• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.553-561
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• 2015

The exponential and power law functionally graded material(FGM) theory is reformulated considering the refined shear and normal deformation theory. This theory has ability to capture the both normal deformation effect and exponential and power law function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported plates on Pasternak elastic foundation. Numerical solutions of vibration analysis of FGM plates are presented using this theory to illustrate the effects of power law index and 3-D theory of exponential and power law function on natural frequency. The relations between 3-D and 2-D higher-order shear deformation theory are discussed by numerical results. Further, effects of (i) power law index, (ii) side-to-thickness ratio, and (iii) elastic foundation parameter on nondimensional natural frequency are studied. To validate the present solutions, the reference solutions are discussed.

• Industrial Engineering and Management Systems
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• v.12 no.3
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• pp.244-253
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• 2013

In industries, shipping is an important issue in improving the forecasting accuracy of sales. This paper introduces a hybrid method and plural methods are compared. Focusing the equation of exponential smoothing method (ESM) that is equivalent to (1, 1) order autoregressive-moving-average (ARMA) model equation, a new method of estimating the smoothing constant in ESM had been proposed previously by us which satisfies minimum variance of forecasting error. Generally, the smoothing constant is selected arbitrarily. However, this paper utilizes the above stated theoretical solution. Firstly, we make estimation of ARMA model parameter and then estimate the smoothing constant. Thus, theoretical solution is derived in a simple way and it may be utilized in various fields. Furthermore, combining the trend removing method with this method, we aim to improve forecasting accuracy. This method is executed in the following method. Trend removing by the combination of linear and 2nd order nonlinear function and 3rd order nonlinear function is executed to the original production data of two kinds of bread. Genetic algorithm is utilized to search the optimal weight for the weighting parameters of linear and nonlinear function. For comparison, the monthly trend is removed after that. Theoretical solution of smoothing constant of ESM is calculated for both of the monthly trend removing data and the non-monthly trend removing data. Then forecasting is executed on these data. The new method shows that it is useful for the time series that has various trend characteristics and has rather strong seasonal trend. The effectiveness of this method should be examined in various cases.

• Journal of the Korean Data Analysis Society
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• v.20 no.6
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• pp.2813-2827
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• 2018

Progressive censoring schemes have become quite popular in reliability study. Under progressive censored data, however, some units can be failed between two points of observation with exact times of failure of these units unobserved. For example, loss may arise in life-testing experiments when the failure times of some units were not observed due to mechanical or experimental difficulties. Therefore, multiply progressive censoring scheme was introduced. So, we derives a maximum likelihood estimator of the parameter of exponential distribution. And we introduced the goodness-of-fit test statistics using order statistic and Lorenz curve. We carried out Monte Carlo simulation to compare the proposed test statistics. In addition, real data set have been analysed. In Weibull and chi-squared distributions, the test statistics using Lorenz curve are more powerful than test statistics using order statistics.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.257-273
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• 2010

One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.83-98
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• 2014

During the last decade, several papers have focused on linear q-difference equations of the form ${\sum}^n_{j=0}a_j(z)f(q^jz)=a_{n+1}(z)$ with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order ${\rho}_{log}$. It is shown, under certain assumptions, that ${\rho}_{log}(f)$ = max${{\rho}_{log}(a_j)}$ + 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.131-141
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• 2014

In the present paper, we introduce the new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give some interesting identities. Finally, by applying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation for this polynomials at negative integers.

• Microbiology and Biotechnology Letters
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• v.14 no.2
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• pp.175-179
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• 1986

In order to develope a protoplast fusion of the genus Cellulomonas having high assimilibility of cellulose, the optimum conditions for the protoplast formation of Cellulomonas flavigena NCIB 12901 was investigated and observed by means of Scanning Electron Microscope. The results suggested that the susceptibility of the cell wall by lysozyme treatment on protoplast formation was considerably depend on the cultural periods of the cells. Cells of C. flavigena at mid exponential phase could more efficiently convert to protoplast cells than those at late exponential phase did. The rate of the protoplast formation was 95%, even though the rate was over 99.9% on counting by indirect method after osmotic shock treatment, when cells of the organism at mid exponential phase were treated with lysozyme (400$\mu\textrm{g}$/$m{\ell}$) for 6 hours and observed by SEM. In the evaluation of protoplast formation of the genus Cellulomonas, direct method of the observation under Scanning Electron Microscope was much more reliable than the counting method of protplasts after osmotic shock treatment. Because defferences between the number of spheroplast and protoplast were not able to be figured out on counting the number of protoplast after osmotic shock treatment.

• Journal of Food Hygiene and Safety
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• v.12 no.3
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• pp.181-187
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• 1997

Lactobacillus acidophilus NCFM, Lactobacillus casei YIT 9018, Bifidobacterium longum 8001, and Bifidobacterium longum 8025 at the level of 106 cfu/$m\ell$ were cultured with 104 cfu/$m\ell$ of Escherichia coli O157:H7 KSC 109 or Salmonella typhimurium ATCC14028, in order to verify the effects of lactic acid bacteria and bifidobacteria on the growth of the pathogens. In the mixed culture of lactic acid bacteria with E. coli O157:H7 KSC 109, Growth inhibition and atypical microcolonies of E. coli O157:H7 KSC 109 were observed. The pathogens inoculated grew for 5 hors (pH 5.3), by the time L. acidophilus NCFM reached the exponential growth phase, and then the surviving pathogens were decreased to 101 cfu/$m\ell$ after 35 hours. When L. caseiYIT 9018 was grown with the pathogens, they grew for 10 hours (pH 4.6), by the time L. casei YIT 9018 reached the end of exponential growth phase, and then the surviving pathogens were decreased drastically. Up to the stationary growth phase of lactic acid bacteria, L. acidophilus NCFM exhibited stronger inhibition against the pathogens than L. casei YIT 9018 did, which might be attributed to its faster growth. Likewise bifidobacteria inhibited the growth of the pathogens tested, bifidobaceria was weaker in the inhibitory activity than lactic acid bacteria. When Bifidobacterium longum 8001 was cultured with the pathogens, E. coli O157:H7 KSC 109 was gradually ingibited at the stationary growth phase of bifidobacteria, atypical microcolonies were formed on Levine EMB medium after 48 hours, and Salmonella grew up to 106 dfu/$m\ell$, then was drastically ingibited at the exponential growth phage of Bifidobacterium longum 8001. But when Bifidobacteriuam longum 8025 was cultured with the pathogens, the pathogens grew to the same level of Bifidobacteriuam longum 8025 was cultured with the pathogens, the pathogens grew to the same lever of Bifidobacteriuam longum 8025 after 10 hours, then the surviving pathogens were decreased drastically.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.581-594
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• 2016

We introduce innovations state space exponential smoothing models (ISS-ESM) that can analyze time series with multiple seasonal patterns. Especially, in order to control complex structure existing in the multiple patterns, the model equations use a matrix consisting of seasonal updating parameters. It enables us to group the seasonal parameters according to their similarity. Because of the grouped parameters, we can accomplish the principle of parsimony. Further, the ISS-ESM can potentially accommodate any number of multiple seasonal patterns. The models are applied to predict electricity demand in Korea that is observed on hourly basis, and we compare their performance with that of the traditional exponential smoothing methods. It is observed that the ISS-ESM are superior to the traditional methods in terms of the prediction and the interpretability of seasonal patterns.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.