Search results for: Time Utility Function/ Utility Accrual (TUF/UA) scheduling

Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

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In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: Wei Zhang, Xin Zhao, Yi-Fan Zhu, Xin-Jian Zhang

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Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, Green function, support vectorregression

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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: Peng Zhang, Lihui Zheng, Xiangchun Wang, Xiaopan Kou

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Quantitative research on the main control factors of lost circulation has few considerations and single data source. Using Unmanned Intervention Algorithm to find the main control factors of lost circulation adopts all measurable parameters. The degree of lost circulation is characterized by the loss rate as the objective function. Geological, engineering and fluid data are used as layers, and 27 factors such as wellhead coordinates and Weight on Bit (WOB) used as dimensions. Data classification is implemented to determine function independent variables. The mathematical equation of loss rate and 27 influencing factors is established by multiple regression method, and the undetermined coefficient method is used to solve the undetermined coefficient of the equation. Only three factors in t-test are greater than the test value 40, and the F-test value is 96.557%, indicating that the correlation of the model is good. The funnel viscosity, final shear force and drilling time were selected as the main control factors by elimination method, contribution rate method and functional method. The calculated values of the two wells used for verification differ from the actual values by -3.036 m3/h and -2.374 m3/h, with errors of 7.21% and 6.35%. The influence of engineering factors on the loss rate is greater than that of funnel viscosity and final shear force, and the influence of the three factors is less than that of geological factors. The best combination of funnel viscosity, final shear force and drilling time is obtained through quantitative calculation. The minimum loss rate of lost circulation wells in Shunbei area is 10 m3/h. It can be seen that man-made main control factors can only slow down the leakage, but cannot fundamentally eliminate it. This is more in line with the characteristics of karst caves and fractures in Shunbei fault solution oil and gas reservoir.

Keywords: Drilling fluid, loss rate, main controlling factors, Unmanned Intervention Algorithm.

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Authors: Li Long, Thomas Ortlepp

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The transport properties of carriers in polycrystalline silicon film affect the performance of polycrystalline silicon-based devices. They depend strongly on the grain structure, grain boundary trap properties and doping concentration, which in turn are determined by the film deposition and processing conditions. Based on the properties of charge carriers, phonons, grain boundaries and their interactions, the thermoelectric properties of polycrystalline silicon are analyzed with the relaxation time approximation of the Boltzmann transport equation. With this approach, thermal conductivity, electrical conductivity and Seebeck coefficient as a function of grain size, trap properties and doping concentration can be determined. Experiment on heavily doped polycrystalline silicon is carried out and measurement results are compared with the model.

Keywords: Conductivity, polycrystalline silicon, relaxation time approximation, Seebeck coefficient, thermoelectric property.

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Authors: Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Alejandro Fuentes-Penna, Daniel Vélez-Díaz, Edith Olaco García

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In this paper, we present the use of the discriminant analysis to select evolutionary algorithms that better solve instances of the vehicle routing problem with time windows. We use indicators as independent variables to obtain the classification criteria, and the best algorithm from the generic genetic algorithm (GA), random search (RS), steady-state genetic algorithm (SSGA), and sexual genetic algorithm (SXGA) as the dependent variable for the classification. The discriminant classification was trained with classic instances of the vehicle routing problem with time windows obtained from the Solomon benchmark. We obtained a classification of the discriminant analysis of 66.7%.

Keywords: Intelligent transportation systems, data-mining techniques, evolutionary algorithms, discriminant analysis, machine learning.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

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In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: Mahmoud M. Tash

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The present study was undertaken to investigate the effect of aging parameters (time and temperature) on the mechanical properties of Be-and/or Zr- treated Al-Mg-Zn (7075) alloys. Ultimate tensile strength, 0.5% offset yield strength and % elongation measurements were carried out on specimens prepared from cast and heat treated 7075 alloys containing Be and/or Zr. Different aging treatment were carried out for the as solution treated (SHT) specimens (after quenching in warm water). The specimens were aged at different conditions; Natural and artificial aging was carried out at room temperature, 120C, 150C, 180C and 220C for different periods of time. Duplex aging was performed for SHT conditions (pre-aged at different time and temperature followed by high temperature aging). Ultimate tensile strength, yield strength and % elongation data results as a function of different aging parameters are analysed. A statistical design of experiments (DOE) approach using fractional factorial design is applied to acquire an understanding of the effects of these variables and their interactions on the mechanical properties of Be- and/or Zr- treated 7075 alloys. Mathematical models are developed to relate the alloy mechanical properties with the different aging parameters.

Keywords: Casting, Aging Treatment, Mechanical Properties, Al-Mg-Zn (7075) alloys, Be- and/or Zr-Treatment, Experimental Correlation.

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Authors: Anupama Pande, Vishik Goel

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A complex valued neural network is a neural network, which consists of complex valued input and/or weights and/or thresholds and/or activation functions. Complex-valued neural networks have been widening the scope of applications not only in electronics and informatics, but also in social systems. One of the most important applications of the complex valued neural network is in image and vision processing. In Neural networks, radial basis functions are often used for interpolation in multidimensional space. A Radial Basis function is a function, which has built into it a distance criterion with respect to a centre. Radial basis functions have often been applied in the area of neural networks where they may be used as a replacement for the sigmoid hidden layer transfer characteristic in multi-layer perceptron. This paper aims to present exhaustive results of using RBF units in a complex-valued neural network model that uses the back-propagation algorithm (called 'Complex-BP') for learning. Our experiments results demonstrate the effectiveness of a Radial basis function in a complex valued neural network in image recognition over a real valued neural network. We have studied and stated various observations like effect of learning rates, ranges of the initial weights randomly selected, error functions used and number of iterations for the convergence of error on a neural network model with RBF units. Some inherent properties of this complex back propagation algorithm are also studied and discussed.

Keywords: Complex valued neural network, Radial BasisFunction, Image recognition.

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Authors: Omid S. Fard, Akbar H. Borzabadi

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In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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Authors: Wei Lo, Ming-En Kuo

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While to minimize the overall project cost is always one of the objectives of construction managers, to obtain the maximum economic return is definitely one the ultimate goals of the project investors. As there is a trade-off relationship between the project time and cost, and the project delivery time directly affects the timing of economic recovery of an investment project, to provide a method that can quantify the relationship between the project delivery time and cost, and identify the optimal delivery time to maximize economic return has always been the focus of researchers and industrial practitioners. Using genetic algorithms, this study introduces an optimization model that can quantify the relationship between the project delivery time and cost and furthermore, determine the optimal delivery time to maximize the economic return of the project. The results provide objective quantification for accurately evaluating the project delivery time and cost, and facilitate the analysis of the economic return of a project.

Keywords: Time-Cost Trade-Off, Genetic Algorithms, Resource Integration, Economic return.

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Authors: Mehmet Nefes, Selman Demirel, Hasan H. Ertok, Cenk Sen

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A typical reliability engineering problem regarding communication satellites has been considered to determine redundancy allocation scheme of power amplifiers within payload transponder module, whose dominant function is to amplify power levels of the received signals from the Earth, through maximizing reliability against mass, power, and other technical limitations. Adding each redundant power amplifier component increases not only reliability but also hardware, testing, and launch cost of a satellite. This study investigates a multi-objective approach used in order to solve Redundancy Allocation Problem (RAP) for a communication satellite payload transponder, focusing on design cost due to redundancy and reliability factors. The main purpose is to find the optimum power amplifier redundancy configuration satisfying reliability and capacity thresholds simultaneously instead of analyzing respectively or independently. A mathematical model and calculation approach are instituted including objective function definitions, and then, the problem is solved analytically with different input parameters in MATLAB environment. Example results showed that payload capacity and failure rate of power amplifiers have remarkable effects on the solution and also processing time.

Keywords: Communication satellite payload, multi-objective optimization, redundancy allocation problem, reliability, transponder.

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Authors: V. Tawiwat, T. Amornthep, P. Pnop

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Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper considers the indirect minimum Jerk method for higher order differential equation in dynamics optimization proposes a simple yet very interesting indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This case considers the linear equation of a simple system, for instance, mass, spring and damping. The simple system uses two mass connected together by springs. The boundary initial is defined the fix end time and end point. The higher differential order is solved by Galerkin-s methods weight residual. As the result, the 6th higher differential order shows the faster solving time.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: Rusliza Ahmad, Harun Budin

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This paper studies the effect of time delay on stability of mutualism population model with limited resources for both species. First, the stability of the model without time delay is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. We analyze the effect of time delay on the stability of the stable equilibrium point. Result showed that the time delay can induce instability of the stable equilibrium point, bifurcation and stability switches.

Keywords: Bifurcation, Delay margin, Mutualism population model, Time delay

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Authors: Gamze Ozel, Selen Cakmakyapan

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We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study. 

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.

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Authors: Jianjun Yuan, Changjun Jiang

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Pairwise testing, which requires that every combination of valid values of each pair of system factors be covered by at lease one test case, plays an important role in software testing since many faults are caused by unexpected 2-way interactions among system factors. Although meta-heuristic strategies like simulated annealing can generally discover smaller pairwise test suite, they may cost more time to perform search, compared with greedy algorithms. We propose a new method, improved Extremal Optimization (EO) based on the Bak-Sneppen (BS) model of biological evolution, for constructing pairwise test suites and define fitness function according to the requirement of improved EO. Experimental results show that improved EO gives similar size of resulting pairwise test suite and yields an 85% reduction in solution time over SA.

Keywords: Covering Arrays, Extremal Optimization, Simulated Annealing, Software Testing.

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Authors: Marzieh Moosavi-Nasab, Behnaz Layegh , Ladan Aminlari, Mohammad B. Hashemi

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Levan, an exopolysaccharide, was produced by Microbacterium laevaniformans and its yield was characterized as a function of concentrations of date syrup, sucrose and the fermentation time. The optimum condition for levan production from sucrose was at concentration of 20% sucrose for 48 h and for date syrup was 25% for 48 h. The results show that an increase in fermentation time caused a decrease in the levan production at all concentrations of date syrup tested. Under these conditions after 48 h in sucrose medium, levan production reached 48.9 g/L and for date syrup reached 10.48 g/L . The effect of pH on the yield of the purified levan was examined and the optimum pH for levan production was determined to be 6.0. Levan was composed mainly of fructose residues when analyzed by TLC and FT-IR spectroscopy. Date syrup is a cheap substrate widely available in Iran and has potential for levan production. The thermal stability of levan was assessed by Thermo Gravimetric Analysis (TGA) that revealed the onset of decomposition near to 49°C for the levan produced from sucrose and 51°C for the levan from date syrup. DSC results showed a single Tg at 98°C for levan produced from sucrose and 206 °C for levan from date syrup.

Keywords: Date syrup, Fermentation, Levan, Microbacteriumlaevaniformans

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Authors: N. A. Ibrahim, A. Kudus, I. Daud, M. R. Abu Bakar

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Competing risks survival data that comprises of more than one type of event has been used in many applications, and one of these is in clinical study (e.g. in breast cancer study). The decision tree method can be extended to competing risks survival data by modifying the split function so as to accommodate two or more risks which might be dependent on each other. Recently, researchers have constructed some decision trees for recurrent survival time data using frailty and marginal modelling. We further extended the method for the case of competing risks. In this paper, we developed the decision tree method for competing risks survival time data based on proportional hazards for subdistribution of competing risks. In particular, we grow a tree by using deviance statistic. The application of breast cancer data is presented. Finally, to investigate the performance of the proposed method, simulation studies on identification of true group of observations were executed.

Keywords: Competing risks, Decision tree, Simulation, Subdistribution Proportional Hazard.

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Authors: Vidyasagar Shilapuram, Nesrin Ozalp, Anam Waheed

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Carboneous catalytical methane decomposition is an attractive process because it produces two valuable products: hydrogen and carbon. Furthermore, this reaction does not emit any green house or hazardous gases. In the present study, experiments were conducted in a thermo gravimetric analyzer using Fluka 05120 as carboneous catalyst to analyze its effectiveness in methane decomposition. Various temperatures and methane partial pressures were chosen and carbon mass gain was observed as a function of time. Results are presented in terms of carbon formation rate, hydrogen production and catalytical activity. It is observed that there is linearity in carbon deposition amount by time at lower reaction temperature (780 °C). On the other hand, it is observed that carbon and hydrogen formation rates are increased with increasing temperature. Finally, we observed that the carbon formation rate is highest at 950 °C within the range of temperatures studied.

Keywords: Catalysis, Fluka 05120, Hydrogen production, Methane decomposition

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Authors: Pearl Goswell, Jun Jo

Abstract:

Creating3D environments, including characters and cities, is a significantly time consuming process due to a large amount of workinvolved in designing and modelling.There have been a number of attempts to automatically generate 3D objects employing shape grammars. However it is still too early to apply the mechanism to real problems such as real-time computer games.The purpose of this research is to introduce a time efficient and cost effective method to automatically generatevarious 3D objects for real-time 3D games. This Shape grammar-based real-time City Generation (RCG) model is a conceptual model for generating 3Denvironments in real-time and can be applied to 3D gamesoranimations. The RCG system can generate even a large cityby applying fundamental principles of shape grammars to building elementsin various levels of detailin real-time.

Keywords: real-time city generation, shape grammars, 3D games, 3D modelling.

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Authors: Fengxia Zheng, Shouming Zhong

Abstract:

ANNARIMA that combines both autoregressive integrated moving average (ARIMA) model and artificial neural network (ANN) model is a valuable tool for modeling and forecasting nonlinear time series, yet the over-fitting problem is more likely to occur in neural network models. This paper provides a hybrid methodology that combines both radial basis function (RBF) neural network and auto regression (AR) model based on binomial smoothing (BS) technique which is efficient in data processing, which is called BSRBFAR. This method is examined by using the data of Canadian Lynx data. Empirical results indicate that the over-fitting problem can be eased using RBF neural network based on binomial smoothing which is called BS-RBF, and the hybrid model–BS-RBFAR can be an effective way to improve forecasting accuracy achieved by BSRBF used separately.

Keywords: Binomial smoothing (BS), hybrid, Canadian Lynx data, forecasting accuracy.

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Authors: Ashish Payal, C. S. Rai, B. V. R. Reddy

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With the increasing use and application of Wireless Sensor Networks (WSN), need has arisen to explore them in more effective and efficient manner. An important area which can bring efficiency to WSNs is the localization process, which refers to the estimation of the position of wireless sensor nodes in an ad hoc network setting, in reference to a coordinate system that may be internal or external to the network. In this paper, we have done comparison and analysed Sigmoidal Feedforward Artificial Neural Networks (SFFANNs) and Radial Basis Function (RBF) networks for developing localization framework in WSNs. The presented work utilizes the Received Signal Strength Indicator (RSSI), measured by static node on 100 x 100 m² grid from three anchor nodes. The comprehensive evaluation of these approaches is done using MATLAB software. The simulation results effectively demonstrate that FFANNs based sensor motes will show better localization accuracy as compared to RBF.

Keywords: Localization, wireless sensor networks, artificial neural network, radial basis function, multi-layer perceptron, backpropagation, RSSI.

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.

Keywords: Bargmann functions, Husimi functions, zeros.

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Authors: Jaemyoung Lee

Abstract:

We present a method to set up system functions through a near filed communication (NFC) of a smartphone. The short communication distance of the NFC which is usually less than 4 cm could prevent any interferences from other devices and establish a secure communication channel between a system and the smartphone. The proposed set-up method for system function values is demonstrated for a blacbox system in a car. In demonstration, system functions of a blackbox which is manipulated through NFC of a smartphone are controls of image quality, sound level, shock sensing level to store images, etc. The proposed set-up method for system function values can be used for any devices with NFC.

Keywords: System set-up, near field communication, smartphone, Android.

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Authors: S. V. Yendiyarov

Abstract:

Pattern discovery from time series is of fundamental importance. Particularly, when information about the structure of a pattern is not complete, an algorithm to discover specific patterns or shapes automatically from the time series data is necessary. The dynamic time warping is a technique that allows local flexibility in aligning time series. Because of this, it is widely used in many fields such as science, medicine, industry, finance and others. However, a major problem of the dynamic time warping is that it is not able to work with structural changes of a pattern. This problem arises when the structure is influenced by noise, which is a common thing in practice for almost every application. This paper addresses this problem by means of developing a novel technique called adaptive dynamic time warping.

Keywords: Pattern recognition, optimal control, quadratic programming, dynamic programming, dynamic time warping, sintering control.

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Authors: R. Kongnuy, E. Naowanich, T. Kruehong

Abstract:

An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

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Authors: Meiyuan Zheng, Jingwu He, Yuexi Xiong

Abstract:

A universal multi-function leaf spring main landing gear was designed for light aircraft. The main landing gear combined with the leaf spring, skidding, and wheels enables it to have a good takeoff and landing performance on various grounds such as the hard, snow, grass and sand grounds. Firstly, the characteristics of different landing sites were studied in this paper in order to analyze the load of the main landing gear on different types of grounds. Based on this analysis, the structural design optimization along with the strength and stiffness characteristics of the main landing gear has been done, which enables it to have good takeoff and landing performance on different types of grounds given the relevant regulations and standards. Additionally, the impact of the skidding on the aircraft during the flight was also taken into consideration. Finally, a universal multi-function leaf spring type of the main landing gear suitable for light aircraft has been developed.

Keywords: Landing gear, multi-function, leaf spring, skidding.

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Authors: Nur Syibrah Muhamad Naim, Mohd Lazim Abdullah, Che Mohd Imran Che Taib, Abu OsmanMd. Tap

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Decision making preferences to certain criteria usually focus on positive degrees without considering the negative degrees. However, in real life situation, evaluation becomes more comprehensive if negative degrees are considered concurrently. Preference is expected to be more effective when considering both positive and negative degrees of preference to evaluate the best selection. Therefore, the aim of this paper is to propose the conflicting bifuzzy preference relations in group decision making by utilization of a novel score function. The conflicting bifuzzy preference relation is obtained by introducing some modifications on intuitionistic fuzzy preference relations. Releasing the intuitionistic condition by taking into account positive and negative degrees simultaneously and utilizing the novel score function are the main modifications to establish the proposed preference model. The proposed model is tested with a numerical example and proved to be simple and practical. The four-step decision model shows the efficiency of obtaining preference in group decision making.

Keywords: Fuzzy preference relations, score function, conflicting bifuzzy, decision making.

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Authors: C. Ardil

Abstract:

Aircraft supplier selection process, which is considered as a fundamental supply chain problem, is a multi-criteria group decision problem that has a significant impact on the performance of the entire supply chain. In practical situations are frequently incomplete and uncertain information, making it difficult for decision-makers to communicate their opinions on candidates with precise and definite values. To solve the aircraft supplier selection problem in an environment of incomplete and uncertain information, proximity measure method is proposed. It uses determinate fuzzy numbers. The weights of each decision maker are equally predetermined and the entropic criteria weights are calculated using each decision maker's decision matrix. Additionally, determinate fuzzy numbers, it is proposed to use the weighted normalized Minkowski distance function and Hausdorff distance function to determine the ranking order patterns of alternatives. A numerical example for aircraft supplier selection is provided to further demonstrate the applicability, effectiveness, validity and rationality of the proposed method.

Keywords: Aircraft supplier selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Minkowski distance function, Hausdorff distance function, PMM, MCDM

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Authors: J. Arneric, A. Rozga

Abstract:

In this paper usefulness of quasi-Newton iteration procedure in parameters estimation of the conditional variance equation within BHHH algorithm is presented. Analytical solution of maximization of the likelihood function using first and second derivatives is too complex when the variance is time-varying. The advantage of BHHH algorithm in comparison to the other optimization algorithms is that requires no third derivatives with assured convergence. To simplify optimization procedure BHHH algorithm uses the approximation of the matrix of second derivatives according to information identity. However, parameters estimation in a/symmetric GARCH(1,1) model assuming normal distribution of returns is not that simple, i.e. it is difficult to solve it analytically. Maximum of the likelihood function can be founded by iteration procedure until no further increase can be found. Because the solutions of the numerical optimization are very sensitive to the initial values, GARCH(1,1) model starting parameters are defined. The number of iterations can be reduced using starting values close to the global maximum. Optimization procedure will be illustrated in framework of modeling volatility on daily basis of the most liquid stocks on Croatian capital market: Podravka stocks (food industry), Petrokemija stocks (fertilizer industry) and Ericsson Nikola Tesla stocks (information-s-communications industry).

Keywords: Heteroscedasticity, Log-likelihood Maximization, Quasi-Newton iteration procedure, Volatility.

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