Search results for: time series modeling.

Authors: Mark Rousell, Di Catherwood, Graham Edgar

Abstract:

The main issue of interest here is whether individuals who differ in arithmetical reasoning ability and levels of imagery ability display different brain activity during the conduct of mental arithmetical reasoning tasks. This was a case study of four participants who represented four extreme combinations of Maths –Imagery abilities: ie., low-low, high-high, high-low, low-high respectively. As the Ps performed a series of 60 arithmetical reasoning tasks, 128-channel EEG recordings were taken and the pre-response interval subsequently analysed using EGI GeosourceTM software. The P who was high in both imagery and maths ability showed peak activity prior to response in BA7 (superior parietal cortex) but other Ps did not show peak activity in this region. The results are considered in terms of the diverse routes that may be employed by individuals during the conduct of arithmetical reasoning tasks and the possible implications of this for mathematics education.

Keywords: Arithmetic, imagery, EEG, education.

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Authors: Y. Madani, H. Achache, B. Boutabout

Abstract:

The purpose of this paper is to analyze numerically by the three-dimensional finite element method, using ABAQUS calculation code, the mechanical behavior of a unidirectional and multidirectional delaminated stratified composite under mechanical loading in Mode II. This study consists of the determination of the energy release rate G in mode II as well as the distribution of equivalent von Mises stresses along the damaged zone by varying several parameters such as the applied load and the delamination length. It allowed us to deduce that the high energy release rate favors delamination at the free edges of a stratified plate subjected to bending.

Keywords: Delamination, energy release rate, finite element method, stratified composite.

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Authors: Wenhua Hou, Xing Liu, Deqiang Chen

Abstract:

The ubiquitous payment problems within construction industry of China are notoriously hard to be resolved, thus lead to a series of impacts to the industry chain. Among of them, the most direct result is affecting the normal operation of contractors negatively. A wealth of research has already discussed reasons of the payment problems by introducing a number of possible improvement strategies. But the causalities of these problems are still far from harsh reality. In this paper, the authors propose a model for cash flow system of construction projects by introducing System Dynamics techniques to explore causal facets of the payment problem. The effects of payment arrears on both cash flow and profitability of project are simulated into four scenarios by using data from real projects. Simulating results show visible clues to help contractors quantitatively determining the consequences for the construction project that arise from payment delay.

Keywords: payment problems, cash flow, profitability, system dynamics.

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Authors: Sh. Shahhosseini, S. Alinia, M. Irani

Abstract:

In this work, axisymetric CFD simulation of fixed bed GTL reactor has been conducted, using computational fluid dynamics (CFD). In fixed bed CFD modeling, when N (tube-to-particle diameter ratio) has a large value, it is common to consider the packed bed as a porous media. Synthesis gas (a mixture of predominantly carbon monoxide and hydrogen) was fed to the reactor. The reactor length was 20 cm, divided to three sections. The porous zone was in the middle section of the reactor. The model equations were solved employing finite volume method. The effects of particle diameter, bed voidage, fluid velocity and bed length on pressure drop have been investigated. Simulation results showed these parameters could have remarkable impacts on the reactor pressure drop.

Keywords: GTL Process, Fixed bed reactor, Pressure drop, CFDsimulation.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Neural networks, stochastic, PTH moment stable, time varying delays, distributed delays.

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Authors: Ioannis P. Panapakidis, Marios N. Moschakis

Abstract:

With the continuous increment of smart meter installations across the globe, the need for processing of the load data is evident. Clustering-based load profiling is built upon the utilization of unsupervised machine learning tools for the purpose of formulating the typical load curves or load profiles. The most commonly used algorithm in the load profiling literature is the K-means. While the algorithm has been successfully tested in a variety of applications, its drawback is the strong dependence in the initialization phase. This paper proposes a novel modified form of the K-means that addresses the aforementioned problem. Simulation results indicate the superiority of the proposed algorithm compared to the K-means.

Keywords: Clustering, load profiling, load modeling, machine learning, energy efficiency and quality.

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Authors: László Lengyel, Tihamér Levendovszky, Hassan Charaf

Abstract:

This paper presents the visual control flow support of Visual Modeling and Transformation System (VMTS), which facilitates composing complex model transformations out of simple transformation steps and executing them. The VMTS Visual Control Flow Language (VCFL) uses stereotyped activity diagrams to specify control flow structures and OCL constraints to choose between different control flow branches. This work discusses the termination properties of VCFL and provides an algorithm to support the termination analysis of VCFL transformations.

Keywords: Control Flow, Metamodel-Based Visual Model Transformation, OCL, Termination Properties, UML.

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Authors: V.P.Subramanyam Rallabandi, S.K.Sett

Abstract:

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to textures, the algorithm can learn basis functions for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised texture classification and segmentation.

Keywords: Gaussian Mixture Model, Independent Component Analysis, Segmentation, Unsupervised Classification.

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Authors: A. T. Eswara

Abstract:

This paper analyses the unsteady, two-dimensional stagnation point flow of an incompressible viscous fluid over a flat sheet when the flow is started impulsively from rest and at the same time, the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. The partial differential equations governing the laminar boundary layer forced convection flow are non-dimensionalised using semi-similar transformations and then solved numerically using an implicit finitedifference scheme known as the Keller-box method. Results pertaining to the flow and heat transfer characteristics are computed for all dimensionless time, uniformly valid in the whole spatial region without any numerical difficulties. Analytical solutions are also obtained for both small and large times, respectively representing the initial unsteady and final steady state flow and heat transfer. Numerical results indicate that the velocity ratio parameter is found to have a significant effect on skin friction and heat transfer rate at the surface. Furthermore, it is exposed that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state (large time solution).

Keywords: Forced flow, Keller-box method, Stagnation point, Stretching flat sheet, Unsteady laminar boundary layer, Velocity ratio parameter.

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Authors: Edlira Donefski, Tina Donefski, Lorenc Ekonomi

Abstract:

Edgeworth Approximation, Bootstrap and Monte Carlo Simulations have a considerable impact on the achieving certain results related to different problems taken into study. In our paper, we have treated a financial case related to the effect that have the components of a Cash-Flow of one of the most successful businesses in the world, as the financial activity, operational activity and investing activity to the cash and cash equivalents at the end of the three-months period. To have a better view of this case we have created a Vector Autoregression model, and after that we have generated the impulse responses in the terms of Asymptotic Analysis (Edgeworth Approximation), Monte Carlo Simulations and Residual Bootstrap based on the standard errors of every series created. The generated results consisted of the common tendencies for the three methods applied, that consequently verified the advantage of the three methods in the optimization of the model that contains many variants.

Keywords: Autoregression, Bootstrap, Edgeworth Expansion, Monte Carlo Method.

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Authors: G. Zazzaro, F.M. Pisano, G. Romano

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During last decades, worldwide researchers dedicated efforts to develop machine-based seismic Early Warning systems, aiming at reducing the huge human losses and economic damages. The elaboration time of seismic waveforms is to be reduced in order to increase the time interval available for the activation of safety measures. This paper suggests a Data Mining model able to correctly and quickly estimate dangerousness of the running seismic event. Several thousand seismic recordings of Japanese and Italian earthquakes were analyzed and a model was obtained by means of a Bayesian Network (BN), which was tested just over the first recordings of seismic events in order to reduce the decision time and the test results were very satisfactory. The model was integrated within an Early Warning System prototype able to collect and elaborate data from a seismic sensor network, estimate the dangerousness of the running earthquake and take the decision of activating the warning promptly.

Keywords: Bayesian Networks, Decision Support System, Magnitude Classification, Seismic Early Warning System

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Authors: Delfim Soares Jr., Webe J. Mansur

Abstract:

The Time-Domain Boundary Element Method (TDBEM) is a well known numerical technique that handles quite properly dynamic analyses considering infinite dimension media. However, when these analyses are also related to nonlinear behavior, very complex numerical procedures arise considering the TD-BEM, which may turn its application prohibitive. In order to avoid this drawback and model nonlinear infinite media, the present work couples two BEM formulations, aiming to achieve the best of two worlds. In this context, the regions expected to behave nonlinearly are discretized by the Domain Boundary Element Method (D-BEM), which has a simpler mathematical formulation but is unable to deal with infinite domain analyses; the TD-BEM is employed as in the sense of an effective non-reflexive boundary. An iterative procedure is considered for the coupling of the TD-BEM and D-BEM, which is based on a relaxed renew of the variables at the common interfaces. Elastoplastic models are focused and different time-steps are allowed to be considered by each BEM formulation in the coupled analysis.

Keywords: Boundary Element Method, Dynamic Elastoplastic Analysis, Iterative Coupling, Multiple Time-Steps.

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Authors: A. Razavykia, A. Esmaeilzadeh, S. Iranmanesh

Abstract:

Many orthopedic implants like proximal humerus cases require lower surface roughness and almost immediate/short lead time surgery. Thus, rapid response from the manufacturer is very crucial. Tool path strategy of milling process has a direct influence on the surface roughness and lead time of medical implant. High-speed milling as promised process would improve the machined surface quality, but conventional or super-abrasive grinding still required which imposes some drawbacks such as additional costs and time. Currently, many CAD/CAM software offers some different tool path strategies to milling free form surfaces. Nevertheless, the users must identify how to choose the strategies according to cutting tool geometry, geometry complexity, and their effects on the machined surface. This study investigates the effect of different tool path strategies for milling a proximal humerus head during finishing operation on stainless steel 316L. Experiments have been performed using MAHO MH700 S vertical milling machine and four machining strategies, namely, spiral outward, spiral inward, and radial as well as zig-zag. In all cases, the obtained surfaces were analyzed in terms of roughness and dimension accuracy compared with those obtained by simulation. The findings provide evidence that surface roughness, dimensional accuracy, and machining time have been affected by the considered tool path strategy.

Keywords: CAD/CAM software, milling, orthopedic implants, tool path strategy.

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Authors: Ahmed El Oualkadi, Abdellah Ait Ouahman

Abstract:

This paper discusses a systematic design of a Σ-Δ fractional-N Phase-Locked Loop based on HDL behavioral modeling. The proposed design consists in describing the mixed behavior of this PLL architecture starting from the specifications of each building block. The HDL models of critical PLL blocks have been described in VHDL-AMS to predict the different specifications of the PLL. The effect of different noise sources has been efficiently introduced to study the PLL system performances. The obtained results are compared with transistor-level simulations to validate the effectiveness of the proposed models for wireless applications in the frequency range around 2.45 GHz.

Keywords: Phase-locked loop, frequency synthesizer, fractional-N PLL, Σ-Δ modulator, HDL models

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Authors: Hsuan-Ku Liu, Ming Long Liu

Abstract:

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: J. Fei

Abstract:

This paper presents the adaptive control scheme with sliding mode compensator for vibration control problem in the presence of disturbance. The dynamic model of the flexible cantilever beam using finite element modeling is derived. The adaptive control with sliding mode compensator using output feedback for output tracking is developed to reject the external disturbance, and to improve the tracking performance. Satisfactory simulation results verify that the effectiveness of adaptive control scheme with sliding mode compensator.

Keywords: finite element model, adaptive control, sliding modecontrol, vibration suppression

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Authors: S. Sarumathi, N. Shanthi, S. Vidhya

Abstract:

In the present world, predicting rainfall is considered to be an essential and also a challenging task. Normally, the climate and rainfall are presumed to have non-linear as well as intricate phenomena. For predicting accurate rainfall, we necessitate advanced computer modeling and simulation. When there is an enhanced understanding of the spatial and temporal distribution of precipitation then it becomes enrichment to applications such as hydrologic, climatic and ecological. Conversely, there may be some kind of challenges occur in the community due to some application which results in the absence of consistent precipitation observation in remote and also emerging region. This survey paper provides a multifarious collection of methodologies which are epitomized by various researchers for predicting the rainfall. It also gives information about some technique to forecast rainfall, which is appropriate to all methods like numerical, traditional and statistical.

Keywords: Satellite Image, Segmentation, Feature Extraction, Classification, Clustering, Precipitation Estimation.

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Authors: Sedat Atmaca, Celal Ceken, Ismail Erturk

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One of the biggest drawbacks of the wireless environment is the limited bandwidth. However, the users sharing this limited bandwidth have been increasing considerably. SDMA technique which entails using directional antennas allows to increase the capacity of a wireless network by separating users in the medium. In this paper, it has been presented how the capacity can be enhanced while the mean delay is reduced by using directional antennas in wireless networks employing TDMA/FDD MAC. Computer modeling and simulation of the wireless system studied are realized using OPNET Modeler. Preliminary simulation results are presented and the performance of the model using directional antennas is evaluated and compared consistently with the one using omnidirectional antennas.

Keywords: Directional Antenna, TDMA, SDMA,

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Authors: N. Sopipan, A. Intarasit, K. Chuarkham

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 In this paper, we forecast the volatility of Baht/USDs using Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecasting Baht/USD volatility. The MRS-GARCH is the best performance model for Baht/USD volatility in short term but the GARCH model is best perform for long term.

Keywords: Volatility, Markov Regime Switching, Forecasting.

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Authors: R.Narmatha Banu, D.Devaraj

Abstract:

This paper presents a genetic algorithm based approach for solving security constrained optimal power flow problem (SCOPF) including FACTS devices. The optimal location of FACTS devices are identified using an index called overload index and the optimal values are obtained using an enhanced genetic algorithm. The optimal allocation by the proposed method optimizes the investment, taking into account its effects on security in terms of the alleviation of line overloads. The proposed approach has been tested on IEEE-30 bus system to show the effectiveness of the proposed algorithm for solving the SCOPF problem.

Keywords: Optimal Power Flow, Genetic Algorithm, FlexibleAC transmission system (FACTS) devices, Severity Index (SI), Security Enhancement, Thyristor controlled series capacitor (TCSC).

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Authors: Ivan Živanović, Žužana Vaštag, Senka Popović, Ljiljana Popović, Draginja Peričin

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The present work represents an investigation of the hydrolysis of hull-less pumpkin (Cucurbita Pepo L.) oil cake protein isolate (PuOC PI) by pepsin. To examine the effectiveness and suitability of pepsin towards PuOC PI the kinetic parameters for pepsin on PuOC PI were determined and then, the hydrolysis process was studied using Response Surface Methodology (RSM). The hydrolysis was carried out at temperature of 30°C and pH 3.00. Time and initial enzyme/substrate ratio (E/S) at three levels were selected as the independent parameters. The degree of hydrolysis, DH, was mesuared after 20, 30 and 40 minutes, at initial E/S of 0.7, 1 and 1.3 mA/mg proteins. Since the proposed second-order polynomial model showed good fit with the experimental data (R2 = 0.9822), the obtained mathematical model could be used for monitoring the hydrolysis of PuOC PI by pepsin, under studied experimental conditions, varying the time and initial E/S. To achieve the highest value of DH (39.13 %), the obtained optimum conditions for time and initial E/S were 30 min and 1.024 mA/mg proteins.

Keywords: Enzymatic hydrolysis, Pepsin, Pumpkin (CucurbitaPepo L.) oil cake protein isolate, Response surface methodology.

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Authors: Hassan Haghighi

Abstract:

Probabilistic techniques in computer programs are becoming more and more widely used. Therefore, there is a big interest in the formal specification, verification, and development of probabilistic programs. In our work-in-progress project, we are attempting to make a constructive framework for developing probabilistic programs formally. The main contribution of this paper is to introduce an intermediate artifact of our work, a Z-based formalism called PZ, by which one can build set theoretical models of probabilistic programs. We propose to use a constructive set theory, called CZ set theory, to interpret the specifications written in PZ. Since CZ has an interpretation in Martin-L¨of-s theory of types, this idea enables us to derive probabilistic programs from correctness proofs of their PZ specifications.

Keywords: formal specification, formal program development, probabilistic programs, CZ set theory, type theory.

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Authors: Wanli Ma, Dat Tran, Dharmendra Sharma

Abstract:

The temporal nature of negative selection is an under exploited area. In a negative selection system, newly generated antibodies go through a maturing phase, and the survivors of the phase then wait to be activated by the incoming antigens after certain number of matches. These without having enough matches will age and die, while these with enough matches (i.e., being activated) will become active detectors. A currently active detector may also age and die if it cannot find any match in a pre-defined (lengthy) period of time. Therefore, what matters in a negative selection system is the dynamics of the involved parties in the current time window, not the whole time duration, which may be up to eternity. This property has the potential to define the uniqueness of negative selection in comparison with the other approaches. On the other hand, a negative selection system is only trained with “normal" data samples. It has to learn and discover unknown “abnormal" data patterns on the fly by itself. Consequently, it is more appreciate to utilize negation selection as a system for pattern discovery and recognition rather than just pattern recognition. In this paper, we study the potential of using negative selection in discovering unknown temporal patterns.

Keywords: Artificial Immune Systems, ComputationalIntelligence, Negative Selection, Pattern Discovery.

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Authors: M. H. M. Rusli, A. Jaffar, M. T. Ali, S. Muhamud @ Kayat

Abstract:

Lean manufacturing is a production philosophy made popular by Toyota Motor Corporation (TMC). It is globally known as the Toyota Production System (TPS) and has the ultimate aim of reducing cost by thoroughly eliminating wastes or muda. TPS embraces the Just-in-time (JIT) manufacturing; achieving cost reduction through lead time reduction. JIT manufacturing can be achieved by implementing Pull system in the production. Furthermore, TPS aims to improve productivity and creating continuous flow in the production by arranging the machines and processes in cellular configurations. This is called as Cellular Manufacturing Systems (CMS). This paper studies on integrating the CMS with the Pull system to establish a Big Island-Pull system production for High Mix Low Volume (HMLV) products in an automotive component industry. The paper will use the build-in JIT system steps adapted from TMC to create the Pull system production and also create a shojinka line which, according to takt time, has the flexibility to adapt to demand changes simply by adding and taking out manpower. This will lead to optimization in production.

Keywords: Big Island layout, Lean manufacturing, Material and Information Flow Chart, Pull system production, TPS.

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Authors: Sun K. Yoo, Hee Cheol Kang

Abstract:

Analysis of amplitude and phase characteristics for delta, theta, and alpha bands at localized time instant from EEG signals is important for the characterizing information processing in the brain. In this paper, complex demodulation method was used to analyze EEG (Electroencephalographic) signal, particularly for auditory evoked potential response signal, with sufficient time resolution and designated frequency bandwidth resolution required. The complex demodulation decomposes raw EEG signal into 3 designated delta, theta, and alpha bands with complex EEG signal representation at sampled time instant, which can enable the extraction of amplitude envelope and phase information. Throughout simulated test data, and real EEG signal acquired during auditory attention task, it can extract the phase offset, phase and frequency changing instant and decomposed amplitude envelope for delta, theta, and alpha bands. The complex demodulation technique can be efficiently used in brain signal analysis in case of phase, and amplitude information required.

Keywords: EEG, Complex Demodulation, Amplitude, Phase.

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Authors: Rasaki O. Olanrewaju

Abstract:

The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.

Keywords: Wiener process, Lévy process, Vasciek model, drift, diffusion, Gaussian density stationary.

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Authors: Wei-Bo Hua, Zhuo Zheng, Xiao-Dong Guo, Ben-He Zhong

Abstract:

The layered structure LiNi1/3Co1/3Mn1/3-xAlxO2 (x = 0 ~ 0.04) series cathode materials were synthesized by a carbonate co-precipitation method, followed by a high temperature calcination process. The influence of Al substitution on the microstructure and electrochemical performances of the prepared materials was investigated by X-Ray diffraction (XRD), scanning electron microscopy (SEM), and galvanostatic charge/discharge test. The results show that the LiNi1/3Co1/3Mn1/3-xAlxO2 has a well-ordered hexagonal α-NaFeO2 structure. Although the discharge capacity of Al-doped samples decreases as x increases, LiNi1/3Co1/3Mn1/3-0.02Al0.02O2 exhibits superior capacity retention at high voltage (4.6 V). Therefore, LiNi1/3Co1/3Mn1/3-0.02Al0.02O2 is a promising material for “green” vehicles.

Keywords: Lithium ion battery, carbonate co-precipitation, microstructure, electrochemical properties.

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Authors: Sumiko Anno, Keiji Imaoka, Takeo Tadono, Tamotsu Igarashi, Subramaniam Sivaganesh, Selvam Kannathasan, Vaithehi Kumaran, Sinnathamby Noble Surendran

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Dengue outbreaks are affected by biological, ecological, socio-economic and demographic factors that vary over time and space. These factors have been examined separately and still require systematic clarification. The present study aimed to investigate the spatial-temporal clustering relationships between these factors and dengue outbreaks in the northern region of Sri Lanka. Remote sensing (RS) data gathered from a plurality of satellites were used to develop an index comprising rainfall, humidity and temperature data. RS data gathered by ALOS/AVNIR-2 were used to detect urbanization, and a digital land cover map was used to extract land cover information. Other data on relevant factors and dengue outbreaks were collected through institutions and extant databases. The analyzed RS data and databases were integrated into geographic information systems, enabling temporal analysis, spatial statistical analysis and space-time clustering analysis. Our present results showed that increases in the number of the combination of ecological factor and socio-economic and demographic factors with above the average or the presence contribute to significantly high rates of space-time dengue clusters.

Keywords: ALOS/AVNIR-2, Dengue, Space-time clustering analysis, Sri Lanka.

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Authors: R. Ziaie Moayed, V. Rashidian, E. Izadi

Abstract:

This paper utilizes a finite element analysis to study the bearing capacity of ring footings on a two-layered soil. The upper layer, that the footing is placed on it, is soft clay and the underneath layer is a cohesionless sand. For modeling soils, Mohr–Coulomb plastic yield criterion is employed. The effects of two factors, the clay layer thickness and the ratio of internal radius of the ring footing to external radius of the ring, have been analyzed. It is found that the bearing capacity decreases as the value of ri / ro increases. Although, as the clay layer thickness increases the bearing capacity was alleviated gradually.

Keywords: Bearing capacity, Ring footing, Two-layered soil

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Authors: Paras Ram, Vikas Kumar

Abstract:

An attempt has been made to study the effect of rotation on incompressible, electrically non-conducting ferrofluid in porous medium on Axi-symmetric steady flow over a rotating disk excluding thermal effects. Here, we solved the boundary layer equations with boundary conditions using Neuringer-Rosensweig model considering the z-axis as the axis of rotation. The non linear boundary layer equations involved in the problem are transformed to the non linear coupled ordinary differential equations by Karman's transformation and solved by power series approximations. Besides numerically calculating the velocity components and pressure for different values of porosity parameter with the variation of Karman's parameter we have also calculated the displacement thickness of boundary layer, the total volume flowing outward the z-axis and angle between wall and ferrofluid. The results for all above variables are obtained numerically and discussed graphically.

Keywords: Ferrofluid, magnetic field porous medium, rotating disk.

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