• 대한수학회논문집
• /
• 제33권2호
• /
• pp.605-618
• /
• 2018

The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

• 한국연소학회:학술대회논문집
• /
• 한국연소학회 1999년도 제19회 KOSCO SYMPOSIUM 논문집
• /
• pp.155-163
• /
• 1999

A numerical study for simulating a swirling pulverized coal combustion in axisymmetric geometry is done here by applying the weighted sum of gray gases model (WSGGM) approach with the discrete ordinate method (DOM) to model the radiative heat transfer equation. In the radiative transfer equation, the same polynomial equation and coefficients for weighting factors as those for gas are adopted for the coal/char particles as a function of partial pressure and particle temperature. The Eulerian balance equations for mass, momentum, energy, and species mass fractions are adopted with the standard ${\kappa}-{\varepsilon}$ turbulence model, whereas the Lagrangian approach is used for the particulate phase for soot. The eddydissipation model is employed for the reaction rate for gaseous mixture, and the single-step first-order reaction model for the devolatilization process for coal. By comparing the numerical results with experimental ones, the models used here are confirmed and found to be one of good alternatives for simulating the combustion as well as radiative characteristics.

• 대한수학회보
• /
• 제32권2호
• /
• pp.221-231
• /
• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• Communications for Statistical Applications and Methods
• /
• 제6권2호
• /
• pp.585-594
• /
• 1999

Let {$X_{nj}$, 1$\leq$j$\leq$n,j$\geq$1} be a triangular array of random variables which are neither independent nor identically distributed. The almost sure convergences of randomly weighted partial sums of the form $$\sum_n^{j=1}$$ $W_{nj}$$X_{nj} are studied where {Wnj 1$\leq$j$\leq$n, j$\geq$1} is a triangular array of random weights. Application regarding the Efron bootstrap is also introduced.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
• /
• pp.1145-1149
• /
• 1990

This paper proposes a numerical method for redundant manipulators using predetermined optimal resolution. In order to obtain optimal joint trajectories, it is desirable to formulate redundancy resolution as an optimization problem having an integral cost criterion. We predetermine the trajectories of redundant joints in terms of the Nth partial sum of the Fourier series, which lead to the solution in the desirable homotopy class. Then optimal coefficients of the Fourier series, which yield the optimal solution within the predetermined class, are searched by the Powell's method. The proposed method is applied to a 3-link planar manipulator for cyclic tasks in Cartesian space. As the results, we can obtain the optimal solution in the desirable homotopy class without topological liftings of the solution. To show the validity of the proposed method, we analyze both optimal and extremal solutions by the Fast Fourier Transform (FFT) and discuss joint trajectories on the phase plane.

• Journal of the Optical Society of Korea
• /
• 제15권2호
• /
• pp.152-154
• /
• 2011

We propose a novel method which detects convex and concave corners using radial projection. The sum of two neighbors' differences at the local maxima or minima of the radial projection is compared with the angle threshold for detecting corners. In addition, the use of oriented bounding box trees and partial circles makes it possible to detect the corners of complex shapes. The experimental results show that the proposed method can separately detect the convex and concave corners, and that this method is scale invariant.

• 디지털산업정보학회논문지
• /
• 제5권4호
• /
• pp.179-187
• /
• 2009

In this paper, an efficient multi-level successive elimination algorithm using the locality in block was proposed for motion estimation. If SAD(sum of absolute difference) is calculated from large absolute difference values to small absolute difference values, SAD is increased rapidly. So, partial distortion elimination in SAD calculation can be done very early. Hence, the computations of SAD calculation can be reduced. In this paper, an efficient algorithm to calculate SAD from large absolute difference values to small absolute difference values by using the locality in block. Experimental results show that the proposed algorithm is an efficient algorithm with 100% motion estimation accuracy for the motion estimation of motion vectors.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
• /
• pp.371-372
• /
• 2007

In this paper we present performance and implementation comparisons of high performance two dimensional forward and inverse Discrete Cosine Transform (2D-DCT/IDCT) algorithm and low power algorithm for $8{\times}8$ 20 DCT and quantization based on partial sum and its corresponding hardware architecture for FPGA in MPEG-4. The architecture used in both low power 20 DCT and 2D IDCT is based on the conventional row-column decomposition method. The use of Fast algorithm and distributed arithmetic(DA) technique to implement the DCT/IDCT reduces the hardware complexity. The design was made using Mentor Graphics Tools for design entry and implementation. Mentor Graphics ModelSim SE6.1f was used for Verilog HDL entry, behavioral Simulation and Synthesis. The 2D DCT/IDCT consumes only 50% of the Operating Power.

• 전자공학회논문지B
• /
• 제29B권10호
• /
• pp.27-36
• /
• 1992

This paper proposes a numerical method of motion planning for manipulators using Foruier series. For a redundant manipulator, we predetermine the trajectories of redundant joints in terms of the Nth partial sum of the fourier series. then the optimal coefficients of the fourier series are searched by the Powell's method. For a nonredundant or redundant manipulator, CS02T-continuous smooth joint trajectory for a point-to-point task can be obtained while considering the frequency response. We apply the proposed method to the 3-link planar manipulator and the PUMA 560 manipulator. To show the validity of the proposed method, we analyze solutions by the Fast Fourier Transform (FFT). Also, several features are discussed to obtain an optimal solution.

• Communications for Statistical Applications and Methods
• /
• 제5권1호
• /
• pp.265-275
• /
• 1998

In testing the partial association between two variables after controlling for the S levels of a third factor, the Mantel and Haenszel (1959) statistic is often used. Since the statistic is based on the asymptotic distribution of the sum X of S hypergeometric variates, a guideline for the minimum requirements for the application of the statistic is useful. Mantel and Fleiss (1980) developed a criterion based on the guideline for the Pearson's $X^2$ statistic. The criterion requires the distance from the expected value to the closer bound of X to be at least five. The Mantel-Fleiss (MF) criterion was studied through a simulation using the hypergeometric sampling scheme. The criterion is not satisfactory. The size of statistic exceeded nominal 0.05 level nearly 1/5 of the cases even when the criteion is met. However, the results show that the statistic is much more unstable and conservative when the criterion is not met.