• Title/Summary/Keyword: double arrays

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MARCINKIEWICZ-TYPE LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS

  • Hong, Dug-Hun;Volodin, Andrei I.
    • Journal of the Korean Mathematical Society
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    • v.36 no.6
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    • pp.1133-1143
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    • 1999
  • Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.

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Evaluation of sequence tracking methods for Compton cameras based on CdZnTe arrays

  • Lee, Jun;Kim, Younghak;Bolotnikov, Aleksey;Lee, Wonho
    • Nuclear Engineering and Technology
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    • v.53 no.12
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    • pp.4080-4092
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    • 2021
  • In this study, the performance of sequence tracking methods for multiple interaction events in specific CdZnTe Compton imagers was evaluated using Monte Carlo simulations. The Compton imager consisted of a 6 × 6 array of virtual Frisch-grid CZT crystals, where the dimensions of each crystal were 5 × 5 × 12 mm3. The sequence tracking methods for another Compton imager that consists of two identical CZT crystals arrays were also evaluated. When 662 keV radiation was incident on the detectors, the percentages of the correct sequences determined by the simple comparison and deterministic methods for two sequential interactions were identical (~80%), while those evaluated using the minimum squared difference method (55-59%) and Three Compton method (45-55%) for three sequential interactions, differed from each other. The reconstructed images of a 662 keV point source detected using single and double arrays were evaluated based on their angular resolution and signal-to-noise ratio, and the results showed that the double arrays outperformed single arrays.

A Study on Optimal Combination of Design Parameters for Improving Handling Performance of a Large Truck Using Design of Experiments (실험계획법을 이용한 대형트럭 조종성 향상을 위한 설계인자 최적조합에 관한 연구)

  • Moon, Il-Dong;Lee, Dong-Hwan;Oh, Chae-Youn
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.28 no.6
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    • pp.799-806
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    • 2004
  • This paper presents a scheme for finding an optimal combination of design parameters affecting on the handling performance of a large truck using design of experiments. The average of the sum of peak-to-peak roll angles at the first and second part of the double lane is used as an objective function for design of experiments. Six design parameters are selected from all possible parameters affecting on the handling performance. The table of orthogonal arrays is made by 27 times simulations. A computational model of a large truck is developed by MSC/NASTRAN and MSC/ADAMS, and verified the reliability of it with the results of vehicle tests performed in a double lane change course. It is used for the simulations. Analyses of variance and factor effect of the table of orthogonal arrays are performed. This paper proposes an optimal combination of those six design parameters for improving the handling performance of the large truck.

Design Optimization of Double-array Bolted Joints in Cylindrical Composite Structures

  • Kim, Myungjun;Kim, Yongha;Kim, Pyeunghwa;Park, Jungsun
    • International Journal of Aeronautical and Space Sciences
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    • v.17 no.3
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    • pp.332-340
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    • 2016
  • A design optimization is performed for the double-bolted joint in cylindrical composite structures by using a simplified analytical method. This method uses failure criteria for the major failure modes of the bolted composite joint. For the double-bolted joint with a zigzag arrangement, it is necessary to consider an interaction effect between the bolt arrays. This paper proposes another failure mode which is determined by angle and distance between two bolts in different arrays and define a failure criterion for the failure mode. The optimal design for the double-bolted joint is carried out by considering the interactive net-tension failure mode. The genetic algorithm (GA) is adopted to determine the optimized parameters; bolt spacing, edge distance, and stacking sequence of the composite laminate. A purpose of the design optimization is to maximize the burst pressure of the cylindrical structures by ensuring structural integrity. Also, a progressive failure analysis (PFA) is performed to verify the results of the optimal design for the double-bolted joint. In PFA, Hashin 3D failure criterion is used to determine the ply that would fail. A stiffness reduction model is then used to reduce the stiffness of the failed ply for the corresponding failure mode.

MEAN CONVERGENCE THEOREMS AND WEAK LAWS OF LARGE NUMBERS FOR DOUBLE ARRAYS OF RANDOM ELEMENTS IN BANACH SPACES

  • Dung, Le Van;Tien, Nguyen Duy
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.467-482
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    • 2010
  • For a double array of random elements {$V_{mn};m{\geq}1,\;n{\geq}1$} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which $k_{mn}^{-\frac{1}{r}}\sum{{u_m}\atop{i=1}}\sum{{u_n}\atop{i=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in $L_r$ (0 < r < 2). The weak law results provide conditions for $k_{mn}^{-\frac{1}{r}}\sum{{T_m}\atop{i=1}}\sum{{\tau}_n\atop{j=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in probability where {$T_m;m\;{\geq}1$} and {${\tau}_n;n\;{\geq}1$} are sequences of positive integer-valued random variables, {$k_{mn};m{{\geq}}1,\;n{\geq}1$} is an array of positive integers. The sharpness of the results is illustrated by examples.

A CMOS Readout Circuit for Uncooled Micro-Bolometer Arrays (비냉각 적외선 센서 어레이를 위한 CMOS 신호 검출회로)

  • 오태환;조영재;박희원;이승훈
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.40 no.1
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    • pp.19-29
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    • 2003
  • This paper proposes a CMOS readout circuit for uncooled micro-bolometer arrays adopting a four-point step calibration technique. The proposed readout circuit employing an 11b analog-to-digital converter (ADC), a 7b digital-to-analog converter (DAC), and an automatic gain control circuit (AGC) extracts minute infrared (IR) signals from the large output signals of uncooled micro-bolometer arrays including DC bias currents, inter-pixel process variations, and self-heating effects. Die area and Power consumption of the ADC are minimized with merged-capacitor switching (MCS) technique adopted. The current mirror with high linearity is proposed at the output stage of the DAC to calibrate inter-pixel process variations and self-heating effects. The prototype is fabricated on a double-poly double-metal 1.2 um CMOS process and the measured power consumption is 110 ㎽ from a 4.5 V supply. The measured differential nonlinearity (DNL) and integrat nonlinearity (INL) of the 11b ADC show $\pm$0.9 LSB and $\pm$1.8 LSB, while the DNL and INL of the 7b DAC show $\pm$0.1 LSB and $\pm$0.1 LSB.

3D Hierarchical Heterostructure of TiO2 Nanorod/Carbon Layer/NiMn-Layered Double Hydroxide Nanosheet

  • Zhao, Wei;Jung, Hyunsung
    • Journal of the Korean institute of surface engineering
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    • v.51 no.6
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    • pp.365-371
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    • 2018
  • 1D core-shell nanostructures have attracted great attention due to their enhanced physical and chemical properties. Specifically, oriented single-crystalline $TiO_2$ nanorods or nanowires on a transparent conductive substrate would be more desirable as the building core backbone. However, a facile approach to produce such structure-based hybrids is highly demanded. In this study, a three-step hydrothermal method was developed to grow NiMn-layered double hydroxide-decorated $TiO_2$/carbon core-shell nanorod arrays on transparent conductive fluorine-doped tin oxide (FTO) substrates. XRD, SEM, TEM, XPS and Raman were used to analyze the obtained samples. The in-situ fabricated hybrid nanostructured materials are expected to be applicable for photoelectrode working in water splitting.