Search results for: model of foot size.

Authors: Shih-Ching Lo

Abstract:

Discrete choice model is the most used methodology for studying traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. In this study, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, different models are compared so as to propose the best one. From the results, systematic equations forecast better than single equation do. Models with the external variable, which is oil price, are better than models based on closed system assumption.

Keywords: forecasting, passenger volume, dynamic competition model, external variable, oil price

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Authors: I. Zohourkari, M. Zohoor

Abstract:

In this paper, an erosion-based model for abrasive waterjet (AWJ) turning process is presented. By using modified Hashish erosion model, the volume of material removed by impacting of abrasive particles to surface of the rotating cylindrical specimen is estimated and radius reduction at each rotation is calculated. Different to previous works, the proposed model considers the continuous change in local impact angle due to change in workpiece diameter, axial traverse rate of the jet, the abrasive particle roundness and density. The accuracy of the proposed model is examined by experimental tests under various traverse rates. The final diameters estimated by the proposed model are in good accordance with experiments.

Keywords: Abrasive, Erosion, impact, Particle, Waterjet, Turning.

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Authors: Yan Shuang Zhang, Taehan Lee, Byung Ho Jeong

Abstract:

A DEA model can generally evaluate the performance using multiple inputs and outputs for the same period. However, it is hard to avoid the production lead time phenomenon some times, such as long-term project or marketing activity. A couple of models have been suggested to capture this time lag issue in the context of DEA. This paper develops a dual-MPO model to deal with time lag effect in evaluating efficiency. A numerical example is also given to show that the proposed model can be used to get efficiency and reference set of inefficient DMUs and to obtain projected target value of input attributes for inefficient DMUs to be efficient.

Keywords: DEA, efficiency, time lag, dual problem.

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Authors: P. Pongsumpun

Abstract:

One of the important tropical diseases is Chikunkunya. This disease is transmitted between the human by the insect-borne virus, of the genus Alphavirus. It occurs in Africa, Asia and the Indian subcontinent. In Thailand, the incidences due to this disease are increasing every year. In this study, the transmission of this disease is studied through dynamical model analysis.

Keywords: Chikunkunya, dynamical model, Endemic region, Routh-Hurwitz criteria.

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Authors: I. A. Farhat

Abstract:

The problem of optimal planning of multiple sources of distributed generation (DG) in distribution networks is treated in this paper using an improved Ant Colony Optimization algorithm (ACO). This objective of this problem is to determine the DG optimal size and location that in order to minimize the network real power losses. Considering the multiple sources of DG, both size and location are simultaneously optimized in a single run of the proposed ACO algorithm. The various practical constraints of the problem are taken into consideration by the problem formulation and the algorithm implementation. A radial power flow algorithm for distribution networks is adopted and applied to satisfy these constraints. To validate the proposed technique and demonstrate its effectiveness, the well-know 69-bus feeder standard test system is employed.cm.

Keywords: About Ant Colony Optimization (ACO), Distributed Generation (DG).

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Authors: Nam Lethanh, Bryan T. Adey

Abstract:

In this paper, the potential use of an exponential hidden Markov model to model a hidden pavement deterioration process, i.e. one that is not directly measurable, is investigated. It is assumed that the evolution of the physical condition, which is the hidden process, and the evolution of the values of pavement distress indicators, can be adequately described using discrete condition states and modeled as a Markov processes. It is also assumed that condition data can be collected by visual inspections over time and represented continuously using an exponential distribution. The advantage of using such a model in decision making process is illustrated through an empirical study using real world data.

Keywords: Deterioration modeling, Exponential distribution, Hidden Markov model, Pavement management

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Authors: Julio Kauss, Miguel Cadillo, David Mauricio

Abstract:

E-commerce is a business model that allows companies to optimize the processes of buying, selling, transferring goods and exchanging services through computer networks or the Internet. In Peru, the electronic commerce is used infrequently. This situation is due, in part to the fact that there is no model that allows companies to implement an e-commerce solution, which means that most SMEs do not have adequate knowledge to adapt to electronic commerce. In this work, a reference model is proposed for the implementation of an e-commerce solution in Peruvian SMEs in the retail sector. It consists of five phases: Business Analysis, Business Modeling, Implementation, Post Implementation and Results. The present model was validated in a SME of the Peruvian retail sector through the implementation of an electronic commerce platform, through which the company increased its sales through the delivery channel by 10% in the first month of deployment. This result showed that the model is easy to implement, is economical and agile. In addition, it allowed the company to increase its business offer, adapt to e-commerce and improve customer loyalty.

Keywords: E-commerce, retail, SMEs, reference model.

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Authors: A. Brinda Lakshmi, J. Lakshmi Priya

Abstract:

Cantaloupes (muskmelon and watermelon) contain biologically active molecules such as carotenoids which are natural pigments used as food colorants and afford health benefits. ß-carotene is the major source of carotenoids present in muskmelon and watermelon shell. Carotenoids were extracted using Microwave assisted extraction (MAE) and Ultrasound assisted extraction (UAE) utilising organic lipophilic solvents such as acetone, methanol, and hexane. Extraction conditions feed-solvent ratio, microwave power, ultrasound frequency, temperature and particle size were varied and optimized. It was found that the yield of carotenoids was higher using UAE than MAE, and muskmelon had the highest yield of carotenoids when was ethanol used as a solvent for 0.5 mm particle size.

Keywords: Carotenoids, extraction, muskmelon shell, watermelon shell.

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Authors: Reza Sirjani, Nobosse Tafem Bolan

Abstract:

Many optimization techniques available in the literature have been developed in order to solve the problem of voltage stability enhancement in power systems. However, there are a number of drawbacks in the use of previous techniques aimed at determining the optimal location and size of reactive compensators in a network. In this paper, an Improved Cuckoo Search algorithm is applied as an appropriate optimization algorithm to determine the optimum location and size of a Static Var Compensator (SVC) in a transmission network. The main objectives are voltage stability improvement and total cost minimization. The results of the presented technique are then compared with other available optimization techniques.

Keywords: Cuckoo search algorithm, optimization, power system, var compensators, voltage stability.

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Authors: I. Grigoraviciute-Puroniene, K. Tsuru, E. Garskaite, Z. Stankeviciute, A. Beganskiene, K. Ishikawa, A. Kareiva

Abstract:

Tricalcium phosphate (β-Ca₃(PO₄)₂, β-TCP) powders were synthesized using wet polymeric precipitation method for the first time to our best knowledge. The results of X-ray diffraction analysis showed the formation of almost single a Ca-deficient hydroxyapatite (CDHA) phase of a poor crystallinity already at room temperature. With continuously increasing the calcination temperature up to 800 °C, the crystalline β-TCP was obtained as the main phase. It was demonstrated that infrared spectroscopy is very effective method to characterize the formation of β-TCP. The SEM results showed that β-TCP solids were homogeneous having a small particle size distribution. The β-TCP powders consisted of spherical particles varying in size from 100 to 300 nm. Fabricated β-TCP specimens were placed to the bones of the rats and maintained for 1-2 months.

Keywords: β-TCP, bone regeneration, wet chemical processing, polymeric precipitation.

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Authors: Jana P. Vejpravova, Daniel Niznansky, Vaclav Vales, Barbara Bittova, Vaclav Tyrpekl, Stanislav Danis, Vaclav Holy, Stephen Doyle

Abstract:

The aim of our work is to study phase composition, particle size and magnetic response of Fe2O3/TiO2 nanocomposites with respect to the final annealing temperature. Those nanomaterials are considered as smart catalysts, separable from a liquid/gaseous phase by applied magnetic field. The starting product was obtained by an ecologically acceptable route, based on heterogeneous precipitation of the TiO2 on modified g-Fe2O3 nanocrystals dispersed in water. The precursor was subsequently annealed on air at temperatures ranging from 200 oC to 900 oC. The samples were investigated by synchrotron X-ray powder diffraction (S-PXRD), magnetic measurements and Mössbauer spectroscopy. As evidenced by S-PXRD and Mössbauer spectroscopy, increasing the annealing temperature causes evolution of the phase composition from anatase/maghemite to rutile/hematite, finally above 700 oC the pseudobrookite (Fe2TiO5) also forms. The apparent particle size of the various Fe2O3/TiO2 phases has been determined from the highquality S-PXRD data by using two different approaches: the Rietveld refinement and the Debye method. Magnetic response of the samples is discussed in considering the phase composition and the particle size.

Keywords: X-ray diffraction, profile analysis, Mössbauer spectroscopy, magnetic properties, TiO2, Fe2O3, Fe2TiO5

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Authors: Do-Jin Jang, Sung-Ah Kim

Abstract:

In designing a kinetic façade, it is hard for the designer to make digital models due to its complex geometry with motion. This paper aims to present a methodology of converting a point cloud of a physical model into a single digital model with a certain topology and motion. The method uses a Microsoft Kinect sensor, and color markers were defined and applied to three paper folding-inspired designs. Although the resulted digital model cannot represent the whole folding range of the physical model, the method supports the designer to conduct a performance-oriented design process with the rough physical model in the reduced folding range.

Keywords: Design media, kinetic façades, tangible user interface, 3D scanning.

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Authors: Faraj El Dabee, Romeo Marian, Yousef Amer

Abstract:

This paper implements the inventory model developed in the first part of this paper in a simplified problem to simultaneously reduce costs and risks in JIT systems. This model is developed to ascertain an optimal ordering strategy for procuring raw materials by using regular multi-external and local backup suppliers to reduce the total cost of the products, and at the same time to reduce the risks arising from this cost reduction within production systems. A comparison between the cost of using the JIT system and using the proposed inventory model shows the superiority of the use of the inventory model.

Keywords: Lean manufacturing, Just-in-Time (JIT), production system, cost-risk reduction, inventory model, eternal supplier, local backup supplier.

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Authors: M. Sedighizadeh, M. Rezaei, V. Najmi

Abstract:

The Proton Exchange Membrane Fuel Cell (PEMFC) control system has an important effect on operation of cell. Traditional controllers couldn-t lead to acceptable responses because of time- change, long- hysteresis, uncertainty, strong- coupling and nonlinear characteristics of PEMFCs, so an intelligent or adaptive controller is needed. In this paper a neural network predictive controller have been designed to control the voltage of at the presence of fluctuations of temperature. The results of implementation of this designed NN Predictive controller on a dynamic electrochemical model of a small size 5 KW, PEM fuel cell have been simulated by MATLAB/SIMULINK.

Keywords: PEMFC, Neural Network, Predictive Control..

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Authors: Liew Yee Ping, Pang Ying Han, Lau Siong Hoe, Ooi Shih Yin, Housam Khalifa Bashier Babiker

Abstract:

In face recognition, feature extraction techniques attempts to search for appropriate representation of the data. However, when the feature dimension is larger than the samples size, it brings performance degradation. Hence, we propose a method called Normalization Discriminant Independent Component Analysis (NDICA). The input data will be regularized to obtain the most reliable features from the data and processed using Independent Component Analysis (ICA). The proposed method is evaluated on three face databases, Olivetti Research Ltd (ORL), Face Recognition Technology (FERET) and Face Recognition Grand Challenge (FRGC). NDICA showed it effectiveness compared with other unsupervised and supervised techniques.

Keywords: Face recognition, small sample size, regularization, independent component analysis.

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Authors: Steven W. Carruthers

Abstract:

The purpose of the present research is to equate two test forms as part of a study to evaluate the educational effectiveness of the ARTé: Mecenas art history learning game. The researcher applied Item Response Theory (IRT) procedures to calculate item, test, and mean-sigma equating parameters. With the sample size n=134, test parameters indicated “good” model fit but low Test Information Functions and more acute than expected equating parameters. Therefore, the researcher applied equipercentile equating and linear equating to raw scores and compared the equated form parameters and effect sizes from each method. Item scaling in IRT enables the researcher to select a subset of well-discriminating items. The mean-sigma step produces a mean-slope adjustment from the anchor items, which was used to scale the score on the new form (Form R) to the reference form (Form Q) scale. In equipercentile equating, scores are adjusted to align the proportion of scores in each quintile segment. Linear equating produces a mean-slope adjustment, which was applied to all core items on the new form. The study followed a quasi-experimental design with purposeful sampling of students enrolled in a college level art history course (n=134) and counterbalancing design to distribute both forms on the pre- and posttests. The Experimental Group (n=82) was asked to play ARTé: Mecenas online and complete Level 4 of the game within a two-week period; 37 participants completed Level 4. Over the same period, the Control Group (n=52) did not play the game. The researcher examined between group differences from post-test scores on test Form Q and Form R by full-factorial Two-Way ANOVA. The raw score analysis indicated a 1.29% direct effect of form, which was statistically non-significant but may be practically significant. The researcher repeated the between group differences analysis with all three equating methods. For the IRT mean-sigma adjusted scores, form had a direct effect of 8.39%. Mean-sigma equating with a small sample may have resulted in inaccurate equating parameters. Equipercentile equating aligned test means and standard deviations, but resultant skewness and kurtosis worsened compared to raw score parameters. Form had a 3.18% direct effect. Linear equating produced the lowest Form effect, approaching 0%. Using linearly equated scores, the researcher conducted an ANCOVA to examine the effect size in terms of prior knowledge. The between group effect size for the Control Group versus Experimental Group participants who completed the game was 14.39% with a 4.77% effect size attributed to pre-test score. Playing and completing the game increased art history knowledge, and individuals with low prior knowledge tended to gain more from pre- to post test. Ultimately, researchers should approach test equating based on their theoretical stance on Classical Test Theory and IRT and the respective  assumptions. Regardless of the approach or method, test equating requires a representative sample of sufficient size. With small sample sizes, the application of a range of equating approaches can expose item and test features for review, inform interpretation, and identify paths for improving instruments for future study.

Keywords: Effectiveness, equipercentile equating, IRT, learning games, linear equating, mean-sigma equating.

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Authors: Yan Rongxin, Sun Wei, Li Weidan

Abstract:

Based on the acoustics cascade sound theory, the mechanism of air leak sound producing, transmitting and signal detecting has been analyzed. A formula of the sound power, leak size and air pressure in the spacecraft has been built, and the relationship between leak sound pressure and receiving direction and distance has been studied. The center frequency in millimeter diameter leak is more than 20 kHz. The situation of air leaking from spacecraft to space has been simulated and an experiment of different leak size and testing distance and direction has been done. The sound pressure is in direct proportion to the cosine of the angle of leak to sensor. The portable ultrasonic leak detector has been developed, whose minimal leak rate is 10^-1 Pa·m³/s, the testing radius is longer than 20 mm, the mass is less than 1.0 kg, and the electric power is less than 2.2 W.

Keywords: Leak detection, manned spacecraft, ultrasonic, sound transmitting.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová

Abstract:

The article presents two mathematical models of the interaction between a rotating shaft and an incompressible fluid. The mathematical model includes both the journal bearings and the axially traversed hydrodynamic sealing gaps of hydraulic machines. A method is shown for the identification of additional effects of the fluid acting on the rotor of the machine, both for a linear and a nonlinear model. The interaction is expressed by matrices of mass, stiffness and damping.

Keywords: CFD modeling, hydrodynamic gap, matrices of mass, stiffness and damping, nonlinear mathematical model.

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Authors: Linda, Sau-ling Lai

Abstract:

This paper adopts a notion of expectation-perception gap of systems users as information systems (IS) failure. Problems leading to the expectation-perception gap are identified and modelled as five interrelated discrepancies or gaps throughout the process of information systems development (ISD). It describes an empirical study on how systems developers and users perceive the size of each gap and the extent to which each problematic issue contributes to the gap. The key to achieving success in ISD is to keep the expectationperception gap closed by closing all 5 pertaining gaps. The gap model suggests that most factors in IS failure are related to organizational, cognitive and social aspects of information systems design. Organization requirement analysis, being the weakest link of IS development, is particularly worthy of investigation.

Keywords: Information Systems Development, Expectation- Perception Gap, Gap Analysis, Organization Analysis.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: Multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, Importance sampling, approximate posterior distribution, Marginal likelihood evidence.

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Authors: H.Hosseini, A.A. Azemati

Abstract:

The fundamental defect inherent to the thermoforming technology is wall-thickness variation of the products due to inadequate thermal processing during production of polymer. A nonlinear viscoelastic rheological model is implemented for developing the process model. This model describes deformation process of a sheet in thermoforming process. Because of relaxation pause after plug-assist stage and also implementation of two stage thermoforming process have minor wall-thickness variation and consequently better mechanical properties of polymeric articles. For model validation, a comparative analysis of the theoretical and experimental data is presented.

Keywords: High-quality polymeric article, Thermal Processing, Rheological model, Minor wall-thickness variation.

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Authors: Pankaj Dutta, Debjani Chakraborty

Abstract:

This paper investigates the effect of product substitution in the single-period 'newsboy-type' problem in a fuzzy environment. It is supposed that the single-period problem operates under uncertainty in customer demand, which is described by imprecise terms and modelled by fuzzy sets. To perform this analysis, we consider the fuzzy model for two-item with upward substitution. This upward substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. We show that the explicit consideration of this substitution opportunity increase the average expected profit. Computational study is performed to observe the benefits of product's substitution.

Keywords: Fuzzy demand, Newsboy, Single-period problem, Substitution.

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Authors: Dahlila Kamat, Ismail Mohd Saaid, Iskandar Dzulkarnain

Abstract:

This paper presents a review on published literature and experimental works on local sands for possible use as proppant, specifically those from Terengganu coastal area. This includes examination on characteristics of sand samples and selection of experiments for proppant testing. Sand samples from identified areas were tested according to particle size distribution, density, roundness and sphericity, turbidity and mineralogy. Results from sand samples were compared against proppant specifications set by API RP 56 and selected commercial proppants. The present study found that the size distribution, sphericity, turbidity and bulk density of Terengganu sands are at par with some of commercial proppants. Nevertheless, Terengganu sand samples do not completely surpass the required roundness for use as proppant.

Keywords: Hydraulic fracturing, Malaysia sand, proppant, wellstimulation.

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Authors: Olga Novikova, Timo Vuori

Abstract:

This paper describes topology of business models in market ecosystem of the emerging electric mobility industry. The business model topology shows that firm-s participation in the ecosystem is associated with different requirements on resources and capabilities, and different levels of risk. Business model concept is used together with concepts of networked value creation and shows that firms can achieve higher levels of sustainable advantage by cooperation, not competition. Hybrid business models provide companies a viable alternative possibility for participation in the market ecosystem.

Keywords: Business model, ecosystem, topology.

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Authors: L. Dzierzbicka-Głowacka, M. Janecki

Abstract:

Seasonal variability of nutrients concentration in the Baltic Sea using the 3D ecosystem numerical model 3D-CEMBS has been investigated. Additionally this study shows horizontal and vertical distribution of nutrients in the Baltic Sea. Model domain is an extended Baltic Sea area divided into 600x640 horizontal grid cells. Aside from standard hydrodynamic parameters 3D-CEMBS produces modeled ecological variables such as: three types of phytoplankton, two detrital classes, dissolved oxygen and the nutrients (nitrate, ammonium, phosphate and silicate). The presented model allows prediction of parameters that describe distribution of nutrients concentration and phytoplankton biomass. 3D-CEMBS can be used to study the effect of different hydrodynamic and biogeochemical processes on distributions of these variables in a larger scale.

Keywords: ecosystem model, nutrients, Baltic Sea

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Authors: Yuan-Jye Tseng, Yi-Shiuan Chen

Abstract:

The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.

Keywords: Closed-loop design, closed-loop supply chain, design evaluation, mathematical model, supply chain management, sustainable design model.

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Authors: Tohru Kawabe

Abstract:

In this paper, a new model predictive PID controller design method for the slip suppression control of EVs (electric vehicles) is proposed. The proposed method aims to improve the maneuverability and the stability of EVs by controlling the wheel slip ratio. The optimal control gains of PID framework are derived by the model predictive control (MPC) algorithm. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: Model Predictive Control, PID controller, Electric Vehicle, Slip suppression

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Authors: Hsiao-Tien Pao, Yi-Ying Li, Hsin-Chia Fu

Abstract:

This paper addressed the impacts of energy consumption, economic growth, financial development, and population size on environmental degradation using grey relational analysis (GRA) for China, where foreign direct investment (FDI) inflows is the proxy variable for financial development. The more recent historical data during the period 2004–2011 are used, because the use of very old data for data analysis may not be suitable for rapidly developing countries. The results of the GRA indicate that the linkage effects of energy consumption–emissions and GDP–emissions are ranked first and second, respectively. These reveal that energy consumption and economic growth are strongly correlated with emissions. Higher economic growth requires more energy consumption and increasing environmental pollution. Likewise, more efficient energy use needs a higher level of economic development. Therefore, policies to improve energy efficiency and create a low-carbon economy can reduce emissions without hurting economic growth. The finding of FDI–emissions linkage is ranked third. This indicates that China do not apply weak environmental regulations to attract inward FDI. Furthermore, China’s government in attracting inward FDI should strengthen environmental policy. The finding of population–emissions linkage effect is ranked fourth, implying that population size does not directly affect CO₂ emissions, even though China has the world’s largest population, and Chinese people are very economical use of energy-related products. Overall, the energy conservation, improving efficiency, managing demand, and financial development, which aim at curtailing waste of energy, reducing both energy consumption and emissions, and without loss of the country’s competitiveness, can be adopted for developing economies. The GRA is one of the best way to use a lower data to build a dynamic analysis model.

Keywords: Grey relational analysis, foreign direct investment, CO2 emissions, China.

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Authors: Maryam Jamela Ismail, Rosdiazli Ibrahim, Idris Ismail

Abstract:

In the oil and gas industry, energy prediction can help the distributor and customer to forecast the outgoing and incoming gas through the pipeline. It will also help to eliminate any uncertainties in gas metering for billing purposes. The objective of this paper is to develop Neural Network Model for energy consumption and analyze the performance model. This paper provides a comprehensive review on published research on the energy consumption prediction which focuses on structures and the parameters used in developing Neural Network models. This paper is then focused on the parameter selection of the neural network prediction model development for energy consumption and analysis on the result. The most reliable model that gives the most accurate result is proposed for the prediction. The result shows that the proposed neural network energy prediction model is able to demonstrate an adequate performance with least Root Mean Square Error.

Keywords: Energy Prediction, Multilayer Feedforward, Levenberg-Marquardt, Root Mean Square Error (RMSE)

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Authors: Dongdong Zhang, Deran Zhang

Abstract:

In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

Keywords: Risk model, ruin probability, Markov jump process, integral equation.

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