• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.947-965
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• 2010

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirichlet L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.377-384
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• 1998

Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

• Journal of Korean Society for Quality Management
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• v.19 no.2
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• pp.125-132
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• 1991

This paper is concerned with the flow shop scheduling problems considering different weighted penalty costs for earliness and lateness, and a common due date. The objective of the paper is to develop an efficient heuristic scheduling algorithm for minimizing total penalty costs and for determining the optimal common due date. The positional weight index and, the product sum method are used. A numerical example is given for illustrating the proposed algorithm.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.529-538
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• 2006

In this paper we derive the central limit theorem for ${\sum}^n_{i=l}\;a_{ni}{\xi}_{i},\;where\;\{a_{ni},\;1\;{\le}\;i\;{\le}n\}$ is a triangular array of non-negative numbers such that $sup_n{\sum}^n_{i=l}\;a^2_{ni}\;<\;{\infty},\;max_{1{\le}i{\le}n\;a_{ni}{\to}\;0\;as\;n{\to}{\infty}\;and\;{\xi}'_{i}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• The KIPS Transactions:PartD
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• v.15D no.3
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• pp.399-410
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• 2008

This paper suggests a new retrieval method using weighted vector sum to resolve a problem of traditional location-based retrieval method, nearest neighbor (NN) query, and NN query using direction. The proposed method filters out data with the radius, and then the remained retrieval area is filtered by a direction information compounded of a user's moving direction, a pre-fixed interesting direction, and a pre-fixed retrieval angle. The moving direction is computed from a vector or a weighted vector sum of several vectors using a weight to adopt several cases. The retrieval angle can be set from traditional $360^{\circ}$ to any degree you want. The retrieval data for this method can be a still and moving image recorded shooting location, and also several type of media like text, web, picture offering to customer with location of company or resort. The suggested method guarantees more accurate retrieval than traditional location-based retrieval methods because that the method selects data within the radius and then removes data of useless areas like passed areas or an area of different direction. Moreover, this method is more flexible and includes the direction based NN.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.9 no.6
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• pp.136-150
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• 2010

Due to the effect of indoor coverage problem, the QoS of the indoor users will be degraded dramatically, with the number of indoor users. The femto cell is a popular solution for such problems. Since the price of the femto base station is usually cheap enough, one can sets up huge number of base stations in a small indoor area to reduce the size of communication cell. In this way, the QoS of the indoor users can be improved significantly. Moreover, the data rate can also be increased. However, how to decide an ideal transmitting power according to the surrounding radio environment is not a trivial problem, that still has not been addressed well. If the transmit power of femto base station is too large, the interference to the macro users will be increased. Conversely, if the transmit power of femto base station is too small; the coverage of femto base station will be reduced. To address this problem, we propose a power configuration method in femto base station using Genetic Algorithm by investigating a new fitness function. Furthermore, we adopt the weighted sum approach to improve the user performance in different modes. The simulation results show that the proposed power configuration method can not only improves the downlink SINR, but also enhance the channel capacity for both the Macro cell systems and Femto cell systems compared with some conventional methods.

• The KSFM Journal of Fluid Machinery
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• v.11 no.1
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• pp.52-60
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• 2008

Staggered dimples printed on opposite walls of an internal cooling channel are formulated numerically and optimized to enhance heat transfer performance. Nusselt number and friction factor based objectives are considered and a weighted average surrogate model is used to approximate the data generated by numerical simulation. The dimpled channel shape is defined by three geometric design variables, and the design point within design space are selected using Latin hypercube sampling. A weighted-sum method for multi-objective optimization is applied to integrate multiple objectives into a single objective. By the optimization, the objective function value is improved largely and heat transfer rate is increase much higher than pressure loss increase due to shape deformation. Channel with vertically non-symmetric optimum dimples is tested and found that the best appears if dimples on opposite wall are displaced by one quarter of dimple spacing.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.261-272
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• 2019

In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the $19^{th}$ and $20^{th}$ Korea National Assembly elections.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.363-370
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• 1995

A famous result of Chow and Robbins [8] asserts that if ${X_n, n \geq 1}$ are independent and identically distributed (i.i.d.) random variables with $E$\mid$X_1$\mid$ = \infty$, then for each sequence of constants ${M_n, n \geq 1}$ either $$ (1) lim inf_{n\to\infty} $\mid$\frac{M_n}{\sum_{j=1}^{n}X_j}$\mid$ = 0 almost certainly (a.c.) $$ or $$ (2) lim sup_{n\to\infty}$\mid$\frac{M_n}{\sum_{j=1}^{n}X_j}$\mid$ = \infty a.c. $$ and thus $P{lim_{n\to\infty} \sum_{j=1}^{n}X_j/M_n = 1} = 0$. Note that both (1) and (2) may indeed prevail.