• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1230-1239
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• 2018

We derive a factorization theorem for the jet mass distribution with a given $p^J_T$ for the inclusive production, where $p^J_T$ is a large jet transverse momentum. Considering the small jet radius limit ($R{\ll}1$), we factorize the scattering cross section into a partonic cross section, the fragmentation function to a jet, and the jet mass distribution function. The decoupled jet mass distributions for quark and gluon jets are well-normalized and scale invariant, and they can be extracted from the ratio of two scattering cross sections such as $d{\sigma}/(dp^J_TdM^2_J)$ and $d{\sigma}/dp^J_T $. When $M_J{\sim}p^J_TR$, the perturbative series expansion for the jet mass distributions works well. As the jet mass becomes small, large logarithms of $M_J/(p^J_TR)$ appear, and they can be systematically resummed through a more refined factorization theorem for the jet mass distribution.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1992.03a
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• pp.159-176
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• 1992

Limit analysis has been rendered versatile in many problems such as structural problems and metal forming problems. In metal forming analysis, a slip-line method and an upper bound method approach to limit solutions is considered as the most challenging areas. In the present work, a general algorithm for limit solutions of plastic flow is developed with the use of finite element limit analysis. The algorithm deals with a generalized Holder inequality, a duality theorem, and a combined smoothing and successive approximation in addition to a general procedure for finite element analysis. The algorithm is robust such that from any initial trial solution, the first iteration falls into a convex set which contains the exact solution(s) of the problem. The idea of the algorithm for limit solution is extended from rigid/perfectly-plastic materials to work-hardening materials by the nature of the limit formulation, which is also robust with numerically stable convergence and highly efficient computing time.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.665-672
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• 2005

By its simplicity and efficiency, subdivision is a widely used technique in computer graphics, computer aided design and data compression. In this paper we prove a regularity theorem for ternary interpolatory subdivision scheme that can be applied to non-stationary subdivision. This theorem converts the convergence of the limit curve of a ternary interpolatory subdivision to the analysis of the rate of the contraction of differences of the polygons.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.267-274
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• 1999

We consider a doubly stochastically perturbed dynamical system {$X_n$} generated by $X_n\Gamma_n(X_{n-1})+W_n where \Gamma_n$ is a Markov chain of random functions and $W_n$ is i.i.d. random elements. Sufficient conditions for stationarity and geometric ergodicity of $X_n$ are obtained by considering asymptotic behaviours of the associated Markov chain. Ergodic theorem and functional central limit theorem are proved.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.359-362
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• 2004

Using the idea of intuitionistic fuzzy set due to Atanassov, we define the notion of intuitionistic fuzzy metric spaces as a natural generalization of fuzzy metric spaces due to George and Veeramani and prove some known results of metric spaces including Baire's theorem and the Uniform limit theorem for intuitionistic fuzzy metric spaces.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.307-324
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• 1993

The limiting distribution of the excess over the boundary is determined for the autoregressive process.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.65-74
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• 2002

In this paper we investigate an origin and development of the classical theory of probability. And we also investigate the law of large numbers and central limit theorem which are very important in tile probability theory.

• Communications of the Korean Mathematical Society
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• v.8 no.4
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• pp.779-791
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• 1993

• Journal of the Korean Society for Precision Engineering
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• v.8 no.3
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• pp.93-104
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• 1991

Limit analysis is based on the duality theorem which equates the least upper bound to the greatest lower bound. In this study, limit analysis of axisymmetric forming problem with workhardening materials is formulated by minimizing the upper bound functional and finite element program is developed for forward estrusion. Limit loads, velocity and flow line fields are directly obtained under various process conditions and deformation characteristics such as strains, strain rates and grid distortion are obtained from the optimum velocity components by numerical calculation. The experimental observation was carried out for extrusion and compared with computed results. The good agreement between theoretical and experimental results is shown that the developed programming is very effective for the analysis of axisymmetric extrusion.

• Journal of Environmental Health Sciences
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• v.45 no.2
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• pp.192-202
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• 2019

Objectives: According to the central limit theorem, the samples in population might be considered to follow normal distribution if a large number of samples are available. Once we assume that toxicity dataset follow normal distribution, we can treat and process data statistically to calculate genus or species mean value with standard deviation. However, little is known and only limited studies are conducted to investigate whether toxicity dataset follows normal distribution or not. Therefore, the purpose of study is to evaluate the generally accepted normality hypothesis of aquatic toxicity dataset Methods: We selected the 8 chemicals, which consist of 4 organic and 4 inorganic chemical compounds considering data availability for the development of species sensitivity distribution. Toxicity data were collected at the US EPA ECOTOX Knowledgebase by simple search with target chemicals. Toxicity data were re-arranged to a proper format based on the endpoint and test duration, where we conducted normality test according to the Shapiro-Wilk test. Also we investigated the degree of normality by simple log transformation of toxicity data Results: Despite of the central limit theorem, only one large dataset (n>25) follow normal distribution out of 25 large dataset. By log transforming, more 7 large dataset show normality. As a result of normality test on small dataset (n<25), log transformation of toxicity value generally increases normality. Both organic and inorganic chemicals show normality growth for 26 species and 30 species, respectively. Those 56 species shows normality growth by log transformation in the taxonomic groups such as amphibian (1), crustacean (21), fish (22), insect (5), rotifer (2), and worm (5). In contrast, mollusca shows normality decrease at 1 species out of 23 that originally show normality. Conclusions: The normality of large toxicity dataset was not always satisfactory to the central limit theorem. Normality of those data could be improved through log transformation. Therefore, care should be taken when using toxicity data to induce, for example, mean value for risk assessment.