed by gravity to appropriately simulate the CCFL phenomenon.

• Journal of Korean Society for Quality Management
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• v.26 no.3
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• pp.60-70
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• 1998

When driving the expected loss generated by the quality deviation, Taguchi(1991b) assumed that an objective characteristic has the uniform distribution in its control limit. But it is reasonable to assume that an objective characteristic has the normal distribution than the uniform distribution. Since the triangular distribution is similar to the normal distribution and easy to handle as well, in this article, we first find the optimum measurement interval and the optimum control limit under the triangular distribution. Under the normal assumption, the modified method is compared to Taguchi's. Secondly we find the numerical value solution of the optimum measurement interval and the optimum control limit under the normal distribution.