Search results for: Simpson’s rule and Volterra integro-differential equations.

Authors: Sanjay K.Srivastava, Bhanu Gupta

Abstract:

In this paper some results on strict stability heve beeb extended for fuzzy differential equations with impulse effect using Lyapunov functions and Razumikhin technique.

Keywords: Fuzzy differential equations, Impulsive differential equations, Strict stability, Lyapunov function, Razumikhin technique.

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Authors: Seyed R Mousavi

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In most rule-induction algorithms, the only operator used against nominal attributes is the equality operator =. In this paper, we first propose the use of the inequality operator, ≠, in addition to the equality operator, to increase the expressiveness of induced rules. Then, we present a new method, Binary Coding, which can be used along with an arbitrary rule-induction algorithm to make use of the inequality operator without any need to change the algorithm. Experimental results suggest that the Binary Coding method is promising enough for further investigation, especially in cases where the minimum number of rules is desirable.

Keywords: Data mining, Inequality operator, Number of rules, Rule-induction.

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Authors: Gunawan Nugroho, Ahmed M. S. Ali, Zainal A. Abdul Karim

Abstract:

Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this paper. Even though, the analytical solution is derived for nonreacting flows, it could reproduce trends for cases including combustion.

Keywords: Navier-Stokes Equations, potential function, turbulent flows.

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Authors: Alireza Tavakolinia

Abstract:

In order to understand the role of the injured party's fault in dividing liability, we studied its historical background. In common law, the traditional contributory negligence rule was a complete defense. Then the legislature and judicial procedure modified that rule to one of apportionment. In Islamic law, too, the Action rule was at first used when the injured party was the sole cause, but jurists expanded the scope of this rule, so this rule was used in cases where both the injured party's fault and that of the other party are involved. There are some popular approaches for apportionment of damages. Some common law countries like Britain had chosen ‘the causal potency approach’ and ‘fixed apportionment’. Islamic countries like Iran have chosen both ‘the relative blameworthiness’ and ‘equal apportionment’ approaches. The article concludes that both common law and Islamic law believe in the division of responsibility between a wrongdoer claimant and the defendant. In contrast, in the apportionment of responsibility, Islamic law mostly believes in equal apportionment that is way easier and saves time and money, but common law legal systems have chosen the causal potency approach which is more complicated than the rival approach but is fairer.

Keywords: Contributory negligence, common law, Islamic Law, Tort Law.

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Authors: Guiheng Zhang, Wei Zhang, Jun Fu, Yudong Wang

Abstract:

A 900 MHz three-stage SiGe power amplifier (PA) with high power gain is presented in this paper. Volterra Series is applied to analyze nonlinearity sources of SiGe HBT device model clearly. Meanwhile, the influence of operating current to IMD3 is discussed. Then a β-helper current mirror bias circuit is applied to improve linearity, since the β-helper current mirror bias circuit can offer stable base biasing voltage. Meanwhile, it can also work as predistortion circuit when biasing voltages of three bias circuits are fine-tuned, by this way, the power gain and operating current of PA are optimized for best linearity. The three power stages which fabricated by 0.18 μm SiGe technology are bonded to the printed circuit board (PCB) to obtain impedances by Load-Pull system, then matching networks are done for best linearity with discrete passive components on PCB. The final measured three-stage PA exhibits 21.1 dBm of output power at 1 dB compression point (OP1dB) with power added efficiency (PAE) of 20.6% and 33 dB power gain under 3.3 V power supply voltage.

Keywords: High gain power amplifier, linearization bias circuit, SiGe HBT model, Volterra Series.

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Authors: Yongxin Yuan, Kezheng Zuo

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In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

Keywords: Matrix equation, Generalized inverse, Generalized singular-value decomposition.

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Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

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Authors: Pankaj Swarnkar, Shailendra Jain, R.K Nema

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Adaptive control involves modifying the control law used by the controller to cope with the fact that the parameters of the system being controlled change drastically due to change in environmental conditions or in system itself. This technique is based on the fundamental characteristic of adaptation of living organism. The adaptive control process is one that continuously and automatically measures the dynamic behavior of plant, compares it with the desired output and uses the difference to vary adjustable system parameters or to generate an actuating signal in such a way so that optimal performance can be maintained regardless of system changes. This paper deals with application of model reference adaptive control scheme in first order system. The rule which is used for this application is MIT rule. This paper also shows the effect of adaptation gain on the system performance. Simulation is done in MATLAB and results are discussed in detail.

Keywords: Adaptive control system, Adaptation gain, MIT rule, Model reference adaptive control.

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Authors: Sarabjeet Kaur Kochhar

Abstract:

With a surge of stream processing applications novel techniques are required for generation and analysis of association rules in streams. The traditional rule mining solutions cannot handle streams because they generally require multiple passes over the data and do not guarantee the results in a predictable, small time. Though researchers have been proposing algorithms for generation of rules from streams, there has not been much focus on their analysis. We propose Association rule profiling, a user centric process for analyzing association rules and attaching suitable profiles to them depending on their changing frequency behavior over a previous snapshot of time in a data stream. Association rule profiles provide insights into the changing nature of associations and can be used to characterize the associations. We discuss importance of characteristics such as predictability of linkages present in the data and propose metric to quantify it. We also show how association rule profiles can aid in generation of user specific, more understandable and actionable rules. The framework is implemented as SUPAR: System for Usercentric Profiling of Association Rules in streaming data. The proposed system offers following capabilities: i) Continuous monitoring of frequency of streaming item-sets and detection of significant changes therein for association rule profiling. ii) Computation of metrics for quantifying predictability of associations present in the data. iii) User-centric control of the characterization process: user can control the framework through a) constraint specification and b) non-interesting rule elimination.

Keywords: Data Streams, User subjectivity, Change detection, Association rule profiles, Predictability.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

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In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.

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Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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Authors: M. Zarebnia, S. Khani

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In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

Keywords: Hammerstein integral equations, quasi-interpolation, Nystrom’s method.

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Authors: R. AliMohammadzadeh, M. Rahgozar, A. Zarnani

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The inherent flexibilities of XML in both structure and semantics makes mining from XML data a complex task with more challenges compared to traditional association rule mining in relational databases. In this paper, we propose a new model for the effective extraction of generalized association rules form a XML document collection. We directly use frequent subtree mining techniques in the discovery process and do not ignore the tree structure of data in the final rules. The frequent subtrees based on the user provided support are split to complement subtrees to form the rules. We explain our model within multi-steps from data preparation to rule generation.

Keywords: XML, Data Mining, Association Rule Mining.

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Authors: Yoshiaki Shikata, Wataru Katagiri, Yoshitaka Takahashi

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We propose a novel prioritized limited processor-sharing (PS) rule and a simulation algorithm for the performance evaluation of this rule. The performance measures of practical interest are evaluated using this algorithm. Suppose that there are two classes and that an arriving (class-1 or class-2) request encounters n1 class-1 and n2 class-2 requests (including the arriving one) in a single-server system. According to the proposed rule, class-1 requests individually and simultaneously receive m / (m * n1+ n2) of the service-facility capacity, whereas class-2 requests receive 1 / (m *n1 + n2) of it, if m * n1 + n2 ≤ C. Otherwise (m * n1 + n2 > C), the arriving request will be queued in the corresponding class waiting room or rejected. Here, m (
1) denotes the priority ratio, and C ( ∞), the service-facility capacity. In this rule, when a request arrives at [or departs from] the system, the extension [shortening] of the remaining sojourn time of each request receiving service can be calculated using the number of requests of each class and the priority ratio. Employing a simulation program to execute these events and calculations enables us to analyze the performance of the proposed prioritized limited PS rule, which is realistic in a time-sharing system (TSS) with a sufficiently small time slot. Moreover, this simulation algorithm is expanded for the evaluation of the prioritized limited PS system with N
3 priority classes.

Keywords: PS rule, priority ratio, service-facility capacity, simulation algorithm, sojourn time, performance measures

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Authors: Ersin Kaya, Bulent Oran, Ahmet Arslan

Abstract:

In this study, fuzzy rule-based classifier is used for the diagnosis of congenital heart disease. Congenital heart diseases are defined as structural or functional heart disease. Medical data sets were obtained from Pediatric Cardiology Department at Selcuk University, from years 2000 to 2003. Firstly, fuzzy rules were generated by using medical data. Then the weights of fuzzy rules were calculated. Two different reasoning methods as “weighted vote method" and “singles winner method" were used in this study. The results of fuzzy classifiers were compared.

Keywords: Congenital heart disease, Fuzzy rule-basedclassifiers, Classification

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Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: M. A. Sedghamiz, S. Raeissi

Abstract:

This study presents three different approaches to estimate bubble point pressures for the binary system of CO2 and ethyl palmitate fatty acid ethyl ester. The first method involves the Peng-Robinson (PR) Equation of State (EoS) with the conventional mixing rule of Van der Waals. The second approach involves the PR EOS together with the Wong Sandler (WS) mixing rule, coupled with the UNIQUAC GE model. In order to model the bubble point pressures with this approach, the volume and area parameter for ethyl palmitate were estimated by the Hansen group contribution method. The last method involved the Peng-Robinson, combined with the Wong-Sandler method, but using NRTL as the GE model. Results using the Van der Waals mixing rule clearly indicated that this method has the largest errors among all three methods, with errors in the range of 3.96-6.22%. The PR-WS-UNIQUAC method exhibited small errors, with average absolute deviations between 0.95 to 1.97 percent. The PR-WS-NRTL method led to the least errors, where average absolute deviations ranged between 0.65-1.7%.

Keywords: Bubble pressure, Gibbs excess energy model, mixing rule, CO2 solubility, ethyl palmitate.

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Authors: İres İskender, Ahmet Karaarslan

Abstract:

In this study, the performance of a high-frequency arc welding machine including a two-switch inverter is analyzed. The control of the system is achieved using two different control techniques i- fuzzy logic control (FLC) ii- state space averaging based sliding control. Fuzzy logic control does not need accurate mathematical model of a plant and can be used in nonlinear applications. The second method needs the mathematical model of the system. In this method the state space equations of the system are derived for two different “on" and “off" states of the switches. The derived state equations are combined with the sliding control rule considering the duty-cycle of the converter. The performance of the system is analyzed by simulating the system using SIMULINK tool box of MATLAB. The simulation results show that fuzzy logic controller is more robust and less sensitive to parameter variations.

Keywords: Fuzzy logic, arc welding, sliding state space control, PWM, current control.

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Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVP­s­) in ordinary differential equations (ODE­s­) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, First Order Ordinary Differential Equations, Hybrid, Self starting.

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

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Authors: D. Sasikala, K. Premalatha

Abstract:

The use of eXtensible Markup Language (XML) in web, business and scientific databases lead to the development of methods, techniques and systems to manage and analyze XML data. Semi-structured documents suffer due to its heterogeneity and dimensionality. XML structure and content mining represent convergence for research in semi-structured data and text mining. As the information available on the internet grows drastically, extracting knowledge from XML documents becomes a harder task. Certainly, documents are often so large that the data set returned as answer to a query may also be very big to convey the required information. To improve the query answering, a Semantic Tree Based Association Rule (STAR) mining method is proposed. This method provides intentional information by considering the structure, content and the semantics of the content. The method is applied on Reuter’s dataset and the results show that the proposed method outperforms well.

Keywords: Semi--structured Document, Tree based Association Rule (TAR), Semantic Association Rule Mining.

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Authors: M. Breška, I. Peruš, V. Stankovski

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The number of Ground Motion Prediction Equations (GMPEs) used for predicting peak ground acceleration (PGA) and the number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.

Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database.

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Authors: Nisha Goyal, R.K. Gupta

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Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: P. C. Tewari, Parveen Kumar

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The paper describes the availability analysis of milling system of a rice milling plant using probabilistic approach. The subsystems under study are special purpose machines. The availability analysis of the system is carried out to determine the effect of failure and repair rates of each subsystem on overall performance (i.e. steady state availability) of system concerned. Further, on the basis of effect of repair rates on the system availability, maintenance repair priorities have been suggested. The problem is formulated using Markov Birth-Death process taking exponential distribution for probable failures and repair rates. The first order differential equations associated with transition diagram are developed by using mnemonic rule. These equations are solved using normalizing conditions and recursive method to drive out the steady state availability expression of the system. The findings of the paper are presented and discussed with the plant personnel to adopt a suitable maintenance policy to increase the productivity of the rice milling plant.

Keywords: Markov process, milling system, availability modeling, rice milling plant.

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Authors: Erika Ann Schaub, Christian J Darken

Abstract:

Sociological models (e.g., social network analysis, small-group dynamic and gang models) have historically been used to predict the behavior of terrorist groups. However, they may not be the most appropriate method for understanding the behavior of terrorist organizations because the models were not initially intended to incorporate violent behavior of its subjects. Rather, models that incorporate life and death competition between subjects, i.e., models utilized by scientists to examine the behavior of wildlife populations, may provide a more accurate analysis. This paper suggests the use of biological models to attain a more robust method for understanding the behavior of terrorist organizations as compared to traditional methods. This study also describes how a biological population model incorporating predator-prey behavior factors can predict terrorist organizational recruitment behavior for the purpose of understanding the factors that govern the growth and decline of terrorist organizations. The Lotka-Volterra, a biological model that is based on a predator-prey relationship, is applied to a highly suggestive case study, that of the Irish Republican Army. This case study illuminates how a biological model can be utilized to understand the actions of a terrorist organization.

Keywords: Biological Models, Lotka-Volterra Predator-Prey Model, Terrorist Organizational Behavior, Terrorist Recruitment.

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Authors: Qianhong Zhang, Wenzhuan Zhang

Abstract:

This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.

Keywords: Difference equations, stability, unstable, global asymptotic behavior.

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Authors: Bhanu Gupta, Sanjay K. Srivastava

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In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.

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Authors: Kriangkrai Maneerat, Chutima Prommak

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This paper presents an analysis of the localization accuracy of indoor positioning systems using Cramer-s rule via IEEE 802.15.4 wireless sensor networks. The objective is to study the impact of the methods used to convert the received signal strength into the distance that is used to compute the object location in the wireless indoor positioning system. Various methods were tested and the localization accuracy was analyzed. The experimental results show that the method based on the empirical data measured in the non line-of-sight (NLOS) environment yield the highest localization accuracy; with the minimum error distance less than 3 m.

Keywords: Indoor positioning systems, localization accuracy, wireless networks, Cramer's rule.

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Authors: Bin Yu, Minghui Wang, Juntao Zhang

Abstract:

By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.

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Authors: Prasan Pitiranggon, Nunthika Benjathepanun, Somsri Banditvilai, Veera Boonjing

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Our study proposes an alternative method in building Fuzzy Rule-Based System (FRB) from Support Vector Machine (SVM). The first set of fuzzy IF-THEN rules is obtained through an equivalence of the SVM decision network and the zero-ordered Sugeno FRB type of the Adaptive Network Fuzzy Inference System (ANFIS). The second set of rules is generated by combining the first set based on strength of firing signals of support vectors using Gaussian kernel. The final set of rules is then obtained from the second set through input scatter partitioning. A distinctive advantage of our method is the guarantee that the number of final fuzzy IFTHEN rules is not more than the number of support vectors in the trained SVM. The final FRB system obtained is capable of performing classification with results comparable to its SVM counterpart, but it has an advantage over the black-boxed SVM in that it may reveal human comprehensible patterns.

Keywords: Fuzzy Rule Base, Rule Extraction, Rule Generation, Support Vector Machine.

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