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I-Statistically Pre-cauchy Triple Sequences of Fuzzy Real Numbers
Sangita Saha,
Bijan Nath,
Santanu Roy
Issue:
Volume 1, Issue 3, September 2016
Pages:
36-43
Received:
14 August 2016
Accepted:
30 August 2016
Published:
18 September 2016
DOI:
10.11648/j.mcs.20160103.11
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Abstract: In this article, using Orlicz function, the concept of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. A necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-statistically Cauchy is established. It is also shown that an I-statistically convergent triple sequence of fuzzy numbers is I-statistically pre-Cauchy.
Abstract: In this article, using Orlicz function, the concept of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. A necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-statistically Cauchy is established. It is also shown that an I-statistically convergent...
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A New Algorithm for Solving Nonlinear Equations by Using Least Square Method
Issue:
Volume 1, Issue 3, September 2016
Pages:
44-47
Received:
22 August 2016
Accepted:
31 August 2016
Published:
18 September 2016
DOI:
10.11648/j.mcs.20160103.12
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Abstract: Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods have been developed for solving nonlinear equations. These methods are given [1-27], in this paper, a new Algorithm for solving nonlinear algebraic equations is obtained by using least square method by fitting a polynomial form of degree two (or parabolic form). This paper compares the present method with the method given by Jutaporn N, Bumrungsak P and Apichat N, 2016 [1], which was used nonlinear regression method in form of logarithm function. We verified on a number of examples and numerical results obtained show that the present method is faster than the method, which used the logarithm function given by [1].
Abstract: Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods have been developed for solving nonlinear equations. These methods are given [1-27], in this paper, a new Algorithm for solving nonlinear algebraic equations is obtained by using least square method by fitting a polynomial form ...
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Discussion on Borehole Wave Modes Excited by Two Types of Acoustic Logging While Drilling Sources
Issue:
Volume 1, Issue 3, September 2016
Pages:
48-55
Received:
6 September 2016
Accepted:
19 September 2016
Published:
29 September 2016
DOI:
10.11648/j.mcs.20160103.13
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Abstract: In this paper, we extend the Real Axis Integration (RAI) method and improve the Finite Difference Time Domain (FDTD) method to investigate the wave fields excited by the monopole and multipole Acoustic Logging While Drilling (ALWD) sources with low and high center frequencies. We simulate the two traditional kinds of source exerting methods by both of the RAI and FDTD methods accurately and efficiently. Mutual verification of the two methods ensures the validity and reliability of our theoretic analysis and modeling results. The modeling results indicate that the ring source can only excite those monopole or multipole wave modes of certain orders. The four azimuthally orthogonal point sources can excite similar wave modes only at the lower frequencies, but at higher frequencies, they might further excite wave modes of higher orders with significant amplitude. These modeling results may help the design of ALWD tools, and also provide an essential basis for the further analysis of the ALWD problems in anisotropic formations and tool eccentric conditions.
Abstract: In this paper, we extend the Real Axis Integration (RAI) method and improve the Finite Difference Time Domain (FDTD) method to investigate the wave fields excited by the monopole and multipole Acoustic Logging While Drilling (ALWD) sources with low and high center frequencies. We simulate the two traditional kinds of source exerting methods by both...
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On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities
Issue:
Volume 1, Issue 3, September 2016
Pages:
56-60
Received:
8 August 2016
Accepted:
18 August 2016
Published:
7 September 2016
DOI:
10.11648/j.mcs.20160103.14
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Abstract: In this paper, we investigate properties of A-self-adjoint operators and other relations on Hilbert spaces. In this context, A is a self-adjoint and an invertible operator. More results on operator equivalences including similarity, unitary and metric equivalences are discussed. We also investigate conditions under which these classes of operators are self- adjoint and unitary. We finally locate their spectra.
Abstract: In this paper, we investigate properties of A-self-adjoint operators and other relations on Hilbert spaces. In this context, A is a self-adjoint and an invertible operator. More results on operator equivalences including similarity, unitary and metric equivalences are discussed. We also investigate conditions under which these classes of operators ...
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Least Absolute Integral Method of Data Fitting Based on Algorithm of Simulated Annealing and Neural Network
Issue:
Volume 1, Issue 3, September 2016
Pages:
61-65
Received:
5 September 2016
Accepted:
18 September 2016
Published:
9 October 2016
DOI:
10.11648/j.mcs.20160103.15
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Abstract: There are many methods related to data fitting, and each method has its distinctive features. The article discusses the method of data fitting function under integral criterion. Since the estimate fitting parameters are complicated, the article combines algorithm of simulated annealing and neural network algorithm to solve the integral with neural network algorithm and solve the unknown parameters with simulated annealing algorithm. By case analog computation of household per capita consumption expenditure of urban and the rural residents in China, it proves that the combination of simulated annealing algorithm and neural network algorithm has strong reliability and high accuracy in terms of new method for least absolute integral data fitting.
Abstract: There are many methods related to data fitting, and each method has its distinctive features. The article discusses the method of data fitting function under integral criterion. Since the estimate fitting parameters are complicated, the article combines algorithm of simulated annealing and neural network algorithm to solve the integral with neural ...
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