This document presents a new multi-step Runge-Kutta method of order two for solving fuzzy differential equations. The method uses harmonic mean of the parameters in the main formula to increase the accuracy of the solution compared to existing Runge-Kutta methods. The paper defines fuzzy numbers and fuzzy derivatives. It presents the fuzzy Cauchy problem and its unique solution. The new second order Runge-Kutta method with harmonic mean is derived. Numerical examples are provided to illustrate the accuracy and efficiency of the proposed method compared to other methods.
IRJET- Wavelet based Galerkin Method for the Numerical Solution of One Dimens...IRJET Journal
This document presents a wavelet-based Galerkin method for numerically solving one-dimensional partial differential equations using Hermite wavelets. Hermite wavelets are used as the basis functions in the Galerkin method. The method is demonstrated on some test problems, and the numerical results obtained from the proposed method are compared to exact solutions and a finite difference method to evaluate the accuracy and efficiency of the proposed wavelet Galerkin approach.
Spectral methods for solving differential equationsRajesh Aggarwal
This project report describes Rajesh Aggarwal's summer research fellowship project on spectral methods for solving differential equations under the guidance of Dr. Pravin Kumar Gupta at IIT Roorkee from June 11, 2014 to August 6, 2014. The report provides background on analytical and numerical methods for solving differential equations, specifically conventional finite difference methods and spectral finite difference methods. It then describes the methodology, codes, and results of applying both methods to solve sample differential equations on a half-space and layered earth problems. Tables and graphs comparing the accuracy of the two methods are presented.
Neural network precept diagnosis on petrochemical pipelines for quality maint...Alexander Decker
This document describes a proposed neural network model for predicting degradation in petrochemical pipelines. It begins with background on pipelines and fatigue crack propagation based on Paris' law. It then discusses stresses in cylindrical pipelines under internal pressure. The model represents crack growth as a function of stress intensity factor and uses a recurrent formula to calculate cumulative damage over time. The goal is to develop a prognostic tool for quality maintenance in pipeline systems.
Time Domain Signal Analysis Using Modified Haar and Modified Daubechies Wavel...CSCJournals
In this paper, time signal analysis and synthesis based on modified Haar and modified Daubechies wavelet transform is proposed. The optimal results for both analysis and synthesis for time domain signals were obtained with the use of the modified Haar and modified Daubechies wavelet transforms. This paper evaluates the quality of filtering using the modified Haar and modified Daubechies wavelet transform. Analysis and synthesis of the time signals is performed for 10 samples and the signal to noise ratio (SNR) of around 25-40 dB is obtained for modified Haar and 24-32 dB for modified Daubechies wavelet. We have observed that as compared to standard Haar and standard Daubechies mother wavelet our proposed method gives better signal quality, which is good for time varying signals.
1.differential approach to cardioid distribution -1-6Alexander Decker
This document presents a differential equation approach to deriving the probability density function of the cardioid distribution. It shows that the cardioid distribution can be obtained as the solution to a second-order non-homogeneous linear differential equation under certain initial conditions. It also describes how the Mobius transformation can be used to map the cardioid distribution on a circle to real-valued Cauchy-type distributions. Specifically, it presents a Mobius transformation that maps points on the unit circle to the real line, allowing the derivation of new unimodal symmetric distributions from the original cardioid distribution.
11.0001www.iiste.org call for paper.differential approach to cardioid distrib...Alexander Decker
This document summarizes a research paper that derives the probability density function (pdf) of the cardioid distribution through solving a differential equation. It then uses a Mobius transformation to map the cardioid distribution on a circle to new symmetric and unimodal distributions on the real line, called Cauchy type models. Graphs of the Cauchy type model pdfs are provided for different parameter values.
Sensitivity Analysis of GRA Method for Interval Valued Intuitionistic Fuzzy M...ijsrd.com
The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights are incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights are completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attributes decision-making with incompletely known attribute weight information. This paper provides a new method for sensitivity analysis of MADM problems so that by sing it and changing the weights of attributes, one can determine changes in the final results for a decision making problem. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
QUALITY OF CLUSTER INDEX BASED ON STUDY OF DECISION TREE IJORCS
Quality of clustering is an important issue in application of clustering techniques. Most traditional cluster validity indices are geometry-based cluster quality measures. This work proposes a cluster validity index based on the decision-theoretic rough set model by considering various loss functions. Real time retail data show the usefulness of the proposed validity index for the evaluation of rough and crisp clustering. The measure is shown to help determine optimal number of clusters, as well as an important parameter called threshold in rough clustering. The experiments with a promotional campaign for the retail data illustrate the ability of the proposed measure to incorporate financial considerations in evaluating quality of a clustering scheme. This ability to deal with monetary values distinguishes the proposed decision-theoretic measure from other distance-based measures. Our proposed system validity index can also be efficient for evaluating other clustering algorithms such as fuzzy clustering.
IRJET- Wavelet based Galerkin Method for the Numerical Solution of One Dimens...IRJET Journal
This document presents a wavelet-based Galerkin method for numerically solving one-dimensional partial differential equations using Hermite wavelets. Hermite wavelets are used as the basis functions in the Galerkin method. The method is demonstrated on some test problems, and the numerical results obtained from the proposed method are compared to exact solutions and a finite difference method to evaluate the accuracy and efficiency of the proposed wavelet Galerkin approach.
Spectral methods for solving differential equationsRajesh Aggarwal
This project report describes Rajesh Aggarwal's summer research fellowship project on spectral methods for solving differential equations under the guidance of Dr. Pravin Kumar Gupta at IIT Roorkee from June 11, 2014 to August 6, 2014. The report provides background on analytical and numerical methods for solving differential equations, specifically conventional finite difference methods and spectral finite difference methods. It then describes the methodology, codes, and results of applying both methods to solve sample differential equations on a half-space and layered earth problems. Tables and graphs comparing the accuracy of the two methods are presented.
Neural network precept diagnosis on petrochemical pipelines for quality maint...Alexander Decker
This document describes a proposed neural network model for predicting degradation in petrochemical pipelines. It begins with background on pipelines and fatigue crack propagation based on Paris' law. It then discusses stresses in cylindrical pipelines under internal pressure. The model represents crack growth as a function of stress intensity factor and uses a recurrent formula to calculate cumulative damage over time. The goal is to develop a prognostic tool for quality maintenance in pipeline systems.
Time Domain Signal Analysis Using Modified Haar and Modified Daubechies Wavel...CSCJournals
In this paper, time signal analysis and synthesis based on modified Haar and modified Daubechies wavelet transform is proposed. The optimal results for both analysis and synthesis for time domain signals were obtained with the use of the modified Haar and modified Daubechies wavelet transforms. This paper evaluates the quality of filtering using the modified Haar and modified Daubechies wavelet transform. Analysis and synthesis of the time signals is performed for 10 samples and the signal to noise ratio (SNR) of around 25-40 dB is obtained for modified Haar and 24-32 dB for modified Daubechies wavelet. We have observed that as compared to standard Haar and standard Daubechies mother wavelet our proposed method gives better signal quality, which is good for time varying signals.
1.differential approach to cardioid distribution -1-6Alexander Decker
This document presents a differential equation approach to deriving the probability density function of the cardioid distribution. It shows that the cardioid distribution can be obtained as the solution to a second-order non-homogeneous linear differential equation under certain initial conditions. It also describes how the Mobius transformation can be used to map the cardioid distribution on a circle to real-valued Cauchy-type distributions. Specifically, it presents a Mobius transformation that maps points on the unit circle to the real line, allowing the derivation of new unimodal symmetric distributions from the original cardioid distribution.
11.0001www.iiste.org call for paper.differential approach to cardioid distrib...Alexander Decker
This document summarizes a research paper that derives the probability density function (pdf) of the cardioid distribution through solving a differential equation. It then uses a Mobius transformation to map the cardioid distribution on a circle to new symmetric and unimodal distributions on the real line, called Cauchy type models. Graphs of the Cauchy type model pdfs are provided for different parameter values.
Sensitivity Analysis of GRA Method for Interval Valued Intuitionistic Fuzzy M...ijsrd.com
The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights are incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights are completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attributes decision-making with incompletely known attribute weight information. This paper provides a new method for sensitivity analysis of MADM problems so that by sing it and changing the weights of attributes, one can determine changes in the final results for a decision making problem. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
QUALITY OF CLUSTER INDEX BASED ON STUDY OF DECISION TREE IJORCS
Quality of clustering is an important issue in application of clustering techniques. Most traditional cluster validity indices are geometry-based cluster quality measures. This work proposes a cluster validity index based on the decision-theoretic rough set model by considering various loss functions. Real time retail data show the usefulness of the proposed validity index for the evaluation of rough and crisp clustering. The measure is shown to help determine optimal number of clusters, as well as an important parameter called threshold in rough clustering. The experiments with a promotional campaign for the retail data illustrate the ability of the proposed measure to incorporate financial considerations in evaluating quality of a clustering scheme. This ability to deal with monetary values distinguishes the proposed decision-theoretic measure from other distance-based measures. Our proposed system validity index can also be efficient for evaluating other clustering algorithms such as fuzzy clustering.
The document discusses the mathematical background of the finite element method. It begins with an overview of concepts from functional analysis including vector spaces, scalar products, linear functionals, and Riesz representation theorem. Green's functions are introduced as the Riesz elements representing linear functionals. Green's identities are then used to derive classical influence functions for displacements and forces. Physically, Green's functions represent monopoles and dipoles with infinite energy, placing them outside the theory of weak boundary value problems. In nonlinear problems, Green's functions can be viewed as Lagrange multipliers at the linearization point.
This document discusses modeling the dynamics of lumped-element systems. It outlines progress made in modeling multi-domain systems by first creating lumped models for individual domains and then coupling domains using a two-port capacitor. The goal is now to move beyond quasistatic analysis and model how such systems behave over time or frequency. It will cover formulating state equations, large-signal analysis, small-signal analysis, and reviewing second-order system dynamics to address how to model the non-linear dynamics of these systems and determine responses like how fast an RF switch can close.
This document describes object-centric debugging. Traditional debuggers step through code and set breakpoints in the source code. However, they have no awareness of objects. Object-centric debuggers intercept access to object runtime state and monitor object interactions. They support live interaction centered on individual objects, like halting on the next message to an object or state change of an object. This approach redefines the debugger UI and requires adaptation through reflection and explicit meta-objects to organize debugging at the meta-level.
11.[5 15]neural network precept diagnosis on petrochemical pipelines for qual...Alexander Decker
This document summarizes a research paper about using neural networks to develop a prognostic model for predicting fatigue damage in petrochemical pipelines. The researchers propose using Paris' law and Miner's law to model crack propagation and cumulative damage. They develop a recurrent neural network model to predict crack length over time under different pressure levels. Simulation results show the model can estimate remaining lifetime under three pressure modes, with lifetimes of around 115 hours for high pressure, 160 hours for middle pressure, and 240 hours for low pressure. The neural network approach allows prognostic evaluation of pipeline condition to support quality maintenance in petrochemical industries.
11.neural network precept diagnosis on petrochemical pipelines for quality ma...Alexander Decker
This document summarizes a research paper about using neural networks to develop a prognostic model for predicting fatigue damage in petrochemical pipelines. The researchers propose using Paris' law and Miner's law to model crack propagation and cumulative damage. They develop a recurrent neural network model to predict crack length over time under different pressure levels. Simulation results show the model can estimate remaining lifetime under three pressure modes, with lifetimes of around 115 hours for high pressure, 160 hours for middle pressure, and 240 hours for low pressure. The neural network approach allows prognosis of pipeline condition to aid quality maintenance in petrochemical industries.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
AN EMPIRICAL COMPARISON OF WEIGHTING FUNCTIONS FOR MULTI-LABEL DISTANCEWEIGHT...cscpconf
Multi-label classification is an extension of classical multi-class one, where any instance can be
associated with several classes simultaneously and thus the classes are no longer mutually
exclusive. It was experimentally shown that the distance-weighted k-nearest neighbour
(DWkNN) algorithm is superior to the original kNN rule for multi-class learning. But, it has not
been investigated whether the distance-weighted strategy is valid for multi-label learning and
which weighting function performs well. In this paper, we provide a concise multi-label DWkNN form (MLC-DWkNN). Furthermore, four weighting functions, Dudani’s linear function varying from 1 to 0, Macleod’s linear function ranging from 1 to 1/2, Dudani’s inverse distance function, and Zavrel’s exponential function, are collected and then investigated by detailed experiments on three benchmark data sets with Manhattan distance. Our study demonstrates that Dudani’s linear and Zavrel’s exponential functions work well, and moreover MLC-DWkNN with such two functions outperforms an existing kNN-based multi-label classifier ML-kNN
This document provides instructions for performing a linear static analysis of a cantilever beam using MSC Nastran. The steps include: 1) creating a finite element model of the beam using bar elements, 2) defining material and section properties, 3) applying boundary conditions and a tip load, 4) generating an input file for analysis, 5) submitting the input file to Nastran, and 6) importing the results file back into MSC Patran for post-processing. The goal is to calculate deflection and stress results and compare to theoretical values.
FINGERPRINTS IMAGE COMPRESSION BY WAVE ATOMScsandit
The document presents a study comparing fingerprint image compression using wavelets and wave atoms transforms. It finds that wave atoms transforms provide better performance than current wavelet-based standards like WSQ. Specifically:
- Wave atoms achieved higher PSNR values and compression ratios than wavelets when reconstructing images from a reduced number of coefficients.
- An algorithm was proposed using wave atom decomposition, non-uniform quantization, and entropy coding that achieved a compression ratio of 18 with a PSNR of 35.04 dB, outperforming the WSQ standard.
- Minutiae detection on original and reconstructed images showed wave atoms better preserved local fingerprint structures. Therefore, wave atoms are concluded to be more suitable than wavelets
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document presents a chain sampling plan for truncated life tests when lifetimes follow a generalized exponential distribution. The plan determines the minimum sample size needed to satisfy producer and consumer risks at specified quality levels in terms of the distribution's median. Tables 1 and 2 show the minimum sample sizes and corresponding acceptance numbers for different confidence levels. They also provide the operating characteristic function values for various ratios of the true scale parameter to the specified scale parameter, given a shape parameter of 2. The plan allows accepting a lot if defects are below an acceptance number and no defects occurred in preceding samples, improving on single sampling plans.
This document compares JPEG and JPEG2000 image compression techniques using objective and perceptual quality measures. JPEG2000 provides higher PSNR values at all bitrates but JPEG has better picture quality scale (PQS) scores, a perceptual measure, at moderate and high bitrates. At very low bitrates below 0.5 bpp, JPEG2000 produces higher quality images according to PQS due to its wavelet-based compression method. The study uses four test images with different spatial and frequency characteristics to evaluate the compression methods.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
05212201 C A L I B R A T I O N A N D E L E C T R O N I C M E A S U R E ...guestd436758
This document contains information about an exam for a calibration and electronic measurements course, including 8 multiple choice questions. Question 1 involves calculating statistics like mean, standard deviation, and error from a set of voltage measurements. Question 2 defines SI units for conductance, magnetic flux, flux density, and inductance, and calculates flux density given magnetic flux. Question 3 provides short note questions on topics like testing, calibration, reliability, and traceability.
Measles Epidemic: Studying the Spread Using Numerical Techniquesflavinjs
Studying past epidemics is a necessary step in understanding and preventing the spread of future contagions. The measles epidemic in New York in the mid-1960s is an ideal case study for mathematical epidemiology because of the detailed records kept on those infected and the unique properties of measles as a disease. Using a Computer Algebra System (CAS), we will revisit the qualitative properties of the measles epidemic model and compare solutions using different numerical techniques.
This document discusses numerical methods for solving initial value problems for ordinary differential equations. It introduces the Taylor series method and Runge-Kutta method for solving initial value problems. Examples are provided to demonstrate solving first and second order differential equations using these two methods and to compare their results. Stability of numerical solutions is also discussed.
This document provides an overview of numerical methods for solving ordinary differential equations. It outlines several numerical methods including Taylor's series method, Picard's method of successive approximation, Euler's method, modified Euler's method, Runge-Kutta methods, and predictor-corrector methods like Milne's method and Adams-Moulton method. Examples of the formulas used in each method are given. The document also lists references and provides context about the course and unit.
MAT210/DiffEq/Runge-Kutta 2nd Order 2013-14John Ham
Numerical methods lecture slides on the Runge-Kutta method for solving 1st order ODEs.
Some parts of this presentation are based on resources at http://nm.MathForCollege.com, primarily http://mathforcollege.com/nm/topics/runge_kutta_2nd_method.html
Numerical solution using runge kutta with programming in c++Vijay Choudhary
This document summarizes a study that uses the Runge-Kutta 4th order method to model and solve a differential equation governing the concentration of bacteria in a polluted lake over time. The model is implemented in C++ and the numerical solutions are obtained for different step sizes and compared to the exact solution. It is found that using a step size of 3.5 weeks provides results closest to the exact solution. The 4th order Runge-Kutta method is also found to provide closer approximations than lower order methods.
The document discusses numerical methods for solving differential equations called Runge-Kutta methods. It provides examples of applying the second-order and fourth-order Runge-Kutta methods to solve differential equations. The second-order method uses slopes at the start and middle of each interval to estimate the next value, while the fourth-order method uses slopes at the start, middle, and end of each interval to provide a more accurate estimate. The document also illustrates Heun's method and the second and fourth-order Runge-Kutta methods through examples.
The document discusses numerical methods for solving ordinary differential equations using Runge-Kutta methods of orders 2, 3, and 4. It defines the Runge-Kutta method of order 2, which calculates approximations k1 and k2 to find the solution increment k as their average. It also defines the Runge-Kutta method of order 3, which calculates approximations k1, k2, k3 to find the solution increment k as a weighted average. Finally, it defines the Runge-Kutta method of order 4, which calculates approximations k1, k2, k3, k4 to find the solution increment k as a weighted average.
The document discusses the mathematical background of the finite element method. It begins with an overview of concepts from functional analysis including vector spaces, scalar products, linear functionals, and Riesz representation theorem. Green's functions are introduced as the Riesz elements representing linear functionals. Green's identities are then used to derive classical influence functions for displacements and forces. Physically, Green's functions represent monopoles and dipoles with infinite energy, placing them outside the theory of weak boundary value problems. In nonlinear problems, Green's functions can be viewed as Lagrange multipliers at the linearization point.
This document discusses modeling the dynamics of lumped-element systems. It outlines progress made in modeling multi-domain systems by first creating lumped models for individual domains and then coupling domains using a two-port capacitor. The goal is now to move beyond quasistatic analysis and model how such systems behave over time or frequency. It will cover formulating state equations, large-signal analysis, small-signal analysis, and reviewing second-order system dynamics to address how to model the non-linear dynamics of these systems and determine responses like how fast an RF switch can close.
This document describes object-centric debugging. Traditional debuggers step through code and set breakpoints in the source code. However, they have no awareness of objects. Object-centric debuggers intercept access to object runtime state and monitor object interactions. They support live interaction centered on individual objects, like halting on the next message to an object or state change of an object. This approach redefines the debugger UI and requires adaptation through reflection and explicit meta-objects to organize debugging at the meta-level.
11.[5 15]neural network precept diagnosis on petrochemical pipelines for qual...Alexander Decker
This document summarizes a research paper about using neural networks to develop a prognostic model for predicting fatigue damage in petrochemical pipelines. The researchers propose using Paris' law and Miner's law to model crack propagation and cumulative damage. They develop a recurrent neural network model to predict crack length over time under different pressure levels. Simulation results show the model can estimate remaining lifetime under three pressure modes, with lifetimes of around 115 hours for high pressure, 160 hours for middle pressure, and 240 hours for low pressure. The neural network approach allows prognostic evaluation of pipeline condition to support quality maintenance in petrochemical industries.
11.neural network precept diagnosis on petrochemical pipelines for quality ma...Alexander Decker
This document summarizes a research paper about using neural networks to develop a prognostic model for predicting fatigue damage in petrochemical pipelines. The researchers propose using Paris' law and Miner's law to model crack propagation and cumulative damage. They develop a recurrent neural network model to predict crack length over time under different pressure levels. Simulation results show the model can estimate remaining lifetime under three pressure modes, with lifetimes of around 115 hours for high pressure, 160 hours for middle pressure, and 240 hours for low pressure. The neural network approach allows prognosis of pipeline condition to aid quality maintenance in petrochemical industries.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
AN EMPIRICAL COMPARISON OF WEIGHTING FUNCTIONS FOR MULTI-LABEL DISTANCEWEIGHT...cscpconf
Multi-label classification is an extension of classical multi-class one, where any instance can be
associated with several classes simultaneously and thus the classes are no longer mutually
exclusive. It was experimentally shown that the distance-weighted k-nearest neighbour
(DWkNN) algorithm is superior to the original kNN rule for multi-class learning. But, it has not
been investigated whether the distance-weighted strategy is valid for multi-label learning and
which weighting function performs well. In this paper, we provide a concise multi-label DWkNN form (MLC-DWkNN). Furthermore, four weighting functions, Dudani’s linear function varying from 1 to 0, Macleod’s linear function ranging from 1 to 1/2, Dudani’s inverse distance function, and Zavrel’s exponential function, are collected and then investigated by detailed experiments on three benchmark data sets with Manhattan distance. Our study demonstrates that Dudani’s linear and Zavrel’s exponential functions work well, and moreover MLC-DWkNN with such two functions outperforms an existing kNN-based multi-label classifier ML-kNN
This document provides instructions for performing a linear static analysis of a cantilever beam using MSC Nastran. The steps include: 1) creating a finite element model of the beam using bar elements, 2) defining material and section properties, 3) applying boundary conditions and a tip load, 4) generating an input file for analysis, 5) submitting the input file to Nastran, and 6) importing the results file back into MSC Patran for post-processing. The goal is to calculate deflection and stress results and compare to theoretical values.
FINGERPRINTS IMAGE COMPRESSION BY WAVE ATOMScsandit
The document presents a study comparing fingerprint image compression using wavelets and wave atoms transforms. It finds that wave atoms transforms provide better performance than current wavelet-based standards like WSQ. Specifically:
- Wave atoms achieved higher PSNR values and compression ratios than wavelets when reconstructing images from a reduced number of coefficients.
- An algorithm was proposed using wave atom decomposition, non-uniform quantization, and entropy coding that achieved a compression ratio of 18 with a PSNR of 35.04 dB, outperforming the WSQ standard.
- Minutiae detection on original and reconstructed images showed wave atoms better preserved local fingerprint structures. Therefore, wave atoms are concluded to be more suitable than wavelets
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document presents a chain sampling plan for truncated life tests when lifetimes follow a generalized exponential distribution. The plan determines the minimum sample size needed to satisfy producer and consumer risks at specified quality levels in terms of the distribution's median. Tables 1 and 2 show the minimum sample sizes and corresponding acceptance numbers for different confidence levels. They also provide the operating characteristic function values for various ratios of the true scale parameter to the specified scale parameter, given a shape parameter of 2. The plan allows accepting a lot if defects are below an acceptance number and no defects occurred in preceding samples, improving on single sampling plans.
This document compares JPEG and JPEG2000 image compression techniques using objective and perceptual quality measures. JPEG2000 provides higher PSNR values at all bitrates but JPEG has better picture quality scale (PQS) scores, a perceptual measure, at moderate and high bitrates. At very low bitrates below 0.5 bpp, JPEG2000 produces higher quality images according to PQS due to its wavelet-based compression method. The study uses four test images with different spatial and frequency characteristics to evaluate the compression methods.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
05212201 C A L I B R A T I O N A N D E L E C T R O N I C M E A S U R E ...guestd436758
This document contains information about an exam for a calibration and electronic measurements course, including 8 multiple choice questions. Question 1 involves calculating statistics like mean, standard deviation, and error from a set of voltage measurements. Question 2 defines SI units for conductance, magnetic flux, flux density, and inductance, and calculates flux density given magnetic flux. Question 3 provides short note questions on topics like testing, calibration, reliability, and traceability.
Measles Epidemic: Studying the Spread Using Numerical Techniquesflavinjs
Studying past epidemics is a necessary step in understanding and preventing the spread of future contagions. The measles epidemic in New York in the mid-1960s is an ideal case study for mathematical epidemiology because of the detailed records kept on those infected and the unique properties of measles as a disease. Using a Computer Algebra System (CAS), we will revisit the qualitative properties of the measles epidemic model and compare solutions using different numerical techniques.
This document discusses numerical methods for solving initial value problems for ordinary differential equations. It introduces the Taylor series method and Runge-Kutta method for solving initial value problems. Examples are provided to demonstrate solving first and second order differential equations using these two methods and to compare their results. Stability of numerical solutions is also discussed.
This document provides an overview of numerical methods for solving ordinary differential equations. It outlines several numerical methods including Taylor's series method, Picard's method of successive approximation, Euler's method, modified Euler's method, Runge-Kutta methods, and predictor-corrector methods like Milne's method and Adams-Moulton method. Examples of the formulas used in each method are given. The document also lists references and provides context about the course and unit.
MAT210/DiffEq/Runge-Kutta 2nd Order 2013-14John Ham
Numerical methods lecture slides on the Runge-Kutta method for solving 1st order ODEs.
Some parts of this presentation are based on resources at http://nm.MathForCollege.com, primarily http://mathforcollege.com/nm/topics/runge_kutta_2nd_method.html
Numerical solution using runge kutta with programming in c++Vijay Choudhary
This document summarizes a study that uses the Runge-Kutta 4th order method to model and solve a differential equation governing the concentration of bacteria in a polluted lake over time. The model is implemented in C++ and the numerical solutions are obtained for different step sizes and compared to the exact solution. It is found that using a step size of 3.5 weeks provides results closest to the exact solution. The 4th order Runge-Kutta method is also found to provide closer approximations than lower order methods.
The document discusses numerical methods for solving differential equations called Runge-Kutta methods. It provides examples of applying the second-order and fourth-order Runge-Kutta methods to solve differential equations. The second-order method uses slopes at the start and middle of each interval to estimate the next value, while the fourth-order method uses slopes at the start, middle, and end of each interval to provide a more accurate estimate. The document also illustrates Heun's method and the second and fourth-order Runge-Kutta methods through examples.
The document discusses numerical methods for solving ordinary differential equations using Runge-Kutta methods of orders 2, 3, and 4. It defines the Runge-Kutta method of order 2, which calculates approximations k1 and k2 to find the solution increment k as their average. It also defines the Runge-Kutta method of order 3, which calculates approximations k1, k2, k3 to find the solution increment k as a weighted average. Finally, it defines the Runge-Kutta method of order 4, which calculates approximations k1, k2, k3, k4 to find the solution increment k as a weighted average.
The document discusses solving ordinary differential equations using Taylor's series method. It presents the Taylor's series for the first order differential equation dy/dx = f(x,y) and gives an example of solving the equation y = x + y, y(0) = 1 using this method. The solution is obtained by taking the Taylor's series expansion and determining the derivatives of y evaluated at x0 = 0. The values of y are computed at x = 0.1 and x = 0.2. A second example solves the differential equation dy/dx = 3x + y^2 using the same approach.
Extended Analysis of Cauchy’s InequalityIRJET Journal
This paper provides a multivariate generalization of Cauchy's inequality 1 + x ≤ ex, where x can be any non-negative real number. Specifically, it proves the inequality (2) where x1, x2, ..., xn are pairwise non-negative distinct real numbers. It shows this inequality only holds when the sum of x values is 0. The paper also analyzes this inequality using an ordinary differential equation approach and direct proofs based on concepts like monotone functions, divided differences, and the Beppo Levi theorem.
Multivariate Analysis of Cauchy’s InequalityIRJET Journal
This paper investigates the multivariate generalization of Cauchy's inequality 1 + x ≤ ex, where x is any non-negative real number. Specifically, it aims to prove the inequality (1 + x1)(1 + x2)...(1 + xn) ≤ e(x1+x2+...+xn), where x1, x2, ..., xn are pairwise distinct non-negative real numbers. The proof is based on notions from empty product conventions and Beppo Levi's theorem of monotone convergence. This inequality is also extended to simultaneous inequalities and its relationship to ordinary differential equation Cauchy problems and population dynamics is explored. Direct approaches using definitions of monotone functions and mean value theore
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
A class of boundary value methods for the complex delay differential equationijscmcj
In this paper, a class of boundary value methods (BVMs) for delay differential equations (DDEs) is considered. The delay dependent stable regions of the extended trapezoidal rules of second kind (ETR2s), which are a class of BVMs, are displayed for the test equation of DDEs. Furthermore, it is showed ETR2s cannot preserve the delay-dependent stability of the complex coefficient test equation considered. Some numerical experiments are given to confirm the theoretical results.
AMS 2000 Mathematics Subject Classification: 65L20, 65M12
The document discusses using the Master's Theorem to analyze the time complexity of recursive algorithms. It provides an overview of the Master's Theorem and its three cases. The paper proposes modifying the theorem to estimate derivatives of iterative functions. It demonstrates applying the modified theorem to examples like the Tower of Hanoi problem and Fibonacci sequence. The modified theorem requires certain conditions on the function, and the paper provides guidelines for identifying these conditions. It discusses potential applications in algorithm analysis and understanding complex functions. Overall, the paper contributes new knowledge on using the Master's Theorem to analyze derivatives and offers a novel perspective.
11.on a non variational viewpoint in newtonian mechanicsAlexander Decker
This document discusses a non-variational viewpoint in Newtonian mechanics without assuming the existence of a Lagrangian or Hamiltonian. It defines a Poisson bracket on the tangent bundle to study dynamics. Some key points made:
1) Certain dynamical systems like one with acceleration-dependent forces cannot be described by a Lagrangian formulation.
2) Dynamical systems may have non-unique or time-dependent Lagrangians even when they exist.
3) Conservation laws can be used to obtain the symmetries of a system via an inversion of Noether's theorem, without assuming an underlying Lagrangian.
Development of implicit rational runge kutta schemes for second order ordinar...Alexander Decker
This document describes the development of a one-stage implicit rational Runge-Kutta method for solving second-order ordinary differential equations. The method is derived by taking Taylor series expansions of the solution equations about the point (xn, yn, yn') and equating terms with the same powers of the step size h. This results in expressions for the parameters of the method in terms of the leading order truncation errors. The method is consistent, as the parameters satisfy constraints that ensure the method approaches the true solution in the limit as h approaches 0.
A study on singular perturbation correction to bond prices under affine term ...Frank Fung
The document discusses applying the technique of singular perturbation to pricing fixed income derivatives. Singular perturbation provides a convenient way to account for stochastic interest rate volatility. The accuracy of a perturbation corrected Vasicek model is evaluated by comparing its yield curve fitting to an exact analytic Fong-Vasicek model. The perturbation scheme achieves comparable accuracy to the exact model while requiring much less computational time. The perturbation scheme is also extended to a CIR model, though the advantage in speed is diminished due to the need for numerical methods.
Cauchy’s Inequality based study of the Differential Equations and the Simple ...IRJET Journal
1. The paper studies the multivariate generalization of Cauchy's inequality 1 + x ≤ ex, where x is a non-negative real number. This generalization can help solve certain ordinary differential equations (ODEs) and population dynamics problems.
2. The paper proves the multivariate generalization of the inequality and shows it only holds when the values are all equal to 0. It also analyzes some qualitative properties of solutions to ODE Cauchy problems using this generalization.
3. Different approaches are taken to directly prove the multivariate inequality using notions of monotone functions, Beppo Levi theorem, and divided differences mean value theorem. Allowed repetitions in the variables are also considered.
This document summarizes a research paper that examines how to estimate inputs for a cooperative and supportive neural network to achieve a desired output. The paper studies how time-varying inputs influence the network's behavior and presents theorems showing that if the inputs satisfy certain conditions, the network's solutions will converge to a pre-specified output. Estimates on restricting the inputs are provided. The results demonstrate that a neural network can be made to approach different outputs without changing its architecture by properly selecting the inputs.
11.[8 17]numerical solution of fuzzy hybrid differential equation by third or...Alexander Decker
This document presents a numerical method called the third order Runge Kutta Nystrom method to solve fuzzy hybrid differential equations. It begins with definitions of fuzzy numbers and fuzzy functions. It then describes hybrid fuzzy differential systems and how they can be modeled as piecewise differentiable systems. The document goes on to develop the third order Runge Kutta Nystrom method for solving these systems numerically. It provides a convergence result and applies the method to a numerical example to illustrate the theory.
Numerical solution of fuzzy hybrid differential equation by third order runge...Alexander Decker
This document presents a numerical method for solving hybrid fuzzy differential equations using the third order Runge-Kutta Nystrom method. It begins with definitions of fuzzy numbers and fuzzy differential equations. It then describes hybrid fuzzy differential systems and develops the Runge-Kutta Nystrom method for approximating their solutions. The method is applied to an example hybrid fuzzy differential equation and results are presented in a table and figure comparing the approximate and exact solutions. The document concludes by discussing the accuracy of the method.
11.numerical solution of fuzzy hybrid differential equation by third order ru...Alexander Decker
This document presents a numerical method for solving hybrid fuzzy differential equations using the third order Runge-Kutta Nystrom method. It begins with introductions to fuzzy numbers, fuzzy differential equations, and hybrid fuzzy differential systems. It then describes the third order Runge-Kutta Nystrom method for solving hybrid fuzzy differential equations. An example is provided to illustrate the method. Tables and figures compare the approximate solutions from this method to exact solutions. The method is shown to provide approximations close to the exact solutions.
Local Model Checking Algorithm Based on Mu-calculus with Partial OrdersTELKOMNIKA JOURNAL
The propositionalμ-calculus can be divided into two categories, global model checking algorithm
and local model checking algorithm. Both of them aim at reducing time complexity and space complexity
effectively. This paper analyzes the computing process of alternating fixpoint nested in detail and designs
an efficient local model checking algorithm based on the propositional μ-calculus by a group of partial
ordered relation, and its time complexity is O(d2(dn)d/2+2) (d is the depth of fixpoint nesting, n is the
maximum of number of nodes), space complexity is O(d(dn)d/2). As far as we know, up till now, the best
local model checking algorithm whose index of time complexity is d. In this paper, the index for time
complexity of this algorithm is reduced from d to d/2. It is more efficient than algorithms of previous
research.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
Numerical disperison analysis of sympletic and adi schemexingangahu
This document discusses numerical dispersion analysis of symplectic and alternating direction implicit (ADI) schemes for computational electromagnetic simulation. It presents Maxwell's equations as a Hamiltonian system that can be written as symplectic or ADI schemes by approximating the time evolution operator. Three high order spatial difference approximations - high order staggered difference, compact finite difference, and scaling function approximations - are analyzed to reduce numerical dispersion when combined with the symplectic and ADI schemes. The document derives unified dispersion relationships for the symplectic and ADI schemes with different spatial difference approximations, which can be used as a reference for simulating large scale electromagnetic problems.
The document analyzes the analytic solution of Burger's equations using the variational iteration method. It begins by introducing the variational iteration method and how it can be used to solve differential equations. It then applies the method to obtain exact solutions for the (1+1), (1+2), and (1+3) dimensional Burger equations. Lengthy iterative solutions are presented for each case. The variational iteration method is shown to provide exact solutions to these Burger equations without requiring linearization.
A class of three stage implicit rational runge kutta schemes for approximatio...Alexander Decker
This document describes the derivation of a 3-stage implicit rational Runge-Kutta method for approximating solutions to second-order ordinary differential equations. It begins by reviewing existing Runge-Kutta methods for solving first and second-order ODEs. It then presents the general form of a 3-stage implicit rational Runge-Kutta scheme using Taylor series expansions. Expressions for the coefficients of the method are obtained by matching terms in the Taylor series expansions. The properties of the derived method are investigated, finding it to be consistent and convergent. Numerical examples demonstrate it gives better approximations than existing methods.
This document discusses strategies for parallelizing spectral methods. Spectral methods are global in nature due to their use of global basis functions, making them challenging to parallelize on fine-grained architectures. However, the document finds that spectral methods can be effectively parallelized. The main computational steps in spectral methods are the calculation of differential operators on functions and solving linear systems, both of which can exploit parallelism. Domain decomposition techniques may also help parallelize computations over non-Cartesian domains.
Similar to New multi step runge kutta method for solving fuzzy differential equations (20)
Abnormalities of hormones and inflammatory cytokines in women affected with p...Alexander Decker
Women with polycystic ovary syndrome (PCOS) have elevated levels of hormones like luteinizing hormone and testosterone, as well as higher levels of insulin and insulin resistance compared to healthy women. They also have increased levels of inflammatory markers like C-reactive protein, interleukin-6, and leptin. This study found these abnormalities in the hormones and inflammatory cytokines of women with PCOS ages 23-40, indicating that hormone imbalances associated with insulin resistance and elevated inflammatory markers may worsen infertility in women with PCOS.
A usability evaluation framework for b2 c e commerce websitesAlexander Decker
This document presents a framework for evaluating the usability of B2C e-commerce websites. It involves user testing methods like usability testing and interviews to identify usability problems in areas like navigation, design, purchasing processes, and customer service. The framework specifies goals for the evaluation, determines which website aspects to evaluate, and identifies target users. It then describes collecting data through user testing and analyzing the results to identify usability problems and suggest improvements.
A universal model for managing the marketing executives in nigerian banksAlexander Decker
This document discusses a study that aimed to synthesize motivation theories into a universal model for managing marketing executives in Nigerian banks. The study was guided by Maslow and McGregor's theories. A sample of 303 marketing executives was used. The results showed that managers will be most effective at motivating marketing executives if they consider individual needs and create challenging but attainable goals. The emerged model suggests managers should provide job satisfaction by tailoring assignments to abilities and monitoring performance with feedback. This addresses confusion faced by Nigerian bank managers in determining effective motivation strategies.
A unique common fixed point theorems in generalized dAlexander Decker
This document presents definitions and properties related to generalized D*-metric spaces and establishes some common fixed point theorems for contractive type mappings in these spaces. It begins by introducing D*-metric spaces and generalized D*-metric spaces, defines concepts like convergence and Cauchy sequences. It presents lemmas showing the uniqueness of limits in these spaces and the equivalence of different definitions of convergence. The goal of the paper is then stated as obtaining a unique common fixed point theorem for generalized D*-metric spaces.
A trends of salmonella and antibiotic resistanceAlexander Decker
This document provides a review of trends in Salmonella and antibiotic resistance. It begins with an introduction to Salmonella as a facultative anaerobe that causes nontyphoidal salmonellosis. The emergence of antimicrobial-resistant Salmonella is then discussed. The document proceeds to cover the historical perspective and classification of Salmonella, definitions of antimicrobials and antibiotic resistance, and mechanisms of antibiotic resistance in Salmonella including modification or destruction of antimicrobial agents, efflux pumps, modification of antibiotic targets, and decreased membrane permeability. Specific resistance mechanisms are discussed for several classes of antimicrobials.
A transformational generative approach towards understanding al-istifhamAlexander Decker
This document discusses a transformational-generative approach to understanding Al-Istifham, which refers to interrogative sentences in Arabic. It begins with an introduction to the origin and development of Arabic grammar. The paper then explains the theoretical framework of transformational-generative grammar that is used. Basic linguistic concepts and terms related to Arabic grammar are defined. The document analyzes how interrogative sentences in Arabic can be derived and transformed via tools from transformational-generative grammar, categorizing Al-Istifham into linguistic and literary questions.
A time series analysis of the determinants of savings in namibiaAlexander Decker
This document summarizes a study on the determinants of savings in Namibia from 1991 to 2012. It reviews previous literature on savings determinants in developing countries. The study uses time series analysis including unit root tests, cointegration, and error correction models to analyze the relationship between savings and variables like income, inflation, population growth, deposit rates, and financial deepening in Namibia. The results found inflation and income have a positive impact on savings, while population growth negatively impacts savings. Deposit rates and financial deepening were found to have no significant impact. The study reinforces previous work and emphasizes the importance of improving income levels to achieve higher savings rates in Namibia.
A therapy for physical and mental fitness of school childrenAlexander Decker
This document summarizes a study on the importance of exercise in maintaining physical and mental fitness for school children. It discusses how physical and mental fitness are developed through participation in regular physical exercises and cannot be achieved solely through classroom learning. The document outlines different types and components of fitness and argues that developing fitness should be a key objective of education systems. It recommends that schools ensure pupils engage in graded physical activities and exercises to support their overall development.
A theory of efficiency for managing the marketing executives in nigerian banksAlexander Decker
This document summarizes a study examining efficiency in managing marketing executives in Nigerian banks. The study was examined through the lenses of Kaizen theory (continuous improvement) and efficiency theory. A survey of 303 marketing executives from Nigerian banks found that management plays a key role in identifying and implementing efficiency improvements. The document recommends adopting a "3H grand strategy" to improve the heads, hearts, and hands of management and marketing executives by enhancing their knowledge, attitudes, and tools.
This document discusses evaluating the link budget for effective 900MHz GSM communication. It describes the basic parameters needed for a high-level link budget calculation, including transmitter power, antenna gains, path loss, and propagation models. Common propagation models for 900MHz that are described include Okumura model for urban areas and Hata model for urban, suburban, and open areas. Rain attenuation is also incorporated using the updated ITU model to improve communication during rainfall.
A synthetic review of contraceptive supplies in punjabAlexander Decker
This document discusses contraceptive use in Punjab, Pakistan. It begins by providing background on the benefits of family planning and contraceptive use for maternal and child health. It then analyzes contraceptive commodity data from Punjab, finding that use is still low despite efforts to improve access. The document concludes by emphasizing the need for strategies to bridge gaps and meet the unmet need for effective and affordable contraceptive methods and supplies in Punjab in order to improve health outcomes.
A synthesis of taylor’s and fayol’s management approaches for managing market...Alexander Decker
1) The document discusses synthesizing Taylor's scientific management approach and Fayol's process management approach to identify an effective way to manage marketing executives in Nigerian banks.
2) It reviews Taylor's emphasis on efficiency and breaking tasks into small parts, and Fayol's focus on developing general management principles.
3) The study administered a survey to 303 marketing executives in Nigerian banks to test if combining elements of Taylor and Fayol's approaches would help manage their performance through clear roles, accountability, and motivation. Statistical analysis supported combining the two approaches.
A survey paper on sequence pattern mining with incrementalAlexander Decker
This document summarizes four algorithms for sequential pattern mining: GSP, ISM, FreeSpan, and PrefixSpan. GSP is an Apriori-based algorithm that incorporates time constraints. ISM extends SPADE to incrementally update patterns after database changes. FreeSpan uses frequent items to recursively project databases and grow subsequences. PrefixSpan also uses projection but claims to not require candidate generation. It recursively projects databases based on short prefix patterns. The document concludes by stating the goal was to find an efficient scheme for extracting sequential patterns from transactional datasets.
A survey on live virtual machine migrations and its techniquesAlexander Decker
This document summarizes several techniques for live virtual machine migration in cloud computing. It discusses works that have proposed affinity-aware migration models to improve resource utilization, energy efficient migration approaches using storage migration and live VM migration, and a dynamic consolidation technique using migration control to avoid unnecessary migrations. The document also summarizes works that have designed methods to minimize migration downtime and network traffic, proposed a resource reservation framework for efficient migration of multiple VMs, and addressed real-time issues in live migration. Finally, it provides a table summarizing the techniques, tools used, and potential future work or gaps identified for each discussed work.
A survey on data mining and analysis in hadoop and mongo dbAlexander Decker
This document discusses data mining of big data using Hadoop and MongoDB. It provides an overview of Hadoop and MongoDB and their uses in big data analysis. Specifically, it proposes using Hadoop for distributed processing and MongoDB for data storage and input. The document reviews several related works that discuss big data analysis using these tools, as well as their capabilities for scalable data storage and mining. It aims to improve computational time and fault tolerance for big data analysis by mining data stored in Hadoop using MongoDB and MapReduce.
1. The document discusses several challenges for integrating media with cloud computing including media content convergence, scalability and expandability, finding appropriate applications, and reliability.
2. Media content convergence challenges include dealing with the heterogeneity of media types, services, networks, devices, and quality of service requirements as well as integrating technologies used by media providers and consumers.
3. Scalability and expandability challenges involve adapting to the increasing volume of media content and being able to support new media formats and outlets over time.
This document surveys trust architectures that leverage provenance in wireless sensor networks. It begins with background on provenance, which refers to the documented history or derivation of data. Provenance can be used to assess trust by providing metadata about how data was processed. The document then discusses challenges for using provenance to establish trust in wireless sensor networks, which have constraints on energy and computation. Finally, it provides background on trust, which is the subjective probability that a node will behave dependably. Trust architectures need to be lightweight to account for the constraints of wireless sensor networks.
This document discusses private equity investments in Kenya. It provides background on private equity and discusses trends in various regions. The objectives of the study discussed are to establish the extent of private equity adoption in Kenya, identify common forms of private equity utilized, and determine typical exit strategies. Private equity can involve venture capital, leveraged buyouts, or mezzanine financing. Exits allow recycling of capital into new opportunities. The document provides context on private equity globally and in developing markets like Africa to frame the goals of the study.
This document discusses a study that analyzes the financial health of the Indian logistics industry from 2005-2012 using Altman's Z-score model. The study finds that the average Z-score for selected logistics firms was in the healthy to very healthy range during the study period. The average Z-score increased from 2006 to 2010 when the Indian economy was hit by the global recession, indicating the overall performance of the Indian logistics industry was good. The document reviews previous literature on measuring financial performance and distress using ratios and Z-scores, and outlines the objectives and methodology used in the current study.
In our second session, we shall learn all about the main features and fundamentals of UiPath Studio that enable us to use the building blocks for any automation project.
📕 Detailed agenda:
Variables and Datatypes
Workflow Layouts
Arguments
Control Flows and Loops
Conditional Statements
💻 Extra training through UiPath Academy:
Variables, Constants, and Arguments in Studio
Control Flow in Studio
"Scaling RAG Applications to serve millions of users", Kevin GoedeckeFwdays
How we managed to grow and scale a RAG application from zero to thousands of users in 7 months. Lessons from technical challenges around managing high load for LLMs, RAGs and Vector databases.
AppSec PNW: Android and iOS Application Security with MobSFAjin Abraham
Mobile Security Framework - MobSF is a free and open source automated mobile application security testing environment designed to help security engineers, researchers, developers, and penetration testers to identify security vulnerabilities, malicious behaviours and privacy concerns in mobile applications using static and dynamic analysis. It supports all the popular mobile application binaries and source code formats built for Android and iOS devices. In addition to automated security assessment, it also offers an interactive testing environment to build and execute scenario based test/fuzz cases against the application.
This talk covers:
Using MobSF for static analysis of mobile applications.
Interactive dynamic security assessment of Android and iOS applications.
Solving Mobile app CTF challenges.
Reverse engineering and runtime analysis of Mobile malware.
How to shift left and integrate MobSF/mobsfscan SAST and DAST in your build pipeline.
[OReilly Superstream] Occupy the Space: A grassroots guide to engineering (an...Jason Yip
The typical problem in product engineering is not bad strategy, so much as “no strategy”. This leads to confusion, lack of motivation, and incoherent action. The next time you look for a strategy and find an empty space, instead of waiting for it to be filled, I will show you how to fill it in yourself. If you’re wrong, it forces a correction. If you’re right, it helps create focus. I’ll share how I’ve approached this in the past, both what works and lessons for what didn’t work so well.
How information systems are built or acquired puts information, which is what they should be about, in a secondary place. Our language adapted accordingly, and we no longer talk about information systems but applications. Applications evolved in a way to break data into diverse fragments, tightly coupled with applications and expensive to integrate. The result is technical debt, which is re-paid by taking even bigger "loans", resulting in an ever-increasing technical debt. Software engineering and procurement practices work in sync with market forces to maintain this trend. This talk demonstrates how natural this situation is. The question is: can something be done to reverse the trend?
In the realm of cybersecurity, offensive security practices act as a critical shield. By simulating real-world attacks in a controlled environment, these techniques expose vulnerabilities before malicious actors can exploit them. This proactive approach allows manufacturers to identify and fix weaknesses, significantly enhancing system security.
This presentation delves into the development of a system designed to mimic Galileo's Open Service signal using software-defined radio (SDR) technology. We'll begin with a foundational overview of both Global Navigation Satellite Systems (GNSS) and the intricacies of digital signal processing.
The presentation culminates in a live demonstration. We'll showcase the manipulation of Galileo's Open Service pilot signal, simulating an attack on various software and hardware systems. This practical demonstration serves to highlight the potential consequences of unaddressed vulnerabilities, emphasizing the importance of offensive security practices in safeguarding critical infrastructure.
Freshworks Rethinks NoSQL for Rapid Scaling & Cost-EfficiencyScyllaDB
Freshworks creates AI-boosted business software that helps employees work more efficiently and effectively. Managing data across multiple RDBMS and NoSQL databases was already a challenge at their current scale. To prepare for 10X growth, they knew it was time to rethink their database strategy. Learn how they architected a solution that would simplify scaling while keeping costs under control.
ScyllaDB is making a major architecture shift. We’re moving from vNode replication to tablets – fragments of tables that are distributed independently, enabling dynamic data distribution and extreme elasticity. In this keynote, ScyllaDB co-founder and CTO Avi Kivity explains the reason for this shift, provides a look at the implementation and roadmap, and shares how this shift benefits ScyllaDB users.
Discover top-tier mobile app development services, offering innovative solutions for iOS and Android. Enhance your business with custom, user-friendly mobile applications.
Essentials of Automations: Exploring Attributes & Automation ParametersSafe Software
Building automations in FME Flow can save time, money, and help businesses scale by eliminating data silos and providing data to stakeholders in real-time. One essential component to orchestrating complex automations is the use of attributes & automation parameters (both formerly known as “keys”). In fact, it’s unlikely you’ll ever build an Automation without using these components, but what exactly are they?
Attributes & automation parameters enable the automation author to pass data values from one automation component to the next. During this webinar, our FME Flow Specialists will cover leveraging the three types of these output attributes & parameters in FME Flow: Event, Custom, and Automation. As a bonus, they’ll also be making use of the Split-Merge Block functionality.
You’ll leave this webinar with a better understanding of how to maximize the potential of automations by making use of attributes & automation parameters, with the ultimate goal of setting your enterprise integration workflows up on autopilot.
Must Know Postgres Extension for DBA and Developer during MigrationMydbops
Mydbops Opensource Database Meetup 16
Topic: Must-Know PostgreSQL Extensions for Developers and DBAs During Migration
Speaker: Deepak Mahto, Founder of DataCloudGaze Consulting
Date & Time: 8th June | 10 AM - 1 PM IST
Venue: Bangalore International Centre, Bangalore
Abstract: Discover how PostgreSQL extensions can be your secret weapon! This talk explores how key extensions enhance database capabilities and streamline the migration process for users moving from other relational databases like Oracle.
Key Takeaways:
* Learn about crucial extensions like oracle_fdw, pgtt, and pg_audit that ease migration complexities.
* Gain valuable strategies for implementing these extensions in PostgreSQL to achieve license freedom.
* Discover how these key extensions can empower both developers and DBAs during the migration process.
* Don't miss this chance to gain practical knowledge from an industry expert and stay updated on the latest open-source database trends.
Mydbops Managed Services specializes in taking the pain out of database management while optimizing performance. Since 2015, we have been providing top-notch support and assistance for the top three open-source databases: MySQL, MongoDB, and PostgreSQL.
Our team offers a wide range of services, including assistance, support, consulting, 24/7 operations, and expertise in all relevant technologies. We help organizations improve their database's performance, scalability, efficiency, and availability.
Contact us: info@mydbops.com
Visit: https://www.mydbops.com/
Follow us on LinkedIn: https://in.linkedin.com/company/mydbops
For more details and updates, please follow up the below links.
Meetup Page : https://www.meetup.com/mydbops-databa...
Twitter: https://twitter.com/mydbopsofficial
Blogs: https://www.mydbops.com/blog/
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Conversational agents, or chatbots, are increasingly used to access all sorts of services using natural language. While open-domain chatbots - like ChatGPT - can converse on any topic, task-oriented chatbots - the focus of this paper - are designed for specific tasks, like booking a flight, obtaining customer support, or setting an appointment. Like any other software, task-oriented chatbots need to be properly tested, usually by defining and executing test scenarios (i.e., sequences of user-chatbot interactions). However, there is currently a lack of methods to quantify the completeness and strength of such test scenarios, which can lead to low-quality tests, and hence to buggy chatbots.
To fill this gap, we propose adapting mutation testing (MuT) for task-oriented chatbots. To this end, we introduce a set of mutation operators that emulate faults in chatbot designs, an architecture that enables MuT on chatbots built using heterogeneous technologies, and a practical realisation as an Eclipse plugin. Moreover, we evaluate the applicability, effectiveness and efficiency of our approach on open-source chatbots, with promising results.
QA or the Highway - Component Testing: Bridging the gap between frontend appl...zjhamm304
These are the slides for the presentation, "Component Testing: Bridging the gap between frontend applications" that was presented at QA or the Highway 2024 in Columbus, OH by Zachary Hamm.
The Department of Veteran Affairs (VA) invited Taylor Paschal, Knowledge & Information Management Consultant at Enterprise Knowledge, to speak at a Knowledge Management Lunch and Learn hosted on June 12, 2024. All Office of Administration staff were invited to attend and received professional development credit for participating in the voluntary event.
The objectives of the Lunch and Learn presentation were to:
- Review what KM ‘is’ and ‘isn’t’
- Understand the value of KM and the benefits of engaging
- Define and reflect on your “what’s in it for me?”
- Share actionable ways you can participate in Knowledge - - Capture & Transfer
Session 1 - Intro to Robotic Process Automation.pdfUiPathCommunity
👉 Check out our full 'Africa Series - Automation Student Developers (EN)' page to register for the full program:
https://bit.ly/Automation_Student_Kickstart
In this session, we shall introduce you to the world of automation, the UiPath Platform, and guide you on how to install and setup UiPath Studio on your Windows PC.
📕 Detailed agenda:
What is RPA? Benefits of RPA?
RPA Applications
The UiPath End-to-End Automation Platform
UiPath Studio CE Installation and Setup
💻 Extra training through UiPath Academy:
Introduction to Automation
UiPath Business Automation Platform
Explore automation development with UiPath Studio
👉 Register here for our upcoming Session 2 on June 20: Introduction to UiPath Studio Fundamentals: https://community.uipath.com/events/details/uipath-lagos-presents-session-2-introduction-to-uipath-studio-fundamentals/
Connector Corner: Seamlessly power UiPath Apps, GenAI with prebuilt connectorsDianaGray10
Join us to learn how UiPath Apps can directly and easily interact with prebuilt connectors via Integration Service--including Salesforce, ServiceNow, Open GenAI, and more.
The best part is you can achieve this without building a custom workflow! Say goodbye to the hassle of using separate automations to call APIs. By seamlessly integrating within App Studio, you can now easily streamline your workflow, while gaining direct access to our Connector Catalog of popular applications.
We’ll discuss and demo the benefits of UiPath Apps and connectors including:
Creating a compelling user experience for any software, without the limitations of APIs.
Accelerating the app creation process, saving time and effort
Enjoying high-performance CRUD (create, read, update, delete) operations, for
seamless data management.
Speakers:
Russell Alfeche, Technology Leader, RPA at qBotic and UiPath MVP
Charlie Greenberg, host
What is an RPA CoE? Session 1 – CoE VisionDianaGray10
In the first session, we will review the organization's vision and how this has an impact on the COE Structure.
Topics covered:
• The role of a steering committee
• How do the organization’s priorities determine CoE Structure?
Speaker:
Chris Bolin, Senior Intelligent Automation Architect Anika Systems
New multi step runge kutta method for solving fuzzy differential equations
1. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.1, No.3, 2011
New Multi-Step Runge –Kutta Method For Solving Fuzzy
Differential Equations
Nirmala. V1* Chenthur Pandian.S2
1. Department of Mathematics, University College of Engineering Tindivanam
(Anna University of Technology Chennai), Tamil Nadu, India, 604001.
2. Department of Electrical and Electronics Engineering,Dr Mahalingam College of Engineering and
Technology,(Anna University of Technology Coimbatore)Pollachi,Tamil Nadu,India
*E-mail of the corresponding auther: nirmala_2005@mail.com
Abstract
This paper presents solution for the first order fuzzy differential equation by Runge –Kutta method of order
two with new parameters and Harmonic mean of ’s which are used in the main formula in order to
increase the order of accuracy of the solution. This method is discussed in detail followed by a complete
error analysis. The accuracy and efficiency of the proposed method is illustrated by solving a fuzzy initial
value problem.
Keywords: Fuzzy differential equations, multi-step Runge-Kutta method, higher order derivative
approximations, harmonic mean.
1. Introduction
Fuzzy Differential Equation (FDE) models have wide range of applications in many branches of
engineering and in the field of medicine. The concept of fuzzy derivative was first introduced by S.L.Chang
and L.A.Zadeh [7].D.Dubois and Prade [8] discussed differentiation with fuzzy features.M.L.puri and
D.A.Ralesec [18] and R.Goetschel and W.Voxman [10] contributed towards the differential of fuzzy
functions. The fuzzy differential equation and initial value problems were extensively studied by O.Kaleva
[11,12] and by S.Seikkala [19].Recently many research papers are focused on numerical solution of fuzzy
initial value problems (FIVPS).Numerical Solution of fuzzy differential equations has been introduced by
M.Ma, M. Friedman, A. Kandel [14] through Euler method and by S.Abbasbandy and T.Allahviranloo [2]
by Taylor method.Runge – Kutta methods have also been studied by authors [3,17]. Numerical Solution of
fuzzy differential equations by Runge –Kutta method of order two with new parameters has been by
V.Nirmala, Saveetha, N and S.Chenthur Pandian[15] and by Runge –Kutta method of order four with new
parameters by V.Nirmala and S.Chenthur Pandian [16].
This paper is organised as follows: In section 2, some basic results on fuzzy numbers and definition of
fuzzy derivative are given. Section 3 contains fuzzy Cauchy problem whose numerical solution is the main
interest of this paper. Second order multi -step Runge –Kutta method with new parameters based on
harmonic mean is discussed in section 4.The proposed method is illustrated by a solved numerical example
in section 5and the result is compared with Euler’s approximation and with the approximation by Runge-
Kutta method proposed in [15] and conclusion is in section 6.
2. Preliminaries
, ;
Consider the initial value problem
(2.1)
, ∞ ∞ with
We assume that
,
1. is defined and continuous in the strip , and finite.
∗ ,| , , ∗ | | ∗|
2. There exists a constant such that for any ‘ ’ in and any two numbers
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These conditions are sufficient to prove that there exists on , , a unique continuous, differentiable
function satisfying (2.1).
∑# " (2.2) Where " ’s are constant for all % and
The basis of all Runge-Kutta methods is to express the difference between the value of at and
$
& ' &, ' ∑)$ ( ) ) *
as
(2.3) Most efforts to increase the order of accuracy of the
Runge-Kutta methods have been accomplished by increasing the number of Taylor’s series terms used
and thus the number of functional evaluations required [6].The method proposed by Goeken .D and
% + 1 to obtain a higher order of accuracy without a corresponding increase in evaluations of‘ ’, but
Johnson .O[9] introduces new terms involving higher order derivatives of ‘ ’ in the Runge-Kutta terms
with the addition of evaluations of .
' '
The second order Runge-Kutta method for autonomous systems proposed by Goeken.D andJohnson.O [9]:
- -
&
Consider (2.4)
& ' '&
Where (2.5)
- - -- . ) (2.6)
New Multi-step Runge- Kutta method with harmonic mean was discussed and used approximate in the
stage - by Ababneh,O.Y,Ahmad,R.,and Ismail,E.S [1]. In this paper, we use exact in stage - .Then,
'
-/0 /1
the new multi-step Runge –Kutta method of order two is given by
/0 /1
&
(2.7)
& ' '&
Where (2.8)
- - -- .
1
) (2.9)
Utilizing the Taylor’s series expansion techniques in (2.7),we get the parameter -
and there is no any order condition to choose -- and hence we take -- 9/10
'/
-/0 /1
Runge-Kutta method of order two is given by:
/1
&
0
(2.10)
& ' ' & 10
5
Where 1 (2.11)
.
, belong to 6 - ,
2 1 1 (2.12)
, 7, such that | , | 7, 8 8 %'B C, then in the
9 :;< = ? :;<
Theorem 2.1. Let and its partial derivatives be bounded and let us assume that
9> : 9. < @ <A0
there exist positive constants ,
≅ 63/30 7 - &G ' H &I .
Runge –Kutta method of order two ,we have([13]),
Definition 2.1. A fuzzy number K is a fuzzy subset of L (ie) K: L → 0,1 satisfying the following
1.K is normal (ie) ∃ P ∈ L with K P 1.
conditions:
2.K is convex fuzzy set
(ie) K P' 1 R minVK P , K W , ∀ ∈ 0,1 , P, ∈ L .
YYYYYYYYYYYYYYYYYYYYYY
3.K is upper semi continuous on L. 4.VP ∈ L, K P + 0W is compact.
Let Z be the class of all fuzzy subsets of L.Then Z is called the space of fuzzy numbers [11].
Clearly, L ⊂Z and L ⊂Z is understood as L V] : %^ K^K _ `a _ KC a`W.
K ` ,K ` ,0 ` 1 that satisfies the following requirements.
An arbitrary fuzzy number is represented by an ordered pair of functions
1.K ` is a bounded left continous non-decreasing function over [0,1],with respect to any ‘r’.
2. K ` is a bounded right continuous non-increasing function over [0,1] with respect to any ‘r’.
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3. K ` K ` , 0 ` 1.
Then the r-level set is K b VP K P R `W, 0 ` 1 is a closed and bounded interval, denoted
by K b K ` , K ` .And clearly, K VP K P + 0W is compact.
Definition 2.2. A triangular fuzzy number K is a fuzzy set in E that is characterized by an ordered triple
Kd , Ke , Kb ∈ L G with Kd Ke Kb such that K Kd ; Kb and K VKe W.
The membership function of the triangular fuzzy number K is given by
, Kd P Ke
]*gh
gi *gh
K P f 1, P Ke
, Ke P Kb
gj *]
.
gj *gi
We will write (i) K + 0, % Kd + 0. (ii) K R 0, % Kd R 0. (iii) K 0, % Ke 0.
(iv) K 0, % Ke 0.
Let I be a real interval. A mapping : l → Z is called a fuzzy process, and its m _ana_ set is denoted
o p ;m , ; m q , ∈ l, 0 m l . The seikkala derivative
p ;m , ; m q , ∈ l, 0 m l, provided that this equation defines
by of a fuzzy process
is defined by o
Lemma2.1. Let K, n
∈ Z and ^ scalar, then for ` ∈ 0,1
a fuzzy number, as in [19].
K'n b K ` ' n ` ,K ` ' n `
K nb K ` n ` ,K ` n `
K, n b minrK ` . n ` , K ` . n ` , K ` . n ` , K ` . n ` s,
max K ` . n ` , K ` . n ` , K ` . n ` , K ` . n ` W ,
V
^K b ^ K b .
3. A Fuzzy Cauchy Problem
, , ∈l 0, v .
Consider the fuzzy initial value problem
0 .
is a continuous mapping from L w L into L and ∈ Z with r-level sets
(3.1)
p 0, ` , 0, ` q , ` ∈ 0,1 .
Where
b
,
, ^ supV { ^ , { W , ^ ∈ L.
The extension principle of Zadeh leads to the following definition of when is a fuzzy
,
, ;` , p
, ; ` q , ` ∈ 0,1 ,
number,
b
, ;` min | , K K ∈ p ` , ` q}, , ;`
It follows that,
max | , K K ∈ p ` , ` q}.
Where
Theorem3.1. Let satisfy ~ ,n , n ~ • , |n n| , R 0, n, n ∈ L, (3.2)
where •: L w L → L is a continuous mapping such that ` → • , ` is non decreasing, the initial
value problem K • ,K ,K 0 K ,
has a solution on L for K + 0 and that K ≡ 0 is the only solution of (3.3) for K 0. Then the
(3.3)
fuzzy initial value problem (3.1 ) has a unique fuzzy solution.
Proof: see [19].
In this paper we suppose (3.1) satisfies the hypothesis of theorem3.1, also.
4 .The Second Order Runge –Kutta Method with Harmonic Mean
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• b ‚• ; ` , • ; ` ƒ is approximated by some b
p ;` , ; ` q.From (2.7) to (2.9), we define
Let the exact solution
/0 >… ,. >… ;b /1 >… ,. >… ;b
;` ;` 2 ;`
/0 >… ,. >… ;b /1 >… ,. >… ;b
(4.1)
;` 2
/0 >… ,. >… ;b /1 >… ,. >… ;b
/0 >… ,. >… ;b /1 >… ,. >… ;b
(4.2)
, ;` min &.
V , K K ∈ p ,` , , ` qW
, ,` max &.
V , K K ∈ p ,` , , ` qW
(4.3)
, ,` min &.
V , K K ∈ p†1 , , ` , †1 , , ` qW.
(4.4)
, ,` max &.
V , K K ∈ p†1 , , ` , †1 , , ` qW
2 (4.5)
- (4.6)
†1 , ,` ,` ' , ,` '
5
Where
†1 , ,` ,` ' , ,` '
5
1 10
min &.
V , K . nK ∈ p ,` , , ` q &n ∈ p , ;` , , ; ` qW
1
.
max &.
V . , K . nK ∈ p ,` , , ` q &n ∈ p , ;` , , ; ` qW
Define,
, ;` - , ;`
ˆ , ;` 2 4.7
, ;` ' - , ;`
, ;` , ;`
‹ , ;` 2 4.8
-
, ;` ' - , ;`
,0 • are denoted by
• ‚• ; ` , • ; ` ƒ and p ;` , ; ` q,respectively
The exact and approximate solutions at
b b
- ⋯…………… •
and&
‘*’
The solution is calculated by grid points at
•
.
• ;` • ;` ' ˆ ,• ,`
Therefore, we have
• ;` • ; ` ' ‹ , • , `
(4.9)
1; ` ;` 'ˆ , ,`
(4.10)
;` ;` ' ‹ , ,`
And (4.11)
(4.12)
i.e., lim”→ ,`
• , ` andlim”→ ,` ,` .
The following lemmas will be applied to show the convergences of theses approximates.
Lemma: 4.1 Let a sequence of numbers V• W $ satisfy |•
• | –|• | ' —, 0 • 1,
for some given positive constants A and B, then |• | – |• | ' — ,0
˜… *
˜*
• 1.
Proof: see [14]
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Lemma: 4.2 Let the sequence of numbers V• W•$ , V™ W•$ satisfy |• | |• | '
–C P V|• |, |™ |W ' —, |™ | |™ | ' –C P V|• |, |™ |W ' —,
for some given positive constants A and B, and denote š |• | ' |™ |, 0 •.
Thenš – š '— ,0 •, where – 1 ' 2– and — 2—
˜… *
˜*
Let ˆ , K, n and ‹ , K, n be obtained by substituting K, n in (4.7&4.8),
Proof: see [14].
b
›0 >,g,œ ›1 >,g,œ
ˆ , K, n 2› ‹ , K, n 2›
›0 >,g,œ ›1 >,g,œ
0 >,g,œ ›1 >,g,œ 0 >,g,œ ›1 >,g,œ
, .
• V , K, n 0 v, ∞ n ∞, ∞ K n W.
The domain where F and G are defined is therefore
Theorem 4.1: let ˆ , K, n and ‹ , K, n belong to 6 - • and let the partial derivatives of F and G
be bounded over K .Then, for arbitrary fixed `, 0 ` 1,the approximate solutions (4.11&4.12)
converge to the exact solutions • ; ` and • ; ` uniformly in t.
Proof: See [14].
5 .Numerical Example
, ∈ 0,1 ,
Example 1. Consider the fuzzy initial value problem,
ž
0 0.75 ' 0.25`, 1.125 0.125` , 0 ` 1.
′
The exact solution is given by• ; ` ; ` a> , • ; ` ; ` a > ,which at 1,
• 1; ` 0.75 ' 0.25` a, 1.125 0.125` a , 0 ` 1.
The exact and approximate solutions obtained by the Euler method and by the Runge-Kutta method of
[New MSRK] with ‘& 0.1’ are given in Table: 1
order two with new parameters [New RK] [15] and by the proposed New Multi-Step Runge-Kutta method
6. Conclusion
fuzzy differential equations. Taking into account the convergence order of the Euler method is H & ,a
In this work, we have used the proposed second-order Runge-Kutta method to find a numerical solution of
higher order of convergence H &G ) is obtained by the proposed method and by the method proposed in
[15]. Comparison of the solutions of example 5.1 shows that the proposed method gives a better solution
than the Euler method and by the Runge-Kutta method of order 2 proposed in [15].
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