Search results for: integrated audit quality model

Authors: T. Mathumathi, S. Ganesh, R. Gunabalan

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This work presents an approach for AC load flow based centralized model for congestion management in the forward markets. In this model, transaction maximizes its profit under the limits of transmission line capacities allocated by Independent System Operator (ISO). The voltage and reactive power impact of the system are also incorporated in this model. Genetic algorithm is used to solve centralized congestion management problem for multilateral transactions. Results obtained for centralized model using genetic algorithm is compared with Sequential Quadratic Programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare are given. Simulation results clearly demonstrate the better performance of genetic algorithm over SQP.

Keywords: Congestion management, Genetic algorithm, Sequential quadratic programming.

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Authors: Zina Saheb, Ezz El-Masry

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As the Silicon oxide scaled down in MOSFET technology to few nanometers, gate Direct Tunneling (DT) in Floating gate (FGMOSFET) devices has become a major concern for analog designers. FGMOSFET has been used in many low-voltage and low-power applications, however, there is no accurate model that account for DT gate leakage in nano-scale. This paper studied and analyzed different simulation models for FGMOSFET using TSMC 90-nm technology. The simulation results for FGMOSFET cascade current mirror shows the impact of DT on circuit performance in terms of current and voltage without the need for fabrication. This works shows the significance of using an accurate model for FGMOSFET in nan-scale technologies.

Keywords: CMOS transistor, direct-tunneling current, floatinggate, gate-leakage current, simulation model.

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Authors: Sadegh Papari, Mohammad Kazemeini, Moslem Fattahi

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In the present study, a heterogeneous and homogeneous gas flow dispersion model for simulation and optimisation of a large-scale catalytic slurry reactor for the direct synthesis of dimethyl ether (DME) from syngas and CO2, using a churn-turbulent regime was developed. In the heterogeneous gas flow model the gas phase was distributed into two bubble phases: small and large, however in the homogeneous one, the gas phase was distributed into only one large bubble phase. The results indicated that the heterogeneous gas flow model was in more agreement with experimental pilot plant data than the homogeneous one.

Keywords: Modelling, Slurry bubble column, Dimethyl ether synthesis, Homogeneous gas flow, Heterogeneous gas flow

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Authors: Sakol Udomsiri, Masahiro Iwahashi

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This paper presents comparative study on recent integer DCTs and a new method to construct a low sensitive structure of integer DCT for colored input signals. The method refers to sensitivity of multiplier coefficients to finite word length as an indicator of how word length truncation effects on quality of output signal. The sensitivity is also theoretically evaluated as a function of auto-correlation and covariance matrix of input signal. The structure of integer DCT algorithm is optimized by combination of lower sensitive lifting structure types of IRT. It is evaluated by the sensitivity of multiplier coefficients to finite word length expression in a function of covariance matrix of input signal. Effectiveness of the optimum combination of IRT in integer DCT algorithm is confirmed by quality improvement comparing with existing case. As a result, the optimum combination of IRT in each integer DCT algorithm evidently improves output signal quality and it is still compatible with the existing one.

Keywords: DCT, sensitivity, lossless, wordlength.

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Authors: R. Rinkeviciene, B. Kundrotas, S. Lisauskas

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In this paper, the authors take a look at advantages of multiphase induction motors comparing them with three phase ones and present the applications where six-phase induction motors are used. They elaborate the mathematical model of six-phase induction motor with two similar stator three phase winding, shifted by 30 degrees in space and three phase winding in rotor, in synchronous reference frame for soft starting and scalar control. The authors simulate and discuss results of speed and torque starting transients.

Keywords: Model, scalar control, six-phase induction motor.

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Authors: Eugenie A. Kachvoryan, Astghik Z. Pepoyan, Maria V. Harutyunova, Anahit M. Manvelyan

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Taking into account the importance of Lake Sevan and Lake Sevan basin-s rivers for Armenian economy, the main goals of our investigations were the documentation of water quality and the biodiversity of invertebrates developed in Lake Sevan basin-s rivers and selected tributaries. Moderately satisfied ecological condition for the biodiversity of Lake Sevan basin-s rivers has been established, and the changes in species- composition of zoobenthos in Lake Sevan were detected. A growing tendency of antibiotic resistance among E. coli isolates in water resources has been shown.

Keywords: Biodiversity, ecosystem, Lake Sevan, water-quality, zoobenthos.

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Authors: Keneilwe Maremi, Marlien Herselman, Adele Botha

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The main purpose and focus of this paper are to determine the Interoperability Maturity Models to consider when using School Management Systems (SMS). The importance of this is to inform and help schools with knowing which Interoperability Maturity Model is best suited for their SMS. To address the purpose, this paper will apply a scoping review to ensure that all aspects are provided. The scoping review will include papers written from 2012-2019 and a comparison of the different types of Interoperability Maturity Models will be discussed in detail, which includes the background information, the levels of interoperability, and area for consideration in each Maturity Model. The literature was obtained from the following databases: IEEE Xplore and Scopus, the following search engines were used: Harzings, and Google Scholar. The topic of the paper was used as a search term for the literature and the term ‘Interoperability Maturity Models’ was used as a keyword. The data were analyzed in terms of the definition of Interoperability, Interoperability Maturity Models, and levels of interoperability. The results provide a table that shows the focus area of concern for each Maturity Model (based on the scoping review where only 24 papers were found to be best suited for the paper out of 740 publications initially identified in the field). This resulted in the most discussed Interoperability Maturity Model for consideration (Information Systems Interoperability Maturity Model (ISIMM) and Organizational Interoperability Maturity Model for C2 (OIM)).

Keywords: Interoperability, Interoperability Maturity Model, School Management System, scoping review.

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Authors: Fariba Haghbin, Othman Bin Ibrahim, Mohammad Reza Attarzadeh Niaki

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With the development of virtual communities, there is an increase in the number of members in Virtual Communities (VCs). Many join VCs with the objective of sharing their knowledge and seeking knowledge from others. Despite the eagerness of sharing knowledge and receiving knowledge through VCs, there is no standard of assessing ones knowledge sharing capabilities and prospects of knowledge sharing. This paper developed a vector space model to assess the knowledge sharing prospect of VC users.

Keywords: Knowledge sharing network, Virtual community, knowledge relationship, Vector Space Model.

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Authors: S.A. Al-Qallaf, S.A. Al-Mawsawi, A. Haider

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Among all FACTS devices, the unified power flow controller (UPFC) is considered to be the most versatile device. This is due to its capability to control all the transmission system parameters (impedance, voltage magnitude, and phase angle). With the growing interest in UPFC, the attention to develop a mathematical model has increased. Several models were introduced for UPFC in literature for different type of studies in power systems. In this paper a novel comparison study between two dynamic models of UPFC with their proposed control strategies.

Keywords: FACTS, UPFC, Dynamic Modeling, PWM, Fundamental Frequency.

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Authors: Rakesh Kumar, A. K. Ghosh

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The paper presents the modeling of nonlinear longitudinal aerodynamics using flight data of Hansa-3 aircraft at high angles of attack near stall. The Kirchhoff-s quasi-steady stall model has been used to incorporate nonlinear aerodynamic effects in the aerodynamic model used to estimate the parameters, thereby, making the aerodynamic model nonlinear. The Maximum Likelihood method has been applied to the flight data (at high angles of attack) for the estimation of parameters (aerodynamic and stall characteristics) using the nonlinear aerodynamic model. To improve the accuracy level of the estimates, an approach of fixing the strong parameters has also been presented.

Keywords: Maximum Likelihood, nonlinear, parameters, stall.

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Authors: Sharifah Sumayyah Engku Alwi, Masrah Azrifah Azmi Murad

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The development of the information technology and Internet has been transforming the healthcare industry. The internet is continuously accessed to seek for health information and there are variety of sources, including search engines, health websites, and social networking sites. Providing more and better information on health may empower individuals, however, ensuring a high quality and trusted health information could pose a challenge. Moreover, there is an ever-increasing amount of information available, but they are not necessarily accurate and up to date. Thus, this paper aims to provide an insight of the models and frameworks related to online health information seeking of consumers. It begins by exploring the definition of information behavior and information seeking to provide a better understanding of the concept of information seeking. In this study, critical factors such as performance expectancy, effort expectancy, and social influence will be studied in relation to the value of seeking health information. It also aims to analyze the effect of age, gender, and health status as the moderator on the factors that influence online health information seeking, i.e. trust and information quality. A preliminary survey will be carried out among the health professionals to clarify the research problems which exist in the real world, at the same time producing a conceptual framework. A final survey will be distributed to five states of Malaysia, to solicit the feedback on the framework. Data will be analyzed using SPSS and SmartPLS 3.0 analysis tools. It is hoped that at the end of this study, a novel framework that can improve online health information seeking is developed. Finally, this paper concludes with some suggestions on the models and frameworks that could improve online health information seeking.

Keywords: Information behavior, information seeking, online health information, technology acceptance model, the theory of planned behavior, UTAUT.

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Authors: Dipen A. Mistry, Bhupelly Dheeraj, Ravit Gautam, Manmohan Singh Meena, Suresh Mikkili

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In recent years the large scale use of the power electronic equipment has led to an increase of harmonics in the power system. The harmonics results into a poor power quality and have great adverse economical impact on the utilities and customers. Current harmonics are one of the most common power quality problems and are usually resolved by using shunt active filter (SHAF). The main objective of this work is to develop PI and Fuzzy logic controllers (FLC) to analyze the performance of Shunt Active Filter for mitigating current harmonics under balanced and unbalanced sinusoidal source voltage conditions for normal load and increased load. When the supply voltages are ideal (balanced), both PI and FLC are converging to the same compensation characteristics. However, the supply voltages are non-ideal (unbalanced), FLC offers outstanding results. Simulation results validate the superiority of FLC with triangular membership function over the PI controller.

Keywords: DC link voltage, Fuzzy logic controller, Harmonics, PI controller, Shunt Active Filter.

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Authors: Sajid Abbas, Joon Pyo Hong, Jung-Ryun Lee, Seungryong Cho

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Computed tomography and laminography are heavily investigated in a compressive sensing based image reconstruction framework to reduce the dose to the patients as well as to the radiosensitive devices such as multilayer microelectronic circuit boards. Nowadays researchers are actively working on optimizing the compressive sensing based iterative image reconstruction algorithm to obtain better quality images. However, the effects of the sampled data’s properties on reconstructed the image’s quality, particularly in an insufficient sampled data conditions have not been explored in computed laminography. In this paper, we investigated the effects of two data properties i.e. sampling density and data incoherence on the reconstructed image obtained by conventional computed laminography and a recently proposed method called spherical sinusoidal scanning scheme. We have found that in a compressive sensing based image reconstruction framework, the image quality mainly depends upon the data incoherence when the data is uniformly sampled.

Keywords: Computed tomography, Computed laminography, Compressive sending, Low-dose.

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Authors: Marichela Sepe

Abstract:

The sustainability of a place depends on a series of factors which contribute to the quality of life, sense of place and recognition of identity. An activity like walking, which in itself is obviously ''sustainable'', can become non sustainable if the context in which it is carried out does not meet the conditions for an adequate quality of life. This work is aimed at proposing the analytical method of Place Maker to identify the elements that do not feature in traditional mapping and which constitute the contemporary identity of the places, and the relative complex map to represent those elements and support sustainable urban identity design. The method's potential for areas with a predominantly pedestrian vocation is illustrated by means of the case study of the Ramblas in Barcelona.

Keywords: Place-identity, PlaceMaker, sustainability, walkability.

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis.

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Authors: Areej Babiker Idris Babiker, Rosdiazli Ibrahim

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Gas chromatography (GC) is the most widely used technique in analytical chemistry. However, GC has high initial cost and requires frequent maintenance. This paper examines the feasibility and potential of using a neural network model as an alternative whenever GC is unvailable. It can also be part of system verification on the performance of GC for preventive maintenance activities. It shows the performance of MultiLayer Perceptron (MLP) with Backpropagation structure. Results demonstrate that neural network model when trained using this structure provides an adequate result and is suitable for this purpose. cm.

Keywords: Analyzer, Levenberg-Marquardt, Gas chromatography, Neural network

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Authors: Ifeyinwa E. Achumba, Djamel Azzi, Rinat Khusainov

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There are three approaches to complete Bayesian Network (BN) model construction: total expert-centred, total datacentred, and semi data-centred. These three approaches constitute the basis of the empirical investigation undertaken and reported in this paper. The objective is to determine, amongst these three approaches, which is the optimal approach for the construction of a BN-based model for the performance assessment of students- laboratory work in a virtual electronic laboratory environment. BN models were constructed using all three approaches, with respect to the focus domain, and compared using a set of optimality criteria. In addition, the impact of the size and source of the training, on the performance of total data-centred and semi data-centred models was investigated. The results of the investigation provide additional insight for BN model constructors and contribute to literature providing supportive evidence for the conceptual feasibility and efficiency of structure and parameter learning from data. In addition, the results highlight other interesting themes.

Keywords: Bayesian networks, model construction, parameterlearning, structure learning, performance index, model comparison.

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Authors: M. Manafi, J. Hesari, H. Peighambardoust, M. Rahimzade Khoyi

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Fruit drying is a well known process mostly used for preservation of fruits. Osmotic dehydration of apricot slices were carried out in three different salt-sucrose concentrations and four different temperatures. Also three different weight ratios of solution to sample were conducted to one set of experiments. The dehydration curves were constructed using Peleg-s model. Increasing the solution volume increased the mass transfer rate and hence the solid gain increased rapidly. Increasing the volume of osmotic media caused an increase in overall mass transfer but a 'solution to sample' ratio of 5:1 gave the best product quality. The best temperature and concentration that had a high water loss to solid gain ratio and an acceptable taste were 40°C and 5%, respectively.

Keywords: Apricot, Effective diffusivities, Osmotic dehydration

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Authors: Paiboon Jeamponk, Tasanee Ponglaa, Patchapon Srisanguan

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The aim of this research paper was based on an examination of sources of water supply and water quality for local consumption, conducted at eco- tourism villages of Suan Luang Sub- District Municipality of Amphawa District, Samut Songkram Province. The study incorporated both questionnaire and field work of water testing as the research tool and method. The sample size of 288 households was based on the population of the district, whereas the selected sample water sources were from 60 households: 30 samples were ground water and another 30 were surface water. Degree of heavy metal contamination in the water including copper, iron, manganese, zinc, cadmium and lead was investigated utilizing the Atomic Absorption- Direct Aspiration method. The findings unveiled that 96.0 percent of household water consumption was based on water supply, while the rest on canal, river and rain water. The household behavior of consumption revealed that 47.2 percent of people routinely consumed water without boiling or filtering prior to consumption. The investigation of water supply quality found that the degree of heavy metal contamination including metal, lead, iron, copper, manganese and cadmium met the standards of the Department of Health.

Keywords: Sources of water supply, water quality, water supply.

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Authors: Yong-Hui Li, Jing-Wen Huang

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As the advancement of technology, online shopping channel develops rapidly in recent years. According to the report of Taiwan Network Information Center, there are almost eighty percents of internet population shopping in online channel. Synthesizing insights from the previous research, this study develops the conceptual model to integrate Theory of Perceived Risk (TPR) and Technology Acceptance Model (TAM) to apply in online shopping. Using data collected from 637 respondents from online survey website, we use structural equation modeling to test measurement and structural models. The results suggest the need for consideration of perceived risk as an antecedent in the Technology Acceptance Model. The limitations and implications are discussed.

Keywords: perceived risk, perceived usefulness, perceived ease of use, behavioral intention, actual purchase behavior

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Authors: Y. Lu, X. S. Qin

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Extensive rainfall disaggregation approaches have been developed and applied in climate change impact studies such as flood risk assessment and urban storm water management.In this study, five rainfall models that were capable ofdisaggregating daily rainfall data into hourly one were investigated for the rainfall record in theChangi Airport, Singapore. The objectives of this study were (i) to study the temporal characteristics of hourly rainfall in Singapore, and (ii) to evaluate the performance of variousdisaggregation models. The used models included: (i) Rectangular pulse Poisson model (RPPM), (ii) Bartlett-Lewis Rectangular pulse model (BLRPM), (iii) Bartlett-Lewis model with 2 cell types (BL2C), (iv) Bartlett-Lewis Rectangular with cell depth distribution dependent on duration (BLRD), and (v) Neyman-Scott Rectangular pulse model (NSRPM). All of these models werefitted using hourly rainfall data ranging from 1980 to 2005 (which was obtained from Changimeteorological station).The study results indicated that the weight scheme of inversely proportional variance could deliver more accurateoutputs for fitting rainfall patterns in tropical areas, and BLRPM performedrelatively better than other disaggregation models.

Keywords: Rainfall disaggregation, statistical properties, poisson processed, Bartlett-Lewis model, Neyman-Scott model.

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Authors: Suttipong Boonphadung, Thassanant Unnanantn

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This research focused on comparing the critical thinking of the teacher students before and after using Miller’s Model learning activities and investigating their opinions. The sampling groups were (1) fourth year 33 student teachers majoring in Early Childhood Education and enrolling in semester 1 of academic year 2013 (2) third year 28 student teachers majoring in English and enrolling in semester 2 of academic year 2013 and (3) third year 22 student teachers majoring in Thai and enrolling in semester 2 of academic year 2013. The research instruments were (1) lesson plans where the learning activities were settled based on Miller’s Model (2) critical thinking assessment criteria and (3) a questionnaire on opinions towards Miller’s Model based learning activities. The statistical treatment was mean, deviation, different scores and T-test. The result unfolded that (1) the critical thinking of the students after the assigned activities was better than before and (2) the students’ opinions towards the critical thinking improvement activities based on Miller’s Model ranged from the level of high to highest.

Keywords: Critical thinking, Miller’s model, Opinions.

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Authors: Cristian Păuna

Abstract:

In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.

Keywords: Algorithmic trading, automated investment system, DAX Deutscher Aktienindex.

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Authors: Ling Liu, Yuan Ye

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In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results.

Keywords: Discrete-time SIR epidemic model, time delay, nonlinear incidence rate, impulse.

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Authors: Mahmood Reza Shakarami, Reza Sedaghati

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Electricity market activities and a growing demand for electricity have led to heavily stressed power systems. This requires operation of the networks closer to their stability limits. Power system operation is affected by stability related problems, leading to unpredictable system behavior. Voltage stability refers to the ability of a power system to sustain appropriate voltage levels through large and small disturbances. Steady-state voltage stability is concerned with limits on the existence of steady-state operating points for the network. FACTS devices can be utilized to increase the transmission capacity, the stability margin and dynamic behavior or serve to ensure improved power quality. Their main capabilities are reactive power compensation, voltage control and power flow control. Among the FACTS controllers, Static Var Compensator (SVC) provides fast acting dynamic reactive compensation for voltage support during contingency events. In this paper, voltage stability assessment with appropriate representations of tap-changer transformers and SVC is investigated. Integrating both of these devices is the main topic of this paper. Effect of the presence of tap-changing transformers on static VAR compensator controller parameters and ratings necessary to stabilize load voltages at certain values are highlighted. The interrelation between transformer off nominal tap ratios and the SVC controller gains and droop slopes and the SVC rating are found. P-V curves are constructed to calculate loadability margins.

Keywords: SVC, voltage stability, P-V curve, reactive power, tap changing transformer.

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Authors: Kejun Zhuang

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With the help of coincidence degree theory, sufficient conditions for existence of periodic solutions for a food chain model with functional responses on time scales are established.

Keywords: time scales, food chain model, coincidence degree, periodic solutions.

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Authors: Anton Golubkov, Gleb Ermachkov, Aleksandr Smerdin, Oleg Sidorov, Victor Philippov

Abstract:

Current collection quality is one of the limiting factors when increasing trains movement speed in the rail sector. With the movement speed growth, the impact forces on the current collector from the rolling stock and the aerodynamic influence increase, which leads to the spread in the contact pressure values, separation of the current collector head from the contact wire, contact arcing and excessive wear of the contact elements. The upcoming trend in resolving this issue is the use of the automatic control systems providing stabilization of the contact pressure value. The present paper considers the features of the contemporary automatic control systems of the current collector’s pressure; their major disadvantages have been stated. A scheme of current collector pressure automatic control has been proposed, distinguished by a proactive influence on undesirable effects. A mathematical model of contact strips wearing has been presented, obtained in accordance with the provisions of the central composition rotatable design program. The analysis of the obtained dependencies has been carried out. The procedures for determining the optimal current collector pressure on the contact wire and the pressure control principle in the pneumatic drive have been described.

Keywords: High-speed running, current collector, contact strip, mathematical model, contact pressure, program control, wear, life cycle.

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Authors: Boonlert Watjatrakul

Abstract:

Mobile marketing through mobile messaging service has highly impressive growth as it enables e-business firms to communicate with their customers effectively. Educational institutions hence start using this service to enhance communication with their students. Previous studies, however, have limited understanding of applying mobile messaging service in education. This study proposes a theoretical model to understand the drivers of students- intentions to use the university-s mobile messaging service. The model indicates that social influence, perceived control and attitudes affect students- intention to use the university-s mobile messaging service. It also provides five antecedents of students- attitudes–perceived utility (information utility, entertainment utility, and social utility), innovativeness, information seeking, transaction specificity (content specificity, sender specificity, and time specificity) and privacy concern. The proposed model enables universities to understand what students concern about the use of a mobile messaging service in universities and handle the service more effectively. The paper discusses the model development and concludes with limitations and implications of the proposed model.

Keywords: education, intention, mobile marketing, mobile messaging.

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Authors: Vahid Nademi

Abstract:

In response to widely used wearable medical devices equipped with a continuous glucose monitor (CGM) and insulin pump, the advanced control methods are still demanding to get the full benefit of these devices. Unlike costly clinical trials, implementing effective insulin-glucose control strategies can provide significant contributions to the patients suffering from chronic diseases such as diabetes. This study deals with a key role of two-layer insulin-glucose regulator based on model-predictive-control (MPC) scheme so that the patient’s predicted glucose profile is in compliance with the insulin level injected through insulin pump automatically. It is achieved by iterative optimization algorithm which is called an integrated perturbation analysis and sequential quadratic programming (IPA-SQP) solver for handling uncertainties due to unexpected variations in glucose-insulin values and body’s characteristics. The feasibility evaluation of the discussed control approach is also studied by means of numerical simulations of two case scenarios via measured data. The obtained results are presented to verify the superior and reliable performance of the proposed control scheme with no negative impact on patient safety.

Keywords: Blood glucose monitoring, insulin pump, optimization, predictive control, diabetes disease.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.

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