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LONG-TIME BEHAVIOR FOR SEMILINEAR DEGENERATE PARABOLIC EQUATIONS ON ℝN

  • Cung, The Anh;Le, Thi Thuy
    • Communications of the Korean Mathematical Society
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    • v.28 no.4
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    • pp.751-766
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    • 2013
  • We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.

Threshold estimation for the composite lognormal-GPD models (로그-정규분포와 파레토 합성 분포의 임계점 추정)

  • Kim, Bobae;Noh, Jisuk;Baek, Changryong
    • The Korean Journal of Applied Statistics
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    • v.29 no.5
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    • pp.807-822
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    • 2016
  • The composite lognormal-GPD models (LN-GPD) enjoys both merits from log-normality for the body of distribution and GPD for the thick tailedness of the observation. However, in the estimation perspective, LN-GPD model performs poorly due to numerical instability. Therefore, a two-stage procedure, that estimates threshold first then estimates other parameters later, is a natural method to consider. This paper considers five nonparametric threshold estimation methods widely used in extreme value theory and compares their performance in LN-GPD parameter estimation. A simulation study reveals that simultaneous maximum likelihood estimation performs good in threshold estimation, but very poor in tail index estimation. However, the nonparametric method performs good in tail index estimation, but introduced bias in threshold estimation. Our method is illustrated to the service time of an Israel bank call center and shows that the LN-GPD model fits better than LN or GPD model alone.

A Packet Dropping Algorithm based on Queue Management for Congestion Avoidance (폭주회피를 위한 큐 관리 기반의 패킷 탈락 알고리즘)

  • 이팔진;양진영
    • Journal of Internet Computing and Services
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    • v.3 no.6
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    • pp.43-51
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    • 2002
  • In this paper, we study the new packet dropping scheme using an active queue management algorithm. Active queue management mechanisms differ from the traditional drop tail mechanism in that in a drop tail queue packets are dropped when the buffer overflows, while in active queue management mechanisms, packets may be dropped early before congestion occurs, However, it still incurs high packet loss ratio when the buffer size is not large enough, By detecting congestion and notifying only a randomly selected fraction of connection, RED causes to the global synchronization and fairness problem. And also, it is the biggest problem that the network traffic characteristics need to be known in order to find the optimum average queue length, We propose a new efficient packet dropping method based on the active queue management for congestion control. The proposed scheme uses the per-flow rate and fair share rate estimates. To this end, we present the estimation algorithm to compute the flow arrival rate and the link fair rate, We shows the proposed method improves the network performance because the traffic generated can not cause rapid fluctuations in queue lengths which result in packet loss

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Krawtchouk Polynomial Approximation for Binomial Convolutions

  • Ha, Hyung-Tae
    • Kyungpook Mathematical Journal
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    • v.57 no.3
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    • pp.493-502
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    • 2017
  • We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

Text Line Segmentation using AHTC and Watershed Algorithm for Handwritten Document Images

  • Oh, KangHan;Kim, SooHyung;Na, InSeop;Kim, GwangBok
    • International Journal of Contents
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    • v.10 no.3
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    • pp.35-40
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    • 2014
  • Text line segmentation is a critical task in handwritten document recognition. In this paper, we propose a novel text-line-segmentation method using baseline estimation and watershed. The baseline-detection algorithm estimates the baseline using Adaptive Head-Tail Connection (AHTC) on the document. Then, the watershed method segments the line region using the baseline-detection result. Finally, the text lines are separated by watershed result and a post-processing algorithm defines the lines more correctly. The scheme successfully segments text lines with 97% accuracy from the handwritten document images in the ICDAR database.

UNIFORM ATTRACTORS FOR NON-AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON ℝN

  • Anh, Cung The;Nguyen, Duong Toan
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1299-1324
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    • 2014
  • We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.

A Bayesian Approach to Gumbel Mixture Distribution for the Estimation of Parameter and its use to the Rainfall Frequency Analysis (Bayesian 기법을 이용한 혼합 Gumbel 분포 매개변수 추정 및 강우빈도해석 기법 개발)

  • Choi, Hong-Geun;Uranchimeg, Sumiya;Kim, Yong-Tak;Kwon, Hyun-Han
    • Journal of The Korean Society of Civil Engineers
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    • v.38 no.2
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    • pp.249-259
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    • 2018
  • More than half of annual rainfall occurs in summer season in Korea due to its climate condition and geographical location. A frequency analysis is mostly adopted for designing hydraulic structure under the such concentrated rainfall condition. Among the various distributions, univariate Gumbel distribution has been routinely used for rainfall frequency analysis in Korea. However, the distributional changes in extreme rainfall have been globally observed including Korea. More specifically, the univariate Gumbel distribution based rainfall frequency analysis is often fail to describe multimodal behaviors which are mainly influenced by distinct climate conditions during the wet season. In this context, we purposed a Gumbel mixture distribution based rainfall frequency analysis with a Bayesian framework, and further the results were compared to that of the univariate. It was found that the proposed model showed better performance in describing underlying distributions, leading to the lower Bayesian information criterion (BIC) values. The mixed Gumbel distribution was more robust for describing the upper tail of the distribution which playes a crucial role in estimating more reliable estimates of design rainfall uncertainty occurred by peak of upper tail than single Gumbel distribution. Therefore, it can be concluded that the mixed Gumbel distribution is more compatible for extreme frequency analysis rainfall data with two or more peaks on its distribution.

Multivariate conditional tail expectations (다변량 조건부 꼬리 기대값)

  • Hong, C.S.;Kim, T.W.
    • The Korean Journal of Applied Statistics
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    • v.29 no.7
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    • pp.1201-1212
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    • 2016
  • Value at Risk (VaR) for market risk management is a favorite method used by financial companies; however, there are some problems that cannot be explained for the amount of loss when a specific investment fails. Conditional Tail Expectation (CTE) is an alternative risk measure defined as the conditional expectation exceeded VaR. Multivariate loss rates are transformed into a univariate distribution in real financial markets in order to obtain CTE for some portfolio as well as to estimate CTE. We propose multivariate CTEs using multivariate quantile vectors. A relationship among multivariate CTEs is also derived by extending univariate CTEs. Multivariate CTEs are obtained from bivariate and trivariate normal distributions; in addition, relationships among multivariate CTEs are also explored. We then discuss the extensibility to high dimension as well as illustrate some examples. Multivariate CTEs (using variance-covariance matrix and multivariate quantile vector) are found to have smaller values than CTEs transformed to univariate. Therefore, it can be concluded that the proposed multivariate CTEs provides smaller estimates that represent less risk than others and that a drastic investment using this CTE is also possible when a diversified investment strategy includes many companies in a portfolio.

Distribution fitting for the rate of return and value at risk (수익률 분포의 적합과 리스크값 추정)

  • Hong, Chong-Sun;Kwon, Tae-Wan
    • Journal of the Korean Data and Information Science Society
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    • v.21 no.2
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    • pp.219-229
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    • 2010
  • There have been many researches on the risk management due to rapid increase of various risk factors for financial assets. Aa a method for comprehensive risk management, Value at Risk (VaR) is developed. For estimation of VaR, it is important task to solve the problem of asymmetric distribution of the return rate with heavy tail. Most real distributions of the return rate have high positive kurtosis and low negative skewness. In this paper, some alternative distributions are used to be fitted to real distributions of the return rate of financial asset. And estimates of VaR obtained by using these fitting distributions are compared with those obtained from real distribution. It is found that normal mixture distribution is the most fitted where its skewness and kurtosis of practical distribution are close to real ones, and the VaR estimation using normal mixture distribution is more accurate than any others using other distributions including normal distribution.

Efficient Inverter Type Compressor System using the Distribution of the Air Flow Rate (공기 변화량 분포를 이용한 효율적인 인버터타입 압축기 시스템)

  • Shim, JaeRyong;Kim, Yong-Chul;Noh, Young-Bin;Jung, Hoe-kyung
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.19 no.10
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    • pp.2396-2402
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    • 2015
  • Air compressor, as an essential equipment used in the factory and plant operations, accounts for around 30% of the total electricity consumption in U.S.A, thereby being proposed advanced technologies to reduce electricity consumption. When the fluctuation of the compressed airflow rate is small, the system stability is increased followed by the reduction of the electricity consumption which results in the efficient design of the energy system. In the statistical analysis, the normal distribution, log normal distribution, gamma distribution or the like are generally used to identify system characteristics. However a single distribution may not fit well the data with long tail, representing sudden air flow rate especially in extremes. In this paper, authors decouple the compressed airflow rate into two parts to present a mixture of distribution function and suggest a method to reduce the electricity consumption. This reduction stems from the fact that a general pareto distribution estimates more accurate quantile value than a gaussian distribution when an airflow rate exceeds over a large number.