Search results for: Mathematical Modelling

Authors: Paula Verdugo-Hernández, Patricio Cumsille

Abstract:

We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of Mathematical Working Spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: Convergence, graphical representations, Mathematical Working Spaces, paradigms of real analysis, real number sequences.

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Authors: L. Al Ahmad, C. Latrille, D. Hainos, D. Blanc, M. Clausse

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A two-dimensional finite volume axisymmetric model is developed to predict the simultaneous heat and mass transfers during the drying of industrial sludge. The simulations were run using COMSOL-Multiphysics 3.5a. The input parameters of the numerical model were acquired from a preliminary experimental work. Results permit to establish correlations describing the evolution of the various parameters as a function of the drying temperature and the sludge water content. The selection and coupling of the equation are validated based on the drying kinetics acquired experimentally at a temperature range of 45-65 °C and absolute pressure range of 200-1000 mbar. The model, incorporating the heat and mass transfer mechanisms at different operating conditions, shows simulated values of temperature and water content. Simulated results are found concordant with the experimental values, only at the first and last drying stages where sludge shrinkage is insignificant. Simulated and experimental results show that sludge drying is favored at high temperatures and low pressure. As experimentally observed, the drying time is reduced by 68% for drying at 65 °C compared to 45 °C under 1 atm. At 65 °C, a 200-mbar absolute pressure vacuum leads to an additional reduction in drying time estimated by 61%. However, the drying rate is underestimated in the intermediate stage. This rate underestimation could be improved in the model by considering the shrinkage phenomena that occurs during sludge drying.

Keywords: Industrial sludge drying, heat transfer, mass transfer, mathematical modelling.

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Authors: Eisa A. Alsafran, Francis T. Edum-Fotwe, Wayne E. Lord

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The degree to which a public client actively participates in Public Private Partnership (PPP) schemes, is seen as a determinant of the success of the arrangement, and in particular, efficiency in the delivery of the assets of any infrastructure development. The asset delivery is often an early barometer for judging the overall performance of the PPP. Currently, there are no defined descriptors for the degree of such participation. The lack of defined descriptors makes the association between the degree of participation and efficiency of asset delivery, difficult to establish. This is particularly so if an optimum effect is desired. In addition, such an association is important for the strategic decision to embark on any PPP initiative. This paper presents a conceptual model of different levels of participation that characterise PPP schemes. The modelling was achieved by a systematic review of reported sources that address essential aspects and structures of PPP schemes, published from 2001 to 2015. As a precursor to the modelling, the common areas of Public Client Participation (PCP) were investigated. Equity and risk emerged as two dominant factors in the common areas of PCP, and were therefore adopted to form the foundation of the modelling. The resultant conceptual model defines the different states of combined PCP. The defined states provide a more rational basis for establishing how the degree of PCP affects the efficiency of asset delivery in PPP schemes.

Keywords: Asset delivery, infrastructure development, public private partnership, public client participation.

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Authors: Jagannath Aryal, Don Kulasiri, Garth A. Carnaby

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This paper provides an overview of auction theory literature. We present a general review on literature of various auctions and focus ourselves specifically on an English auction. We are interested in modelling bidder-s behavior in an English auction environment. And hence, we present an overview of the New Zealand wool auction followed by a model that would describe a bidder-s decision making behavior from the New Zealand wool auction. The mathematical assumptions in an English auction environment are demonstrated from the perspective of the New Zealand wool auction.

Keywords: Bidder, English auction, New Zealand, Wool

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Authors: Masrour Dowlatabadi, Jalil Shirazi

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In this paper, an improved edge detection algorithm based on fuzzy combination of mathematical morphology and wavelet transform is proposed. The combined method is proposed to overcome the limitation of wavelet based edge detection and mathematical morphology based edge detection in noisy images. Experimental results show superiority of the proposed method, as compared to the traditional Prewitt, wavelet based and morphology based edge detection methods. The proposed method is an effective edge detection method for noisy image and keeps clear and continuous edges.

Keywords: Edge detection, Wavelet transform, Mathematical morphology, Fuzzy logic.

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Authors: Keny Ordaz-Hernandez, Xavier Fischer, Fouad Bennis

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This article illustrates a model selection management approach for virtual prototypes in interactive simulations. In those numerical simulations, the virtual prototype and its environment are modelled as a multiagent system, where every entity (prototype,human, etc.) is modelled as an agent. In particular, virtual prototyp ingagents that provide mathematical models of mechanical behaviour inform of computational methods are considered. This work argues that selection of an appropriate model in a changing environment,supported by models? characteristics, can be managed by the deter-mination a priori of specific exploitation and performance measures of virtual prototype models. As different models exist to represent a single phenomenon, it is not always possible to select the best one under all possible circumstances of the environment. Instead the most appropriate shall be selecting according to the use case. The proposed approach consists in identifying relevant metrics or indicators for each group of models (e.g. entity models, global model), formulate their qualification, analyse the performance, and apply the qualification criteria. Then, a model can be selected based on the performance prediction obtained from its qualification. The authors hope that this approach will not only help to inform engineers and researchers about another approach for selecting virtual prototype models, but also assist virtual prototype engineers in the systematic or automatic model selection.

Keywords: Virtual prototype models, domain, qualification criterion, model qualification, model assessment, environmental modelling.

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Authors: Roberto Iglesias, Theocharis Kyriacou, Ulrich Nehmzow, Steve Billings

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Fundamental sensor-motor couplings form the backbone of most mobile robot control tasks, and often need to be implemented fast, efficiently and nevertheless reliably. Machine learning techniques are therefore often used to obtain the desired sensor-motor competences. In this paper we present an alternative to established machine learning methods such as artificial neural networks, that is very fast, easy to implement, and has the distinct advantage that it generates transparent, analysable sensor-motor couplings: system identification through nonlinear polynomial mapping. This work, which is part of the RobotMODIC project at the universities of Essex and Sheffield, aims to develop a theoretical understanding of the interaction between the robot and its environment. One of the purposes of this research is to enable the principled design of robot control programs. As a first step towards this aim we model the behaviour of the robot, as this emerges from its interaction with the environment, with the NARMAX modelling method (Nonlinear, Auto-Regressive, Moving Average models with eXogenous inputs). This method produces explicit polynomial functions that can be subsequently analysed using established mathematical methods. In this paper we demonstrate the fidelity of the obtained NARMAX models in the challenging task of robot route learning; we present a set of experiments in which a Magellan Pro mobile robot was taught to follow four different routes, always using the same mechanism to obtain the required control law.

Keywords: Mobile robotics, system identification, non-linear modelling, NARMAX.

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Authors: R. Kongnuy, E. Naowanich

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In this paper we develop and analyze the model for the spread of Leptospirosis by age group in Thailand, between 1997 and 2010 by using mathematical modeling and computer simulation. Leptospirosis is caused by pathogenic spirochetes of the genus Leptospira. It is a zoonotic disease of global importance and an emerging health problem in Thailand. In Thailand, leptospirosis is a reportable disease, the top three age groups are 23.31% in 35-44 years olds group, 22.76% in 25-34 year olds group, 17.60% in 45-54 year olds group from reported leptospirosis between 1997 and 2010, with a peak in 35-44 year olds group. Our paper, the Leptosipirosis transmission by age group in Thailand is studied on the mathematical model. Some analytical and simulation results are presented.

Keywords: Age Group, Equilibrium State, Leptospirosis, Mathematical Modeling.

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Authors: Marcin Michalak

Abstract:

Due to the increasing efforts on saving our natural environment a change in the structure of energy resources can be observed - an increasing fraction of a renewable energy sources. In many countries traditional underground coal mining loses its significance but there are still countries, like Poland or Germany, in which the coal based technologies have the greatest fraction in a total energy production. This necessitates to make an effort to limit the costs and negative effects of underground coal mining. The longwall complex is as essential part of the underground coal mining. The safety and the effectiveness of the work is strongly dependent of the diagnostic state of powered roof supports. The building of a useful and reliable diagnostic system requires a lot of data. As the acquisition of a data of any possible operating conditions it is important to have a possibility to generate a demanded artificial working characteristics. In this paper a new approach of modelling a leg pressure in the single unit of powered roof support. The model is a result of the analysis of a typical working cycles.

Keywords: Machine modelling, underground mining, coal mining.

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Authors: J. Aryal, D. Kulasiri, G. A. Carnaby

Abstract:

This paper provides an overview of auction theory literature. We present a general review on literature of various auctions and focus ourselves specifically on an English auction. We are interested in modelling bidder's behavior in an English auction environment. And hence, we present an overview of the New Zealand wool auction followed by a model that would describe a bidder's decision making behavior from the New Zealand wool auction. The mathematical assumptions in an English auction environment are demonstrated from the perspective of the New Zealand wool auction.

Keywords: Bidder, English auction, New Zealand, wool.

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Authors: M.A. Kamely, S.M. Kamil, C.W. Chong

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A mathematical model of the surface roughness has been developed by using response surface methodology (RSM) in grinding of AISI D2 cold work tool steels. Analysis of variance (ANOVA) was used to check the validity of the model. Low and high value for work speed and feed rate are decided from design of experiment. The influences of all machining parameters on surface roughness have been analyzed based on the developed mathematical model. The developed prediction equation shows that both the feed rate and work speed are the most important factor that influences the surface roughness. The surface roughness was found to be the lowers with the used of low feed rate and low work speed. Accuracy of the best model was proved with the testing data.

Keywords: Mathematical Modeling, Response surfacemethodology, Surface roughness, Cylindrical Grinding.

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Authors: Benjamin Gorry, Andrew Ireland, Peter King

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Verification of real-time software systems can be expensive in terms of time and resources. Testing is the main method of proving correctness but has been shown to be a long and time consuming process. Everyday engineers are usually unwilling to adopt formal approaches to correctness because of the overhead associated with developing their knowledge of such techniques. Performance modelling techniques allow systems to be evaluated with respect to timing constraints. This paper describes PARTES, a framework which guides the extraction of performance models from programs written in an annotated subset of C.

Keywords: Performance Modelling, Real-time, SensitivityAnalysis.

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Authors: M. Mokhtar, A. Shuib, D. Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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Authors: Panagiotis Kyratsis, Dr. Ing. Nikolaos Bilalis, Dr. Ing. Aristomenis Antoniadis

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Twist drills are geometrical complex tools and thus various researchers have adopted different mathematical and experimental approaches for their simulation. The present paper acknowledges the increasing use of modern CAD systems and using the API (Application Programming Interface) of a CAD system, drilling simulations are carried out. The developed DRILL3D software routine, creates parametrically controlled tool geometries and using different cutting conditions, achieves the generation of solid models for all the relevant data involved (drilling tool, cut workpiece, undeformed chip). The final data derived, consist a platform for further direct simulations regarding the determination of cutting forces, tool wear, drilling optimizations etc.

Keywords: Drilling, CAD based simulation, 3D-modelling.

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Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

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A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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Authors: Dibyendu Ghoshal, Pinaki Pratim Acharjya

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Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.

Keywords: Image segmentation, linear transform, bilinear transform, conformal transform, mathematical morphology.

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Authors: M. B. El_Mashade, I. I. Mahamoud, M. S. El_Tokhy

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Improving the performance of the QCL through block diagram as well as mathematical models is the main scope of this paper. In order to enhance the performance of the underlined device, the mathematical model parameters are used in a reliable manner in such a way that the optimum behavior was achieved. These parameters play the central role in specifying the optical characteristics of the considered laser source. Moreover, it is important to have a large amount of radiated power, where increasing the amount of radiated power represents the main hopping process that can be predicted from the behavior of quantum laser devices. It was found that there is a good agreement between the calculated values from our mathematical model and those obtained with VisSim and experimental results. These demonstrate the strength of mplementation of both mathematical and block diagram models.

Keywords: Quantum Cascaded Lasers (QCLs), Modeling, Block Diagram Programming, Intersubband transitions

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

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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: Sandhya Dixit, Tilak Raj

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Flexible Manufacturing System (FMS) is seen as an option for industries which want to boost productivity as well as respond quickly to an increasingly changing marketplace. FMS produces in mid variety, mid volume range and can meet the changing market demands very quickly. But still the impact of adoption of FMS on the productivity of any industry is not very clear. In this paper an attempt has been made to model the various factors affecting the productivity of FMS installation using Total Interpretive Structural Modelling (TISM) Technique.

Keywords: Flexible manufacturing system, productivity, total interpretive structural modelling.

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Authors: E. A. Kiridi, A. O. Ogunlela

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Pollutants from aquacultural practices constitute environmental problems and phytoremediation could offer cheaper environmentally sustainable alternative since equipment using advanced treatment for fish tank effluent is expensive to import, install, operate and maintain, especially in developing countries. The main objective of this research was, therefore, to develop a mathematical model for phytoremediation by aquatic plants in aquaculture wastewater. Other objectives were to evaluate the retention times on phytoremediation rates using the model and to measure the nutrient level of the aquaculture effluent and phytoremediation rates of three aquatic macrophytes, namely; water hyacinth (Eichornia crassippes), water lettuce (Pistial stratoites) and morning glory (Ipomea asarifolia). A completely randomized experimental design was used in the study. Approximately 100 g of each macrophyte were introduced into the hydroponic units and phytoremediation indices monitored at 8 different intervals from the first to the 28^th day. The water quality parameters measured were pH and electrical conductivity (EC). Others were concentration of ammonium–nitrogen (NH4⁺ -N), nitrite- nitrogen (NO₂^- -N), nitrate- nitrogen (NO₃^- -N), phosphate –phosphorus (PO₄^3- -P), and biomass value. The biomass produced by water hyacinth was 438.2 g, 600.7 g, 688.2 g and 725.7 g at four 7–day intervals. The corresponding values for water lettuce were 361.2 g, 498.7 g, 561.2 g and 623.7 g and for morning glory were 417.0 g, 567.0 g, 642.0 g and 679.5g. Coefficient of determination was greater than 80% for EC, TDS, NO₂^- -N, NO₃^- -N and 70% for NH₄⁺ -N using any of the macrophytes and the predicted values were within the 95% confidence interval of measured values. Therefore, the model is valuable in the design and operation of phytoremediation systems for aquaculture effluent.

Keywords: Phytoremediation, macrophytes, hydroponic unit, aquaculture effluent, mathematical model.

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Authors: Abdullah A. H. Alzahrani, Majd Zohri Yafi, Fawaz K. Alarfaj

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Unified Modelling Language (UML) is a software modelling language that is widely used and accepted. One significant drawback, of which, is that the language lacks formality. This makes carrying out any type of rigorous analysis difficult process. Many researchers attempt to introduce their approaches to formalise UML diagrams. However, it is always hard to decide what language and/or approach to use. Therefore, in this paper, we highlight some of the advantages and disadvantages of number of those approaches. We also try to compare different counterpart approaches. In addition, we draw some guidelines to help in choosing the suitable approach. Special concern is given to the formalisation of the static aspects of UML shown is class diagrams.

Keywords: UML formalisation, Object Constraints Language (OCL), Description Logic (DL), Z language.

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Authors: Kamel Hashem, Ibrahim Arman

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Information and Communication Technologies (ICT) in mathematical education is a very active field of research and innovation, where learning is understood to be meaningful and grasping multiple linked representation rather than rote memorization, a great amount of literature offering a wide range of theories, learning approaches, methodologies and interpretations, are generally stressing the potentialities for teaching and learning using ICT. Despite the utilization of new learning approaches with ICT, students experience difficulties in learning concepts relevant to understanding mathematics, much remains unclear about the relationship between the computer environment, the activities it might support, and the knowledge that might emerge from such activities. Many questions that might arise in this regard: to what extent does the use of ICT help students in the process of understanding and solving tasks or problems? Is it possible to identify what aspects or features of students' mathematical learning can be enhanced by the use of technology? This paper will highlight the interest of the integration of information and communication technologies (ICT) into the teaching and learning of mathematics (quadratic functions), it aims to investigate the effect of four instructional methods on students- mathematical understanding and problem solving. Quantitative and qualitative methods are used to report about 43 students in middle school. Results showed that mathematical thinking and problem solving evolves as students engage with ICT activities and learn cooperatively.

Keywords: Dynamic Geometry Software, Information and Communication Technologies, Visualization, Mathematical Education.

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Authors: Alexander N. Savostyanov, Tatiana A. Dolgorukova, Elena A. Esipenko, Mikhail S. Zaleshin, Margherita Malanchini, Anna V. Budakova, Alexander E. Saprygin, Tatiana A. Golovko, Yulia V. Kovas

Abstract:

EEG correlates of mathematical and trait anxiety level were studied in 52 healthy Russian-speakers during execution of error-recognition tasks with lexical, arithmetic and algebraic conditions. Event-related spectral perturbations were used as a measure of brain activity. The ERSP plots revealed alpha/beta desynchronizations within a 500-3000 ms interval after task onset and slow-wave synchronization within an interval of 150-350 ms. Amplitudes of these intervals reflected the accuracy of error recognition, and were differently associated with the three conditions. The correlates of anxiety were found in theta (4-8 Hz) and beta2 (16- 20 Hz) frequency bands. In theta band the effects of mathematical anxiety were stronger expressed in lexical, than in arithmetic and algebraic condition. The mathematical anxiety effects in theta band were associated with differences between anterior and posterior cortical areas, whereas the effects of trait anxiety were associated with inter-hemispherical differences. In beta1 and beta2 bands effects of trait and mathematical anxiety were directed oppositely. The trait anxiety was associated with increase of amplitude of desynchronization, whereas the mathematical anxiety was associated with decrease of this amplitude. The effect of mathematical anxiety in beta2 band was insignificant for lexical condition but was the strongest in algebraic condition. EEG correlates of anxiety in theta band could be interpreted as indexes of task emotionality, whereas the reaction in beta2 band is related to tension of intellectual resources.

Keywords: EEG, brain activity, lexical and numerical error-recognition tasks, mathematical and trait anxiety.

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Authors: H. Dornhackl, K. Kadletz, R. Luh, P. Tavolato

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In this paper, we describe the use of formal methods to model malware behaviour. The modelling of harmful behaviour rests upon syntactic structures that represent malicious procedures inside malware. The malicious activities are modelled by a formal grammar, where API calls’ components are the terminals and the set of API calls used in combination to achieve a goal are designated non-terminals. The combination of different non-terminals in various ways and tiers make up the attack vectors that are used by harmful software. Based on these syntactic structures a parser can be generated which takes execution traces as input for pattern recognition.

Keywords: Malware behaviour, modelling, parsing, search, pattern matching.

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Authors: Meysam Lak, Mohammad Fatehi Marji, Alireza Yarahamdi Bafghi, Abolfazl Abdollahipour

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A wellbore is a hole that is drilled to aid in the exploration and recovery of natural resources including oil and gas. Occasionally, in order to increase productivity index and porosity of the wellbore and reservoir, the well stimulation methods have been used. Hydraulic fracturing is one of these methods. Moreover, several explosions at the end of the well can stimulate the reservoir and create fractures around it. In this study, crack initiation in rock around the wellbore has been numerically modeled due to explosion. One, two, three, and four pairs of explosion have been set at the end of the wellbore on its wall. After each stage of the explosion, results have been presented and discussed. Results show that this method can initiate and probably propagate several fractures around the wellbore.

Keywords: Crack initiation, explosion, finite difference modelling, well productivity.

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Authors: Susmita Sahoo, Madhumanti Datta, Rajib Kar

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Fast delay estimation methods, as opposed to simulation techniques, are needed for incremental performance driven layout synthesis. On-chip inductive effects are becoming predominant in deep submicron interconnects due to increasing clock speed and circuit complexity. Inductance causes noise in signal waveforms, which can adversely affect the performance of the circuit and signal integrity. Several approaches have been put forward which consider the inductance for on-chip interconnect modelling. But for even much higher frequency, of the order of few GHz, the shunt dielectric lossy component has become comparable to that of other electrical parameters for high speed VLSI design. In order to cope up with this effect, on-chip interconnect has to be modelled as distributed RLCG line. Elmore delay based methods, although efficient, cannot accurately estimate the delay for RLCG interconnect line. In this paper, an accurate analytical delay model has been derived, based on first and second moments of RLCG interconnection lines. The proposed model considers both the effect of inductance and conductance matrices. We have performed the simulation in 0.18μm technology node and an error of as low as less as 5% has been achieved with the proposed model when compared to SPICE. The importance of the conductance matrices in interconnect modelling has also been discussed and it is shown that if G is neglected for interconnect line modelling, then it will result an delay error of as high as 6% when compared to SPICE.

Keywords: Delay Modelling; On-Chip Interconnect; RLCGInterconnect; Ramp Input; Damping; VLSI

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Authors: I. V. Pinto, M. R. Sooriyarachchi

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It can be frequently observed that the data arising in our environment have a hierarchical or a nested structure attached with the data. Multilevel modelling is a modern approach to handle this kind of data. When multilevel modelling is combined with a binary response, the estimation methods get complex in nature and the usual techniques are derived from quasi-likelihood method. The estimation methods which are compared in this study are, marginal quasi-likelihood (order 1 & order 2) (MQL1, MQL2) and penalized quasi-likelihood (order 1 & order 2) (PQL1, PQL2). A statistical model is of no use if it does not reflect the given dataset. Therefore, checking the adequacy of the fitted model through a goodness-of-fit (GOF) test is an essential stage in any modelling procedure. However, prior to usage, it is also equally important to confirm that the GOF test performs well and is suitable for the given model. This study assesses the suitability of the GOF test developed for binary response multilevel models with respect to the method used in model estimation. An extensive set of simulations was conducted using MLwiN (v 2.19) with varying number of clusters, cluster sizes and intra cluster correlations. The test maintained the desirable Type-I error for models estimated using PQL2 and it failed for almost all the combinations of MQL. Power of the test was adequate for most of the combinations in all estimation methods except MQL1. Moreover, models were fitted using the four methods to a real-life dataset and performance of the test was compared for each model.

Keywords: Goodness-of-fit test, marginal quasi-likelihood, multilevel modelling, type-I error, penalized quasi-likelihood, power, quasi-likelihood.

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Authors: Ilija Plecas, Uranija Kozmidis-Luburic, Radojica Pesic

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The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: bentonite, cement , radioactive waste, composite, disposal, diffusion

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Authors: Khair Eddin Sabri, Ridha Khedri, Jason Jaskolka

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Cryptographic protocols are widely used in various applications to provide secure communications. They are usually represented as communicating agents that send and receive messages. These agents use their knowledge to exchange information and communicate with other agents involved in the protocol. An agent knowledge can be partitioned into explicit knowledge and procedural knowledge. The explicit knowledge refers to the set of information which is either proper to the agent or directly obtained from other agents through communication. The procedural knowledge relates to the set of mechanisms used to get new information from what is already available to the agent. In this paper, we propose a mathematical framework which specifies the explicit knowledge of an agent involved in a cryptographic protocol. Modelling this knowledge is crucial for the specification, analysis, and implementation of cryptographic protocols. We also, report on a prototype tool that allows the representation and the manipulation of the explicit knowledge.

Keywords: Information Algebra, Agent Knowledge, CryptographicProtocols

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Authors: V. S. Klimash, Ye Min Thu

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Thyristor rectifiers, inverters grid-tied, and AC voltage regulators are widely used in industry, and on electrified transport, they have a lot in common both in the power circuit and in the control system. They have a common mathematical structure and switching processes. At the same time, the rectifier, but the inverter units and thyristor regulators of alternating voltage are considered separately both theoretically and practically. They are written about in different books as completely different devices. The aim of this work is to combine them into one class based on the unity of the equations describing electromagnetic processes, and then, to show this unity on the mathematical model and experimental setup. Based on research from mathematics to the product, a conclusion is made about the methodology for the rapid conduct of research and experimental design work, preparation for production and serial production of converters with a unified bundle. In recent years, there has been a transition from thyristor circuits and transistor in modular design. Showing the example of thyristor rectifiers and AC voltage regulators, we can conclude that there is a unity of mathematical structures and grid-tied thyristor converters.

Keywords: Direct current, alternating current, rectifier, AC voltage regulator, generalized mathematical model.

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