• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.203-211
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• 2003

A new result of weak convergence of the empirical process is established for a stationary ${\phi}-mixing$ sequence of random variables, which relaxes the existing conditions on mixing coefficients. The result is basically obtained from bounds for even moments of sums of ${\phi}-mixing$ r.v.'s useful for handling triangular arrays with entries decreasing in size.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.7
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• pp.818-825
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• 2004

In this paper, the study of effects of flow parameters on flame structure and NOx emission concentration was performed in co-axial. laminar partially premixed methane/air flames. Such (low parameters as equivalence ratio(${\Phi}$), fuel split percentage($\sigma$), and mixing distance(x/D$\_$i/) were defined as a premixing degree and varied within ${\Phi}$=1.36∼9.52, $\sigma$=50∼100, and x/D$\_$i/=5∼20. The image of OH$\^$*/ and NOx concentration were obtained with an ICCD camera and a NOx analyzer. The flame structure observations show a categorization of partially premixed flames into three distinct flame regimes corresponding to ${\Phi}$<1.7(premixed flame structure), 1.7<${\Phi}$<3.3(hybrid structure), and ${\Phi}$>3.3(diffusion flame structure existing a luminous sooting region) at $\sigma$=75%, and x/D$\_$i/=10. As o decreases from 100% to 50%, and x/D$\_$i/ decreases, nonpremixed flame structure appear at low equivalence ratio relatively. In addition, the measured emissions for NOx rise steeply from ${\Phi}$=1.7, to ${\Phi}$=3.3, then constants ${\Phi}$>4.76. NOx emissions decrease with increase the level of premixing level. In conclusion, the main effect on flame structure and NOx production was at first equivalence ratio(${\Phi}$), and next fuel split percentage($\sigma$), and finally mixing distance(x/D$\_$i/).

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.48-54
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• 2004

The effects of injector spacing s and injector diameter d on mixing are numerically investigated in supersonic combustor with perpendicular injection behind a backward-facing step. Simulations are reported for airstream Mach number of 2.4. Parameters are changed on following 4 cases to investigate the effects of injector configuration on mixing efficiency $\eta_m$. In the case of varying d or s, dynamic pressure ratio $Rq(=(pu^2)_j/(pu^2)_a)$ is also varied to keep bulk equivalence ratio $\Phi({\oe})Rq.d^2/s)$ constant. (l) Injector spacing s is varied at constant $\Phi$=0.5, 1, 2 for injector diameter d=6mm. In the case of $\Phi$=1, $\eta_m$ has its maximum value at s=24mm. The reason is that increase of $\eta_m$. , by widening spacing at Rq=constant competes with decrease of $\eta_m$ by increasing Rq at s=constant. When spacing is narrow, the flow field of vicinity of injector becomes two-dimensional because adjacent jets interferes each other. By widening spacing, air is easily entrained by three-dimensional effect. This mechanism also appears in the case of $\Phi$=0.5, 2 for d=6mm, and $\eta_m$. reaches its maximum value at s=24mm for $\Phi$=0.5 and at s=42mm for $\Phi$=2. (2) In the case of injector diameter d varied at $\Phi$=1 for s=30mm, $\eta_m$. has its maximum value at d=3mm. The reason is that decrease of $\eta_m$ by increasing injector diameter competes with increase of $\eta_m$ by decreasing Rq at d=constant.(3) In the case of s varied at $\Phi$=0.5, 1,2 for d=3mm, the injector spacing at which mixing efficiency has its maximum value is s= 18mm for $\Phi$=0.5, s=24mm for $\Phi$=1, s=24mm for $\Phi$=2. Therefore it is found that d=3mm and s=24mm can be optimum configuration over a range of $\Phi$=0.5~2.(4) The effect of h on the optimum spacing is investigated. s is varied for d=6mm at step height h=4, 6, 8mm. The simulation results do not show significant change on the step height.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.343-352
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• 2018

We study the complete convergence for sequences of dependent random variables in Hilbert spaces. Results are obtained for negatively associated random variables and ${\phi}$-mixing random variables in Hilbert spaces.

• 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.

• Journal of Korean Ophthalmic Optics Society
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• v.11 no.3
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• pp.225-229
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• 2006

In our angle configuration, several peculiar characteristic behaviors of MR could be observed, the mixing of positive MR(PMR) and negative MR(NMR) in the inclined sample was observed. The complete mixing angle, ${\phi}_{mix}$ as a function of inclination angle, ${\theta}$ was observed to fit well to the relation of ${\phi}_{mix}=tan^{-1}(1+tan{\theta})$ in nickel films. The above theoretical relation was obtained by decomposing the magnetic field into the components parallel and perpendicular to the current flow and identifying ${\phi}_{mix}$ as the angle satisfying that the above two components of magnetic field were identical. We also observed that the data of ${\phi}_{mix}$ did not satisfy the above theoretical relation in the iron film. This was explained by the fact that the growth direction in the iron film was an intermediate direction of magnetization, while the growth direction in the nickel film was an easy axis of magnetization.

• Carbon letters
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• v.15 no.2
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• pp.117-124
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• 2014

Conductive polymer composites (CPCs) consist of a polymeric matrix and a conductive filler, for example, carbon black, carbon fibers, graphite or carbon nanotubes (CNTs). The critical amount of the electrically conductive filler necessary to build up a continuous conductive network, and accordingly, to make the material conductive; is referred to as the percolation threshold. From technical and economical viewpoints, it is desirable to decrease the conductive-filler percolation-threshold as much as possible. In this study, we investigated the effect of polymer/conductive-filler interactions, as well as the processing and morphological development of low-percolation-threshold (${\Phi}c$) conductive-polymer composites. The aim of the study was to produce conductive composites containing less multi-walled CNTs (MWCNTs) than required for pure polypropylene (PP) through two approaches: one using various mixing methods and the other using immiscible polymer blends. Variants of the conductive PP composite filled with MWCNT was prepared by dry mixing, melt mixing, mechanofusion, and compression molding. The percolation threshold (${\Phi}c$) of the MWCNT-PP composites was most successfully lowered using the mechanofusion process than with any other mixing method (2-5 wt%). The mechanofusion process was found to enhance formation of a percolation network structure, and to ensure a more uniform state of dispersion in the CPCs. The immiscible-polymer blends were prepared by melt mixing (internal mixer) poly(vinylidene fluoride) (PVDF, PP/PVDF, volume ratio 1:1) filled with MWCNT.

• 한국연소학회:학술대회논문집
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• 2003.12a
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• pp.75-81
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• 2003

In this paper, the study of effects of flow variables on flame structure and NOx emission concentration was performed in co-axial laminar partially premixed methane/air flames. the objectives are to reveal its effect as parameters were varied and to understand the correlation between flame structure and NOx emission characteristics in the reaction zone. equivalence ratio(${\Phi}$), fuel split degree(${\sigma}$), and mixing distance(x/D) were defined as a premixing degree and varied within $1.36{\sim}3.17$(equivalence ratio), $50{\sim}100$(fuel split degree), and $5{\sim}20$(mixing distance). the image of $OH{\ast}$ and $CH{\ast}$, and NOx concentration were obtained with an ICCD camera and a NOx analyzer. additionally the maximum intensity location of $OH{\ast}$ chemiluminescence and $CH{\ast}$ chemiluminescence were measured to compare each flame structures. In conclusion flame structure and NOx emission characteristics were changed from diffused to premixed flame when mixing degree was on the increase. the main effect on flame structure and NOx production was at first equivalence ratio(${\Phi}$), and next fuel split degree(${\sigma}$), and finally mixing distance(x/D).

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.345-354
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• 2004

Boente and Fraiman [2] studied robust nonparametric estimators for regression or autoregression problems when the observations exhibit serial dependence. They established strong consistency of two families of M-type robust equivariant estimators for $\phi$-mixing processes. In this paper we extend their results to weaker $\alpha$$alpha$-mixing processes.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.355-365
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• 2008

Let ${Y_i;-\infty<i<\infty}$ be a doubly infinite sequence of identically distributed and $\phi$-mixing random variables with zero means and finite variances and ${a_i;-\infty<i<\infty}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of ${{\sum}_{k=1}^{n}\;{\sum}_{i=-\infty}^{\infty}\;a_{i+k}Y_i/n^{1/p};n\geq1}$ under some suitable conditions.