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Hydraulic conductivity, a fundamental property in groundwater hydrology, plays a pivotal role in understanding subsurface flow dynamics and environmental assessments. Accurate estimation of hydraulic conductivity is essential for groundwater resource management, environmental impact assessments, and geotechnical engineering. This study delves into the assessment of different hydraulic conductivity estimation methods across diverse soil types and locations, with a specific emphasis on the influence of grain size. The research spans multiple study locations, each characterized by distinct soil types, ranging from coarse sands to fine gravels. Expected hydraulic conductivity ranges were established for each soil type, providing a critical benchmark for accuracy assessment. The study incorporates 16 widely used estimation methods, including Hazen, Hazen K (cm/s) = d10 (mm), Slichter, Terzaghi, Beyer, Sauerbrei, Kruger, Kozeny-Carmen, Zunker, Zamarin, USBR, Barr, and Alyamani and Sen, Chapuis, Krumbein and Monk, and Shepherd. These methods were selected based on their prevalence in groundwater modeling and geotechnical engineering. Findings from this research reveal significant variability in hydraulic conductivity estimations among the different methods. Notably, the Beyer, Zunker, and Shepherd methods consistently demonstrate superior accuracy across a range of soil types. Beyer's estimations align closely with the expected hydraulic conductivity ranges for various soil types, showcasing its applicability and reliability. Conversely, some methods, such as Zunker and Shepherd, yield estimations that deviate from expected ranges, particularly for fine gravel and coarse gravel. These discrepancies highlight the importance of method selection based on soil type and geological conditions. [ABSTRACT FROM AUTHOR]

Recently, the fluctuations of oil prices and unstable product demands resulting in disruption at procurement, production, and inventory stages have led to increased awareness among managers and decision-makers to include uncertainty in the refinery planning. Among the most prominent approach in handling optimization under uncertainty is stochastic programming. However, it is critical and challenging to construct a representation of random variables that describe the uncertainty behaviour. Thus, this study proposes the model and forecasting of oil prices and petroleum products demand under uncertainty to incorporate Hurst parameter values and structural break approach as input parameters to the stochastic programming. In modelling oil price, the information on whether the structural break exists is crucial due to the long memory property that might be camouflaged by the existence of the structural break. The Hurst parameter, connected to the fractional differencing parameter, was used to characterize the long memory process. The time series will be modelled and forecasted based on the Hurst value, and stochastic differential equations will be explored to analyze the uncertainty of oil prices. Meanwhile, the Holt-Winter method is adopted to describe the uncertainties of petroleum product demand. The result indicates that Geometric Brownian Motion (GBM) and mean-reverting Ornstein-Uhlenbeck (OU) are accurate forecast models to forecast future oil prices, and Holt-Winter seasonal method is an accurate model to forecast future petroleum products demand due to mean absolute percentage error (MAPE) value is less than 10. Thus, we conclude that the coherent probabilistic scenario can then be constructed with this stochastic model framework to formulate a deterministic equivalent of stochastic programming. [ABSTRACT FROM AUTHOR]

A nonhomogeneous forced Korteweg-de Vries (fKdV) equation with some certain forcing term is investigated using a semi-analytic method called Homotopy Analysis Method (HAM). HAM is a summation of infinite series whereby its approximation solution converges immediately to the exact solution. Theoretical model, fKdV incorporating forcing term representing underwater bottom topography is used to analyze the wave interaction patterns over different inclination plane. The relationship between the three underwater sloping regions corresponding to wave interaction patterns are investigated. HAM solution found the higher inclination plane triggers higher amplitude wave interaction patterns. [ABSTRACT FROM AUTHOR]

This study aims to measure the dependence between individual lifetimes by applying multivariate Tweedie distribution to the lifetime data. Dependence between lifetimes incorporated in the mortality model is a new form of idea that gives significant impact on the risk of the annuity portfolio which is actually against the idea of standard actuarial methods that assumes independent between lifetimes. Hence, this paper applies Tweedie family distribution to the portfolio of lifetimes to induce the dependence between lives. Tweedie distribution is chosen since it contains symmetric and non-symmetric, as well as light-tailed and heavy-tailed distributions. Parameter estimation is modified in order to fit the Tweedie distribution to the data. This procedure is developed by using method of moments. In addition, the comparison stage is made to check for the adequacy between the observed mortality and expected mortality. Finally, the importance of including systematic mortality risk in the model is justified by the Pearson's chi-squared test. [ABSTRACT FROM AUTHOR]

Science, Technology, Engineering and Mathematics (STEM) research techniques and results are fundamental to the development of industrial innovation. Given the increasingly profound connection between innovation, science, and mathematical sciences, it is natural to inquire whether the interface between these three activities is functioning in an optimal way via STEM teachings and researches. We believe that these STEM teachings and researches are somewhat strengthened and essentially driven by industrial mathematics. However, due to the nature of industrial mathematics as an enabling technology for the new industry, its contribution is rarely visible in the final product that industry delivers. This paper will present the current scenario of this interface in Malaysia and to suggest mechanisms for intensifying the connection between industrial mathematics and industry. In particular we explore the degree of rapport between academia and industry, the contemporary trends in teachings and researches in the industrial mathematics, and to share the world wide experiences of the mutually beneficial relationship between industrial mathematicians and related STEM researchers in academia and industry. The paper will showcase the specific problem solving in collaboration with academics and industry practitioners during the Malaysian MISG 2011, 2014 and 2015. [ABSTRACT FROM AUTHOR]

Recently, crude oil price becomes volatile and have been the popular issue to be discussed in every country. Oil price fluctuations have major impact on the overall economy and finally will lead to increase in the inflation rate. It is important to describe these oil price fluctuations mathematically. This study aims to describe the above phenomena using geometric Brownian motion. Two crude oil prices, namely WTI and Brent have been analyzed based on daily oil price data from year 2000 until year 2015. Through the analysis using model assessment and model determination, crude oil price after year 2000 follows geometric Brownian motion process. We conclude that oil price fluctuations follow a geometric Brownian motion process without considering unexpected incidents. [ABSTRACT FROM AUTHOR]

Two-step method is introduced as an alternative method to classical methods in estimating the drift and diffusion parameters of the Stochastic Differential Equations (SDEs) models. Previous studies indicated that this method provides high percentage of accuracy of the estimated diffusion parameter of Lotka-Volterra model with simulated data. In this paper, a new improvement of two-step method is acquired to avoid the chosen of knots by applying Nadaraya- Watson kernel regression estimator in the first step of this method as a replacement of regression spline with truncated power series basis. The estimated parameters of Bachelier model by using modified two-step method are presented, including comparisons between two different kernel bandwidth methods, namely Asymptotic Mean Integrated Square Error (AMISE) for optimal bandwidth and Maximum Likelihood Cross-Validation (MLCV) technique. The performance of the new proposed method is evaluated with different number of sample sizes by using simulated data. Results indicate high percentage of accuracy of the estimated drift and estimated diffusion parameters of Bachelier model when AMISE for optimal bandwidth is applied compared to MLCV technique. [ABSTRACT FROM AUTHOR]

Riverbank filtration system is river water treatment approach based on natural removal of contaminants due to physical, chemical and biological processes. In this article, an analytical model is developed by using Green's function method to simulate the effects of pumping well and microbial activity that occurs in riverbed sediments on contaminant transport and evolution of water chemistry. The model is tested with data collected previously for RBF site in France. The results are compared with numerical simulation conducted in the literature by using finite difference method. Graphically, it is noticed that both numerical and analytical results have almost the same behavior. Also it is found that the model can simulate the decreasing of one pollutant concentration at the zone where the bacteria starts to consume this pollutant. [ABSTRACT FROM AUTHOR]

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution. [ABSTRACT FROM AUTHOR]

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits. [ABSTRACT FROM AUTHOR]

This paper proposes to investigate the interplay between time delay and external noise in explaining the behaviour of the microbial growth in batch fermentation process. Time delay and noise are modelled jointly via stochastic delay differential equations (SDDEs). The typical behaviour of cell concentration in batch fermentation process under this model is investigated. Milstein scheme is applied for solving this model numerically. Simulation results illustrate the effects of time delay and external noise in explaining the lag and stationary phases, respectively for the cell growth of fermentation process. [ABSTRACT FROM AUTHOR]

River pollution has been recognized as a contributor to a wide range of health problems and disorders in human. It can pose health dangers to humans who come into contact with it, either directly or indirectly. Therefore, it is most important to measure the concentration of Biochemical Oxygen Demand (BOD) as a water quality parameter since the parameter has long been the basic means for determining the degree of water pollution in rivers. In this study, BOD is used as a parameter to estimate the water quality at Sungai Perlis. It has been observed that Sungai Perlis is polluted due to lack of management and improper use of resources. Therefore, it is of importance to model the Sungai Perlis water quality in order to describe and predict the water quality systems. The BOD concentration secondary data set is used which was extracted from the Drainage and Irrigation Department Perlis State website. The first order differential equation from Streeter - Phelps model was utilized as a deterministic model. Then, the model was developed into a stochastic model. Results from this study shows that the stochastic model is more adequate to describe and predict the BOD concentration and the water quality systems in Sungai Perlis by having smaller value of mean squared error (MSE). [ABSTRACT FROM AUTHOR]

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well. [ABSTRACT FROM AUTHOR]

This paper studies the Ornstein-Uhlenbeck model that incorporates long memory stochastic volatility which is known as fractional Ornstein-Uhlenbeck model. The determination of the existence of long range dependence of the index prices of FTSE Bursa Malaysia KLCI is measured by the Hurst exponent. The empirical distribution of unobserved volatility is estimated using the particle filtering method. The performance between fractional Ornstein -Uhlenbeck and standard Ornstein -Uhlenbeck process had been compared. The mean square errors of the fractional Ornstein-Uhlenbeck model indicated that the model describes index prices better than the standard Ornstein-Uhlenbeck process. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits. [ABSTRACT FROM AUTHOR]

The paper considers the natural-gas storage valuation based on the information-based pricing framework of Brody-Hughston-Macrina (BHM). As opposed to many studies which the associated filtration is considered pre-specified, this work tries to construct the filtration in terms of the information provided to the market. The value of the storage is given by the sum of the discounted expectations of the cash flows under risk-neutral measure, conditional to the constructed filtration with the Brownian bridge noise term. In order to model the flow of information about the cash flows, we assume the existence of a fixed pricing kernel with liquid, homogenous and incomplete market without arbitrage. [ABSTRACT FROM AUTHOR]