Search results for: mixed variables

Authors: Autcha Araveeporn

Abstract:

The Random Coefficient Dynamic Regression (RCDR) model is to developed from Random Coefficient Autoregressive (RCA) model and Autoregressive (AR) model. The RCDR model is considered by adding exogenous variables to RCA model. In this paper, the concept of the Maximum Likelihood (ML) method is used to estimate the parameter of RCDR(1,1) model. Simulation results have shown the AIC and BIC criterion to compare the performance of the the RCDR(1,1) model. The variables as the stationary and weakly stationary data are good estimates where the exogenous variables are weakly stationary. However, the model selection indicated that variables are nonstationarity data based on the stationary data of the exogenous variables.

Keywords: Autoregressive, Maximum Likelihood Method, Nonstationarity, Random Coefficient Dynamic Regression, Stationary.

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Authors: Libin Wu, Bainian Li

Abstract:

In This Article We establish moment inequality of dependent random variables,furthermore some theorems of strong law of large numbers and complete convergence for sequences of dependent random variables. In particular, independent and identically distributed Marcinkiewicz Law of large numbers are generalized to the case of m0-dependent sequences.

Keywords: Lacunary System, Generalized Gaussian, NA sequences, strong law of large numbers.

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Authors: Jingbo Yang, Hong Li, Yang Liu, Siriguleng He

Abstract:

In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.

Keywords: Pseudo-hyperbolic partial integro-differential equations, Nonconforming mixed element method, Semilinear, Error estimates.

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Authors: A. S. Mousa, F. Shoman

Abstract:

We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Keywords: Coherent strategy, split strategy, pure strategy, mixed strategy, Nash Equilibrium, game theory.

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Authors: Areej R. Banjar, Abraham G. Campbell

Abstract:

The use of Mixed Reality (MR) in teaching and training is growing popular and can improve students’ ability to perform technical procedures. This paper outlines the creation of an interactive educational MR 3D application that aims to improve the quality of instruction for dentistry students. This application is called ”MR-Implantology” and aims to teach and train dentistry students on single dental implant placement. MR-Implantology uses cone-beam computed tomography (CBCT) images as the source for 3D dental models that dentistry students will be able to freely manipulate within a 3D MR world to aid their learning process.

Keywords: Cone-Beam Computed Tomography, dentistry education, implantology, Mixed Reality, MR.

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Authors: Pil Woo Heo

Abstract:

Water contains dissolved oxygen that a fish needs to breathe. It is important to increase the amounts of separation of dissolved oxygen from water for diverse applications using the separation system. In this paper, a separation system of dissolved gases from water concurrently variable mixed with the exhalations using a compressor is proposed. This system takes use of exhalations to increase the amounts of separation of dissolved oxygen from water. A compressor with variable off-time and on-time is used to control the exhalations mixed with inlet water. Exhalations contain some portion of carbon dioxide, oxygen, and nitrogen. Separation of dissolved gases containing dissolved oxygen is enhanced by using exhalations. The amounts of separation and the compositions of carbon dioxide and oxygen are measured. Higher amounts of separation can make the size of the separation device smaller, and then, application areas are diversified.

Keywords: Concurrently, variable mixed, exhalations, separation, hollow fiber.

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Authors: Sang Hwan Bak, Min Jung Kim, Dong Bok Lee

Abstract:

Fe-2%Mn-0.5%Si-0.2C steel was welded and corroded at 600, 700 and 800oC for 20 h in 1 atm of N2/H2S/H2O-mixed gas in order to characterize the high-temperature corrosion behavior of the welded joint. Corrosion proceeded fast and almost linearly. It increased with an increase in the corrosion temperature. H2S formed FeS owing to sulfur released from H2S. The scales were fragile and nonadherent.

Keywords: Fe-Mn-Si Steel, Corrosion, Welding, Sulfidation, H2S Gas.

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Authors: Thea Freese

Abstract:

Environmental legislation to protect North and Baltic Sea areas from harmful vessel-source emissions has received increased political attention in recent years. Legislative measures are expected to show positive effects on the health of the marine environment and society. At the same time, compliance might increase the costs to industry and have effects on freight rates and volumes shipped with potential negative repercussions on the environment. Building on an exploratory sequential mixed methods approach, this research project will study the economic effects of maritime environmental legislation in two phases. In Phase I, exploratory in-depth interviews were conducted with 12 experts from various stakeholder groups aiming at identifying variables influencing the relationship between environmental legislation, freight rates and volumes shipped. Influencing factors like compliance, enforcement and modal shift were identified and studied. Phase II will comprise of a quantitative study conducted with the aim of verifying the theory build in Phase I and quantifying economic effects of rules on shipping pollution. Research in this field might inform policy-makers about determinants of behaviour of ship operators in the face of the law and might further the development of a comprehensive legal system for marine environmental protection. At the present stage of research, first tentative results from the qualitative phase may be examined and open research questions to be addressed in the quantitative phase as well as possible research designs for phase II may be discussed. Input from other researchers will be highly valuable at this point.

Keywords: Clean shipping operations, compliance, maritime environmental legislation, maritime law and economics, mixed methods research, North and Baltic Sea area.

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Authors: Nur Irmawati, H.A. Mohammed

Abstract:

In the present study, mixed convection in a horizontal rectangular duct using Al2O3 is numerically investigated. The effects of different Rayleigh number, Reynolds number and radiation on flow and heat transfer characteristics are studied in detail. This study covers Rayleigh number in the range of 2 × 10^6 ≤ Ra ≤ 2 × 10^7 and Reynolds number in the range of 100 ≤ Re ≤ 1100. Results reveal that the Nusselt number increases as Reynolds and Rayleigh numbers increase. It is also found that the dimensionless temperature distribution increases as Rayleigh number increases.

Keywords: Numerical simulation, Mixed convection, Horizontal rectangular duct, Nanofluids.

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Authors: Chun-Ying Lee, Mei-Wen Wu, Li-Yi Cheng, Chiang-Ho Cheng

Abstract:

This research studies the electroplating of zinc coating in the zinc chloride bath mixed with supercritical CO2. The sodium fluoride (NaF) was used as the bath additive to change the structure and property of the coating, and therefore the roughness and corrosion resistance of the zinc coating was investigated. The surface characterization was performed using optical microscope (OM), X-ray diffractometer (XRD), and α-step profilometer. Moreover, the potentiodynamic polarization measurement in 3% NaCl solution was employed in the corrosion resistance evaluation. Because of the emulsification of the electrolyte mixed in Sc-CO2, the electroplated zinc produced the coating with smoother surface, smaller grain, better throwing power and higher corrosion resistance. The main role played by the NaF was to reduce the coating’s roughness and grain size. In other words, the CO2 mixed with the electrolyte under the supercritical condition performed the similar function as brighter and leveler in zinc electroplating to enhance the throwing power and corrosion resistance of the coating.

Keywords: Supercritical CO2, zinc-electroplating, sodium fluoride.

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Authors: Bassam Baroma

Abstract:

The main objective of this study is to test the relationship between numbers of variables representing the firm characteristics (market-related variables) and the extent of voluntary disclosure levels (forward-looking disclosure) in the annual reports of Egyptian firms listed on the Egyptian Stock Exchange. The results show that audit firm size is significantly positively correlated (in all the three years) with the level of forward-looking disclosure. However, industry type variable (which divided to: industries, cement, construction, petrochemicals and services), is found being insignificantly association with the level of forward-looking information disclosed in the annual reports for all the three years.

Keywords: Forward-looking disclosure, market-related variables, annual reports, Egyptian Stock Exchange.

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Authors: M. Cizmesija, N. Erjavec, V. Bahovec

Abstract:

While the European Union (EU) harmonized methodology is a benchmark of worldwide used business survey (BS) methodology, the choice of variables that are components of the confidence indicators, as the leading indicators, is not strictly determined and unique. Therefore, the aim of this paper is to investigate and to quantify the relationship between all business survey variables in manufacturing industry and industrial production as a reference macroeconomic series in Croatia. The assumption is that there are variables in the business survey, that are not components of Industrial Confidence Indicator (ICI) and which can accurately (and sometimes better then ICI) predict changes in Croatian industrial production. Empirical analyses are conducted using quarterly data of BS variables in manufacturing industry and Croatian industrial production over the period from the first quarter 2005 to the first quarter 2013. Research results confirmed the assumption: three BS variables which is not components of ICI (competitive position, demand and liquidity) are the best leading indicator then ICI, in forecasting changes in Croatian industrial production instantaneously, with one, two or three quarter ahead.

Keywords: Balance, Business Survey, Confidence Indicators, Industrial Production, Forecasting.

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Authors: M. R. Mustafa, M. H. Isa, R. B. Rezaur

Abstract:

The use of artificial neural network (ANN) modeling for prediction and forecasting variables in water resources engineering are being increasing rapidly. Infrastructural applications of ANN in terms of selection of inputs, architecture of networks, training algorithms, and selection of training parameters in different types of neural networks used in water resources engineering have been reported. ANN modeling conducted for water resources engineering variables (river sediment and discharge) published in high impact journals since 2002 to 2011 have been examined and presented in this review. ANN is a vigorous technique to develop immense relationship between the input and output variables, and able to extract complex behavior between the water resources variables such as river sediment and discharge. It can produce robust prediction results for many of the water resources engineering problems by appropriate learning from a set of examples. It is important to have a good understanding of the input and output variables from a statistical analysis of the data before network modeling, which can facilitate to design an efficient network. An appropriate training based ANN model is able to adopt the physical understanding between the variables and may generate more effective results than conventional prediction techniques.

Keywords: ANN, discharge, modeling, prediction, sediment,

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Authors: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

Abstract:

Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: J. Y. Woo, J. Lee, N. Kim, C.-S. Han

Abstract:

This paper reports on the enhanced photoluminescence (PL) of nanocomposites through the layered structuring of phosphor and quantum dot (QD). Green phosphor of Sr2SiO4:Eu, red QDs of CdSe/CdS/CdZnS/ZnS core-multishell, and thermo-curable resin were used for this study. Two kinds of composite (layered and mixed) were prepared, and the schemes for optical energy transfer between QD and phosphor were suggested and investigated based on PL decay characteristics. It was found that the layered structure is more effective than the mixed one in the respects of PL intensity, PL decay and thermal loss. When this layered nanocomposite (QDs on phosphor) is used to make white light emitting diode (LED), the brightness is increased by 37 %, and the color rendering index (CRI) value is raised to 88.4 compared to the mixed case of 80.4.

Keywords: Quantum Dot, Nanocomposites, Photoluminescence, Light Emitting Diode

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Authors: Zhanli Zhang, Wei Chen, Xin Jiang, Lili Ma, Shaoting Tang, Zhiming Zheng

Abstract:

A new class of percolation model in complex networks, in which nodes are characterized by hidden variables reflecting the properties of nodes and the occupied probability of each link is determined by the hidden variables of the end nodes, is studied in this paper. By the mean field theory, the analytical expressions for the phase of percolation transition is deduced. It is determined by the distribution of the hidden variables for the nodes and the occupied probability between pairs of them. Moreover, the analytical expressions obtained are checked by means of numerical simulations on a particular model. Besides, the general model can be applied to describe and control practical diffusion models, such as disease diffusion model, scientists cooperation networks, and so on.

Keywords: complex networks, percolation transition, hidden variable, occupied probability.

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Authors: Kureshi Abdul Kadir, Mohd. Hasan

Abstract:

Each new semiconductor technology node brings smaller transistors and wires. Although this makes transistors faster, wires get slower. In nano-scale regime, the standard copper (Cu) interconnect will become a major hurdle for FPGA interconnect due to their high resistivity and electromigration. This paper presents the comprehensive evaluation of mixed CNT bundle interconnects and investigates their prospects as energy efficient and high speed interconnect for future FPGA routing architecture. All HSPICE simulations are carried out at operating frequency of 1GHz and it is found that mixed CNT bundle implemented in FPGAs as interconnect can potentially provide a substantial delay and energy reduction over traditional interconnects at 32nm process technology.

Keywords: CMOS, Copper Interconnect, Mixed CNT Bundle Interconnect, FPGAs.

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Authors: M. Lloret-Climent, J. Nescolarde-Selva

Abstract:

The aim of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on a pre-designed algorithm and applying our interpretation of chaos theory developed in the context of General Systems Theory. This article sets out the causal relationships associated with tourist flows in order to enable the formulation of appropriate strategies. Our results can be applied to numerous cases. For example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups and to analyse tourist behaviour in terms of the most relevant variables. Unlike statistical analyses that merely provide information on current data, our method uses orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.

Keywords: Attractor, invariant set, orbits, tourist variables.

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Authors: W. Wongthatsanekorn, N. Matheekrieangkrai

Abstract:

This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: Bee Colony Optimization, Ready Mixed Concrete Problem.

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Authors: Tapano Kumar Hotta, S P Venkateshan

Abstract:

Steady state experiments have been conducted for natural and mixed convection heat transfer, from five different sized protruding discrete heat sources, placed at the bottom position on a PCB and mounted on a vertical channel. The characteristic length ( Lh ) of heat sources vary from 0.005 to 0.011 m. The study has been done for different range of Reynolds number and modified Grashof number. From the experiment, the surface temperature distribution and the Nusselt number of discrete heat sources have been obtained and the effects of Reynold number and Richardson number on them have been discussed. The objective is to find the rate of heat dissipation from heat sources, by placing them at the bottom position on a PCB and to compare both modes of cooling of heat sources.

Keywords: Discrete heat source, mixed convection, natural convection, vertical channel

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Authors: Wipada Ploysuksai, Pramoch Rangsunvigit, Santi Kulprathipanja

Abstract:

In this work, effects of catalysts (TiO2, and Nb2O5) were investigated on the hydrogen desorption of Mg(BH4)2. LiBH4 and MgCl2 with 2:1 molar ratio were mixed by using ball milling to prepare Mg(BH4)2. The desorption behaviors were measured by thermo-volumetric apparatus. The hydrogen desorption capacity of the mixed sample milled for 2 h was 4.78 wt% with a 2-step released. The first step occurred at 214 °C and the second step appeared at 374 °C. The addition of 16 wt% Nb2O5 decreased the desorption temperature in the second step about 66 °C and increased the hydrogen desorption capacity to 4.86 wt% hydrogen. The addition of TiO2 also improved the desorption temperature in the second step and the hydrogen desorption capacity. It decreased the desorption temperature about 71°C and showed a high amount of hydrogen, 5.27 wt%, released from the mixed sample. The hydrogen absorption after desorption of Mg(BH4)2 was also studied under 9.5 MPa and 350 °C for 12 h.

Keywords: hydrogen storage, LiBH4, metal hydride, Mg(BH4)2

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Authors: Y. Rathiranee, D. M. Semasinghe

Abstract:

This study attempts to identify the factors influencing on women empowerment of rural area in Sri Lanka through micro finance services. Data were collected from one hundred (100) rural women involving self-employment activities through a questionnaire using direct personal interviews. Judgment and Convenience Random sampling technique was used to select the sample size from three Divisional Secretariat divisions of Kandawalai, Poonakari and Karachchi in Kilinochchi District. The factor analysis was performed on fourteen (14) variables for screening and reducing the variables to identify the influencing factors on empowerment. Multiple regression analysis was used to identify the relationship between the three empowerment factors and the impact of micro finance on overall empowerment of rural women. The result of this study summarized the variables into three factors namely decision making, freedom to mobility and family support and which are positively associated with empowerment. In addition to this the value of adjusted R2 is 0.248 indicates that all the variables extracted can be explained 24.8% of the variation in the women empowerment through microfinance. Independent variables of these three factors have positive correlation with women empowerment as well as significant values at 5 percent level.

Keywords: Influencing factors, Micro finance, rural women and women empowerment.

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Authors: Xiaomei Wang, Shouming Zhong

Abstract:

In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.

Keywords: Bi-directional associative memory (BAM) neural networks, mixed delays, Lyapunov stability theory, contraction mapping theorem, existence, equilibrium, globally exponential stability.

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Authors: Arash Karimipour, M. Afrand, M. M. Bazofti

Abstract:

The periodic mixed convection of a water-copper nanofluid inside a rectangular cavity with aspect ratio of 3 is investigated numerically. The temperature of the bottom wall of the cavity is assumed greater than the temperature of the top lid which oscillates horizontally with the velocity defined as u = u0 sin (ω t). The effects of Richardson number, Ri, and volume fraction of nanoparticles on the flow and thermal behavior of the nanofluid are investigated. Velocity and temperature profiles, streamlines and isotherms are presented. It is observed that when Ri < 1, heat transfer rate is much greater than when Ri > 1. The higher value of Ri corresponds to a lower value of the amplitude of the oscillation of Num in the steady periodic state. Moreover, increasing the volume fraction of the nanoparticles increases the heat transfer rate.

Keywords: Nanofluid, Top lid oscillation, Mixed convection, Volume fraction

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Authors: Snezhana G. Gocheva-Ilieva, Maya P. Stoimenova

Abstract:

Ambient air pollution with fine particulate matter (PM10) is a systematic permanent problem in many countries around the world. The accumulation of a large number of measurements of both the PM10 concentrations and the accompanying atmospheric factors allow for their statistical modeling to detect dependencies and forecast future pollution. This study applies the classification and regression trees (CART) method for building and analyzing PM10 models. In the empirical study, average daily air data for the city of Pleven, Bulgaria for a period of 5 years are used. Predictors in the models are seven meteorological variables, time variables, as well as lagged PM10 variables and some lagged meteorological variables, delayed by 1 or 2 days with respect to the initial time series, respectively. The degree of influence of the predictors in the models is determined. The selected best CART models are used to forecast future PM10 concentrations for two days ahead after the last date in the modeling procedure and show very accurate results.

Keywords: Cross-validation, decision tree, lagged variables, short-term forecasting.

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Authors: R. Rajendiran, S. Gayathri devi, B.T. SureshKumar, V. Arul Priya

Abstract:

Plackett-Burman statistical screening of media constituents and operational conditions for extracellular lipase production from isolate Trichoderma viride has been carried out in submerged fermentation. This statistical design is used in the early stages of experimentation to screen out unimportant factors from a large number of possible factors. This design involves screening of up to 'n-1' variables in just 'n' number of experiments. Regression coefficients and t-values were calculated by subjecting the experimental data to statistical analysis using Minitab version 15. The effects of nine process variables were studied in twelve experimental trials. Maximum lipase activity of 7.83 μmol /ml /min was obtained in the 6th trail. Pareto chart illustrates the order of significance of the variables affecting the lipase production. The present study concludes that the most significant variables affecting lipase production were found to be palm oil, yeast extract, K2HPO4, MgSO4 and CaCl2.

Keywords: lipase, submerged fermentation, statistical optimization, Trichoderma viride

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Authors: Z. Sadeghi, M. R. Omidkhah, M. E. Masoomi

Abstract:

The purpose of this paper is to examine gas transport behavior of mixed matrix membranes (MMMs) combined with porous particles. Main existing models are categorized in two main groups; two-phase (ideal contact) and three-phase (non-ideal contact). A new coefficient, J, was obtained to express equations for estimating effect of the particle porosity in two-phase and three-phase models. Modified models evaluates with existing models and experimental data using Matlab software. Comparison of gas permeability of proposed modified models with existing models in different MMMs shows a better prediction of gas permeability in MMMs.

Keywords: Mixed Matrix Membrane, Permeation Models, Porous particles, Porosity.

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Authors: Akinola Ikudayisi, Josiah Adeyemo

Abstract:

The correct estimation of reference evapotranspiration (ETₒ) is required for effective irrigation water resources planning and management. However, there are some variables that must be considered while estimating and modeling ETₒ. This study therefore determines the multivariate analysis of correlated variables involved in the estimation and modeling of ETₒ at Vaalharts irrigation scheme (VIS) in South Africa using Principal Component Analysis (PCA) technique. Weather and meteorological data between 1994 and 2014 were obtained both from South African Weather Service (SAWS) and Agricultural Research Council (ARC) in South Africa for this study. Average monthly data of minimum and maximum temperature (°C), rainfall (mm), relative humidity (%), and wind speed (m/s) were the inputs to the PCA-based model, while ETₒ is the output. PCA technique was adopted to extract the most important information from the dataset and also to analyze the relationship between the five variables and ETₒ. This is to determine the most significant variables affecting ETₒ estimation at VIS. From the model performances, two principal components with a variance of 82.7% were retained after the eigenvector extraction. The results of the two principal components were compared and the model output shows that minimum temperature, maximum temperature and windspeed are the most important variables in ETₒ estimation and modeling at VIS. In order words, ETₒ increases with temperature and windspeed. Other variables such as rainfall and relative humidity are less important and cannot be used to provide enough information about ETₒ estimation at VIS. The outcome of this study has helped to reduce input variable dimensionality from five to the three most significant variables in ETₒ modelling at VIS, South Africa.

Keywords: Irrigation, principal component analysis, reference evapotranspiration, Vaalharts.

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Authors: Javier Rivas, Olga Gimeno, Maria Carbajo, Teresa Borralho

Abstract:

Potassium monopersulfate has been decomposed in aqueous solution in the presence of Co(II). The effect of the main operating variables has been assessed. Minimum variations in pH exert a considerable influence on the process kinetics. Thus, when no pH adjustment is considered, the actual effect of variables like initial monopersulfate and/or catalyst concentration may be hindered. As expected, temperature enhances the monopersulfate decomposition rate by following the Arrhenius law. The activation energy in the proximity of 85 kJ/mol has been obtained. Amongst the different solids tested in the monopersulfate decomposition, only the perovskite LaTi0.15Cu0.85O3 has shown a significant catalytic activity.

Keywords: Monopersulfate, Oxone®, Sulfate radicals, Watertreatment.

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Authors: Roghayyeh Motallebzadeh, Shahin Hajizadeh, Mohammad Reza Ghasemi

Abstract:

Laminar mixed Convection heat transfer of a nanofluid with prescribed constant heat flux on the inner wall of horizontal annular tube has been studied numerically based on two-phase mixture model in different Rayleigh Numbers and Azimuth angles. Effects of applying of different volume fractions of Al₂O₃ nanoparticles in water as a base fluid on hydrodynamic and thermal behaviors of the fluid flow such as axial velocity, secondary flow, temperature, heat transfer coefficient and friction coefficient at the inner and outer wall region, has been investigated. Conservation equations in elliptical form has been utilized and solved in three dimensions for a steady flow. It is observed that, there is a good agreement between results in this work and previously published experimental and numerical works on mixed convection in horizontal annulus. These particles cause to increase convection heat transfer coefficient of the fluid, meanwhile there is no considerable effect on friction coefficient.

Keywords: Buoyancy force, Laminar mixed convection, Mixture model, Nanofluid, Two-phase.

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