• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.855-865
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• 1996

In this paper, we establish the weak convergences of processes occurring in a generalized Curie-Weiss model and its dual.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.193-197
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• 2013

Almost sure central limit theorems are established for a stationary bootstrap sample mean of strong mixing processes. Both weak and strong consistencies are obtained.

• Journal of the Korean Chemical Society
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• v.39 no.10
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• pp.763-768
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• 1995

The theory previously proposed to simulate hole depth in the weak burn intensity limit is extended to examine the hole depth at arbitrary burn intensity using 3-level system model. The hole spectrum simulated using constant fluence gives different hole depth for strong burn intensity while it gives same hole depth for weak burn intensity region. The calculated hole growth curves are compared with published experimental data for oxazine720 in glycerol and tetracene in MTHF glass.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.359-367
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• 2005

Let A be a Banach algebra, we say that A has the strongly double limit property (SDLP) if for each bounded net $(a_\alpha)$ in A and each bounded net $(a^{\ast}\;_\beta)\;in\;A^{\ast},\;lim_\alpha\;lim_\beta=lim_\beta\;lim_\alpha$ whenever both iterated limits exist. In this paper among other results we show that if A has the SDLP and $A^{\ast\ast}$ is (n - 2)-weakly amenable, then A is n-weakly amenable. In particular, it is shown that if $A^{\ast\ast}$ is weakly amenable and A has the SDLP, then A is weakly amenable.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.231-243
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• 1997

In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1139-1153
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• 2010

Let {$X_j,\;j\geq1$} be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with $EX_1$ = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {$X_j$} under the condition that L(x) := $EX_1^2I{|X_1|{\leq}x}$ is a slowly varying function at $\infty$, without any higher moment conditions.

• Transactions of Materials Processing
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• v.7 no.4
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• pp.354-363
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• 1998

In order to analyze the stretch forming characteristics of tailored blanks, laser welded blanks of different thickness and strength combinations were prepared and stretching tests were done. The stretching formability of laser welded blanks was reduced as increasing the deformation restraining force ($strength{\times}thickness$) ratio between two welded sheets. Weld line movement was attributed to strain concentration at weaker sheets and resulted in fracture at weaker sid, so that fracture could be predicted by the forming limit of the weak sheet. In the case of a welded blank with the similar deformation restraining force rations between two welded sheets, crack occurred at weld and its forming limit was about 15% less than the base sheet. The effects of lubrication and weld line position on stretch-ing formability were also investigated by experiments. Lower friction did not always give better formability for tailored blanks. Stretching formability was observed to be improved as increasing the area of weak sheet.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.625-633
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• 1995

Classical Fatous' theorem asserts that the non-tangential limit of the Poisson integral of an integrals function on $[\pi, \pi]$ exists a.e.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.421-433
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• 2020

Masonry infills are normally considered as non-structural elements in design practice, therefore, the interaction between the bounding frame and the strength contribution of masonry infills is commonly ignored in the seismic analysis work of the RC frames. However, a number of typical RC frames with irregular distributed masonry infills have suffered from undesirable weak-story failure in major earthquakes, which indicates that ignoring the influence of masonry infills may cause great seismic collapse risk of RC frames. This paper presented the investigation on the risk of seismic collapse of RC frames with irregularly distributed masonry infills through a large number of nonlinear time history analyses (NTHAs). Based on the results of NTHAs, seismic fragility curves were developed for RC frames with various distribution patterns of masonry infills. It was found that the existence of masonry infills generally reduces the collapse risk of the RC frames under both frequent happened and very strong earthquakes, however, the severe irregular distribution of masonry infills, such as open ground story scenario, results in great risk of forming a weak story failure. The strong-column weak-beam (SCWB) ratio has been widely adopted in major seismic design codes to control the potential of weak story failures, where a SCWB ratio value about 1.2 is generally accepted as the lower limit. In this study, the effect of SCWB ratio on inter-story drift distribution was also parametrically investigated. It showed that improving the SCWB ratio of the RC frames with irregularly distributed masonry infills can reduce inter-story drift concentration index under earthquakes, therefore, prevent weak story failures. To achieve the same drift concentration index limit of the bare RC frame with SCWB ratio of about 1.2, which is specified in ACI318-14, the SCWB ratio of masonry-infilled RC frames should be no less than 1.5. For the open ground story scenario, this value can be as high as 1.8.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.945-966
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• 2017

The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.