4 results
Search Results
2. Approximate Analytical Solutions of Bright Optical Soliton for Nonlinear Schrödinger Equation of Power Law Nonlinearity
- Author
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Adem Kilicman, Ishak Hashim, Che Haziqah Che Hussin, Amirah Azmi, and Ahmad Izani Md. Ismail
- Subjects
General Computer Science ,020209 energy ,General Mathematics ,General Physics and Astronomy ,02 engineering and technology ,Adomian polynomials ,01 natural sciences ,General Biochemistry, Genetics and Molecular Biology ,Schrödinger equation ,symbols.namesake ,nonlinear Schrodinger equations of power law nonlinearity ,Multistep Modified Reduced Differential Transform Method ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,0101 mathematics ,Representation (mathematics) ,lcsh:Science ,Nonlinear Schrödinger equation ,Convergent series ,Mathematics ,General Chemistry ,Agricultural and Biological Sciences (miscellaneous) ,Term (time) ,010101 applied mathematics ,Nonlinear system ,symbols ,Power law nonlinearity ,lcsh:Q ,Soliton ,multistep approach - Abstract
This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM.
- Published
- 2021
3. Using Evolving Algorithms to Cryptanalysis Nonlinear Cryptosystems
- Author
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Faez Hassan Ali and Riyam Noori Jawad
- Subjects
Discrete mathematics ,Ant Colony Optimization (ACO), Cryptanalysis, Genetic Algorithm (GA), Shrinking Generator, Stream Cipher ,General Computer Science ,General Mathematics ,General Physics and Astronomy ,010103 numerical & computational mathematics ,02 engineering and technology ,General Chemistry ,01 natural sciences ,Agricultural and Biological Sciences (miscellaneous) ,General Biochemistry, Genetics and Molecular Biology ,law.invention ,law ,0202 electrical engineering, electronic engineering, information engineering ,Cryptosystem ,020201 artificial intelligence & image processing ,lcsh:Q ,0101 mathematics ,Hardware_ARITHMETICANDLOGICSTRUCTURES ,Cryptanalysis ,lcsh:Science ,Stream cipher ,Mathematics ,Shrinking generator - Abstract
In this paper, new method have been investigated using evolving algorithms (EA's) to cryptanalysis one of the nonlinear stream cipher cryptosystems which depends on the Linear Feedback Shift Register (LFSR) unit by using cipher text-only attack. Genetic Algorithm (GA) and Ant Colony Optimization (ACO) which are used for attacking one of the nonlinear cryptosystems called "shrinking generator" using different lengths of cipher text and different lengths of combined LFSRs. GA and ACO proved their good performance in finding the initial values of the combined LFSRs. This work can be considered as a warning for a stream cipher designer to avoid the weak points, which may be found in the stream cipher, and may be explored by the cryptanalysts. This work can find the optimal solution for text with minimum lengths of 20 characters and 100 iteration were very enough to find the real initial values of key stream.
- Published
- 2020
4. Comparison of Some Suggested Estimators Based on Differencing Technique in the Partial Linear Model Using Simulation
- Author
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Saja Mohammad Hussein
- Subjects
Statistics::Theory ,021103 operations research ,General Computer Science ,General Mathematics ,0211 other engineering and technologies ,General Physics and Astronomy ,02 engineering and technology ,General Chemistry ,01 natural sciences ,Agricultural and Biological Sciences (miscellaneous) ,General Biochemistry, Genetics and Molecular Biology ,010104 statistics & probability ,DAUGRR, DGJR, DGRR, Differences technique, DMJGR, NW estimator ,Statistics ,Statistics::Methodology ,lcsh:Q ,Partial linear model ,0101 mathematics ,lcsh:Science ,Mathematics - Abstract
In this paper new methods were presented based on technique of differences which is the difference- based modified jackknifed generalized ridge regression estimator(DMJGR) and difference-based generalized jackknifed ridge regression estimator(DGJR), in estimating the parameters of linear part of the partially linear model. As for the nonlinear part represented by the nonparametric function, it was estimated using Nadaraya Watson smoother. The partially linear model was compared using these proposed methods with other estimators based on differencing technique through the MSE comparison criterion in simulation study.
- Published
- 2019
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