• Title/Summary/Keyword: Exponential equation

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CHARACTERIZATIONS OF STABILITY OF ABSTRACT DYNAMIC EQUATIONS ON TIME SCALES

  • Hamza, Alaa E.;Oraby, Karima M.
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.185-202
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    • 2019
  • In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form $$\{u^{\Delta}(t)=Au(t)+f(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ and $$\{u^{\Delta}(t)=Au(t)+f(t,u),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ in terms of the stability of the homogeneous equation $$\{u^{\Delta}(t)=Au(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ where f is rd-continuous in $t{\in}{\mathbb{T}}$ and with values in a Banach space X, with f(t, 0) = 0, and A is the generator of a $C_0$-semigroup $\{T(t):t{\in}{\mathbb{T}}\}{\subset}L(X)$, the space of all bounded linear operators from X into itself. Here D(A) is the domain of A and ${\mathbb{T}}{\subseteq}{\mathbb{R}}^{{\geq}0}$ is a time scale which is an additive semigroup with property that $a-b{\in}{\mathbb{T}}$ for any $a,b{\in}{\mathbb{T}}$ such that a > b. Finally, we give illustrative examples.

E-commerce adoption within SME's in Ghana, a Tool for Growth?

  • Agyapong, Christian Sarfo
    • 한국벤처창업학회:학술대회논문집
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    • 2018.11a
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    • pp.269-275
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    • 2018
  • Electronic commerce, the act of trading online, with its myriad of potential has been seldom looked at within the context of developing countries. E-commerce presents SMEs in developing economies the opportunity to adequately compete on a global stage. The exponential growth of e-commerce in developed economies further widens the financial gap between developed and developing economies. This study looks at a practical e-commerce adoption framework for Ghanaian SMEs and by extension, developing economies and looks at the net benefits that are available to current adopters. The study uses structural equation modeling, using Partial least squares (PLS) regression to analyze the data in the research. Using PLS algorithms as well as bootstrapping calculations. It combines the use of surveys (154) and interviews (38) as means of data collection. The findings of the research indicate that there is a need for legislation on e-commerce trading to regulate the trade in Ghana, with policies such as e-contracting and e-signature laws among others. Also, a current call for an expansion of the mobile payment methods within the country. For the private investor, a ripe market for logistics services. The study also proposes a simple guideline for SMEs looking to adopt or expand their e-commerce usage, that considers technological, organizational and environmental factors that come to play within e-commerce adoption.

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Development of a Predictive Model Describing the Growth of Staphylococcus aureus in Ready-to-Eat Sandwiches (즉석섭취 샌드위치에서의 Staphylococcus aureus 성장예측모델 개발)

  • Park, Hae-Jung;Bae, Hyun-Joo
    • Journal of the FoodService Safety
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    • v.2 no.2
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    • pp.91-96
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    • 2021
  • This study was performed to provide fundamental data on hygiene and quality control of ready-to-eat sandwiches. Predictive models were developed to the kinetics of Staphylococcus aureus growth in these sandwiches as a function of temperature (10, 15, 25, and 35℃). The result of the primary model that used the Gompertz equation showed that the lag phase duration (LPD) and generation time (GT) decreased and the exponential growth rate (EGR) increased with increasing storage temperature. The secondary model showed an R2 for M and B of 0.9967 and 09916, respectively. A predictive growth model of the growth degree as a function of temperature was developed. L(t)=A+Cexp(-exp(-B(t-M))) (A=Initial contamination level, C=MPD-A, B=0.473166-0.045040*Temp-0.001718*Temp*Temp, M=19.924824-0.627442*Temp-0.004493*Temp*Temp, t=time, Temp=temperature). This model showed an R2 value of 0.9288. All the models developed in this study showed a good fit.

Fractional radioactive decay law and Bateman equations

  • Cruz-Lopez, C.A.;Espinosa-Paredes, G.
    • Nuclear Engineering and Technology
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    • v.54 no.1
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    • pp.275-282
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    • 2022
  • The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

Analytical Approximation Algorithm for the Inverse of the Power of the Incomplete Gamma Function Based on Extreme Value Theory

  • Wu, Shanshan;Hu, Guobing;Yang, Li;Gu, Bin
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.15 no.12
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    • pp.4567-4583
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    • 2021
  • This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

A spent nuclear fuel source term calculation code BESNA with a new modified predictor-corrector scheme

  • Duy Long Ta ;Ser Gi Hong ;Dae Sik Yook
    • Nuclear Engineering and Technology
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    • v.54 no.12
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    • pp.4722-4730
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    • 2022
  • This paper introduces a new point depletion-based source term calculation code named BESNA (Bateman Equation Solver for Nuclear Applications), which is aimed to estimate nuclide inventories and source terms from spent nuclear fuels. The BESNA code employs a new modified CE/CM (Constant Extrapolation - Constant Midpoint) predictor-corrector scheme in depletion calculations for improving computational efficiency. In this modified CE/CM scheme, the decay components leading to the large norm of the depletion matrix are excluded in the corrector, and hence the corrector calculation involves only the reaction components, which can be efficiently solved with the Talyor Expansion Method (TEM). The numerical test shows that the new scheme substantially reduces computing time without loss of accuracy in comparison with the conventional scheme using CRAM (Chebyshev Rational Approximation Method), especially when the substep calculations are applied. The depletion calculation and source term estimation capability of BESNA are verified and validated through several problems, where results from BESNA are compared with those calculated by other codes as well as measured data. The analysis results show the computational efficiency of the new modified scheme and the reliability of BESNA in both isotopic predictions and source term estimations.

A Study on the Thernal Conductivity Characteristics of Discarded Tire Powder-Soil Mixture (폐타이어 파우더 혼합토의 열전도율 특성에 관한 연구)

  • Kim, Hak-Sam;Seo, Sang-Youl;NakamuRa, Dai;Yamashita, Satoshi;Suzuki, Teruyuki
    • Journal of the Korean Geotechnical Society
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    • v.26 no.5
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    • pp.27-36
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    • 2010
  • Thermal conductivities using the thermal probe method were determined for frost susceptible soil with three types of discarded tire powder under the condition of a temperature variation from $-20^{\circ}C{\sim}+10^{\circ}C$. Also, the amount of unfrozen water contents was measured by the pulsed NMR method. The variation of unfrozen water content in the experimental condition could be expressed as a function of temperature given by an exponential equation. A new model for calculating the thermal conductivity of frozen soil was proposed. It is extended from the two element method and subdivided into three constituent elements.

GARCH-X(1, 1) model allowing a non-linear function of the variance to follow an AR(1) process

  • Didit B Nugroho;Bernadus AA Wicaksono;Lennox Larwuy
    • Communications for Statistical Applications and Methods
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    • v.30 no.2
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    • pp.163-178
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    • 2023
  • GARCH-X(1, 1) model specifies that conditional variance follows an AR(1) process and includes a past exogenous variable. This study proposes a new class from that model by allowing a more general (non-linear) variance function to follow an AR(1) process. The functions applied to the variance equation include exponential, Tukey's ladder, and Yeo-Johnson transformations. In the framework of normal and student-t distributions for return errors, the empirical analysis focuses on two stock indices data in developed countries (FTSE100 and SP500) over the daily period from January 2000 to December 2020. This study uses 10-minute realized volatility as the exogenous component. The parameters of considered models are estimated using the adaptive random walk metropolis method in the Monte Carlo Markov chain algorithm and implemented in the Matlab program. The 95% highest posterior density intervals show that the three transformations are significant for the GARCHX(1, 1) model. In general, based on the Akaike information criterion, the GARCH-X(1, 1) model that has return errors with student-t distribution and variance transformed by Tukey's ladder function provides the best data fit. In forecasting value-at-risk with the 95% confidence level, the Christoffersen's independence test suggest that non-linear models is the most suitable for modeling return data, especially model with the Tukey's ladder transformation.

Exploring the Relationship between the Kinetic Energy and Intensity of Rainfall in Sangju, Korea

  • Van, Linh Nguyen;Le, Xuan-Hien;Yeon, Minho;Thi, Tuyet-May Do;Lee, Giha
    • Proceedings of the Korea Water Resources Association Conference
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    • 2022.05a
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    • pp.151-151
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    • 2022
  • The impact of raindrops on the soil surface causes soil detachment, which may be estimated by measuring the kinetic energy (KE) of the raindrops. Since direct measurements of rainfall force on ground surfaces are not generally available, empirical equations are an alternative option to estimate KE from rainfall intensity (I), which has the greatest influence over soil erosion and is easily accessible. Establishing the optimal formulation for the relationship between kinetic energy and rainfall intensity has proven to be difficult. Thus, this research considered thirty-seven rainfall events observed from June 2020 to December 2021 using a laster optical disdrometer erected in Kyungpook National University to examine the characteristics of KE-I relationships. We concentrated our discussion on the formation of two different expressions of the KE, including KE expenditure (KEexp) and KE content (KEcon). The following conclusions were drawn: (1) We employed statistical analysis to demonstrate that the KEexp is more suitable expression for establishing an empirical rule between KE and I than the KEcon. (2) A power-law model was used to find the best correlation between KEexp-I relationship, whereas the best match between KEcon and I were found using an exponential equation.

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An Estimation of Roughness Coefficient in a Channel with Roughness Correction Blocks (조도보정 블록 수로에서의 조도계수 추정)

  • Choi, Heung Sik;Kim, Si Hoon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.34 no.1
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    • pp.107-116
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    • 2014
  • A volume density of roughness correction blocks in a channel is defined and the corresponding roughness coefficient(n) is estimated by analyzing the diverse hydraulic characteristics of VR, the product of the average velocity and the hydraulic radius, block Reynolds number ($Re^*$), drag coefficient ($\acute{C}_D$), and the roughness coefficient ($n_b$) of bottom shear. The increase of VR and block Reynolds number causes the exponential decrease of roughness coefficient converged to a constant value as expected. The drag coefficient also exponentially decreases as block Reynolds number increases as well. The drag force is governed by the block shape defined by volume density in high block Reynolds number of turbulent flow region. For more accurate estimation of roughness coefficient the use of the correlation equation of it is required by block Reynolds number and volume density. The regression equations for n-VR, $\acute{C}_D-Re^*$, and $n_b-\acute{C}_D$ are presented. The regression equations of roughness coefficient are also presented by block Reynolds number and volume density. The developed equation of roughness coefficient by block Reynolds number and volume density has practical use by confirming the coincidence between the experimental results and the results of HEC-RAS using the developed equation.