scholarly journals Computer tools for the construction and analysis of some efficient root-finding simultaneous methods

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2151-2169
Author(s):  
Ivan Petkovic ◽  
Djordje Herceg
Keyword(s):  
High Efficiency ◽  
Algebraic Polynomials ◽  
Convergence Properties ◽  
Simultaneous Methods ◽  
Computer Tools ◽  
Root Finding ◽  
Accelerated Methods ◽  
The Stability ◽  
Additional Arithmetic ◽  
Complex Zeros

Using the tools provided by computer algebra system Mathematica, we consider two iterative methods of high efficiency for the simultaneous approximation of simple or multiple (real or complex) zeros of algebraic polynomials. The proposed methods are based on the fourth-order Schr?der-like methods of the first and second kind. We prove that the order of convergence of both basic total-step simultaneous methods is equal to five. Using corrective approximations produced by methods of order two, three and four for finding a single multiple zero, the convergence order is increased from five to six, seven, and eight, respectively. The increased convergence speed is attained with negligible number of additional arithmetic operations, which significantly increases the computational efficiency of the accelerated methods. Convergence properties of the proposed methods are demonstrated by numerical examples and graphics visualization by plotting trajectories of zero approximations. Flows of iterative processes, presented by these trajectories, point to the stability and robustness of the proposed methods.

scholarly journals Family of simultaneous methods with corrections for approximating zeros of analytic functions

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2217-2225
Author(s):  
Lidija Rancic
Keyword(s):  
Analytic Functions ◽  
Computational Cost ◽  
Convergence Properties ◽  
Simultaneous Methods ◽  
Good Convergence ◽  
Basic Family ◽  
Complex Zeros ◽  
Low Computational Cost ◽  
Theoretical Results ◽  
Methods Numerical

A family of accelerated iterative methods for the simultaneous approximation of complex zeros of a class of analytic functions is proposed. Considered analytic functions have only simple zeros inside a simple smooth closed contour in the complex plane. It is shown that the order of convergence of the basic family can be increased from four to five and six using Newton?s and Halley?s corrections, respectively. The improved convergence is achieved on the account of additional calculations of low computational cost, which significantly increases the computational efficiency of the accelerated methods. Numerical examples demonstrate a good convergence properties, fitting very well theoretical results.

REMOVAL OF HEAVY METAL Cr (II), Ni (II), Cu (II), Zn (II), Cd (II), Pb (II) IONS FROM AQUEOUS SOLUTION BY MENTHA PIPERITA EXTRACT

2020 ◽  
pp. 15-20
Author(s):  
Ersin Yucel ◽  
Mine Yucel
Keyword(s):  
Aqueous Solution ◽  
Metal Ions ◽  
High Efficiency ◽  
Correlation Coefficients ◽  
Langmuir Model ◽  
Mentha Piperita ◽  
Freundlich Model ◽  
Biosorption Capacity ◽  
Peppermint Extract ◽  
The Stability

In this study, the usage of the peppermint (Mentha piperita) for extracting the metal ions [Mg (II), Cr (II), Ni (II), Cu (II), Zn (II), Cd (II), Pb (II)] that exist at water was investigated. In order to analyze the stability properties, Langmuir, Freundlich, Temkin and Dubinin-Radushkevich isotherms were used at removing the metal ions and the highest correlation coefficients (R2) were obtained at Langmuir isotherm. Therefore, it is seen that the Langmuir model is more proper than the Freundlich model. However, it was found that the correlation coefficients of removing Ni and Cd is higher at Freundlich model than Langmuir and low at Dubinin-Radushkevich isotherm. It is established that the biosorption amount increase depends on the increase of biosorbent and it can be achieved high efficiency (95%) even with small amount (0.6 mg, peppermint extract) at lead ions. It is also determined that the peppermint extracted that is used at this study shows high biosorption capacity for metal ions and can be used for immobilization of metals from polluted areas.

An Application and Research of Gray-Relation for Color Classification in Dyeing Textile

2013 ◽  
Vol 694-697 ◽  
pp. 2881-2885
Author(s):  
Hai Yan Wang ◽  
Jian Xin Zhang
Keyword(s):  
System Analysis ◽  
High Efficiency ◽  
Information Management System ◽  
Space Distribution ◽  
Color Classification ◽  
Uniform Sampling ◽  
Forecast Precision ◽  
Internal Instability ◽  
The Stability

Dyeing textile’s information management system is the basis of accurate classification of color， machine studying methods have became a popular area of research for application in color classification. Traditional classification methods have high efficiency and are very simple ， but they are dependent on the distribution of sample spaces. If the sample data properties are not independent， forecast precision will been affected badly and internal instability will appear. An application of Gray-Relation for dyeing textile color classification has been designed， which offsets the discount in mathematical statistics method for system analysis. It is applicable regardless of variant in sample size， while quantizing structure is in agreement with qualitative analysis. On the basis of theoretical analysis， Dyeing textile color classification was conducted in the conditions of random sampling、 uniform sampling and stratified sampling. The experimental results proofs that by using Gray-Relation， dyeing textile color classification does not need to be dependent on sample space distribution， and increases the stability of classification.

scholarly journals Posttranscriptional regulation of hsp70 expression in human cells: effects of heat shock, inhibition of protein synthesis, and adenovirus infection on translation and mRNA stability.

1987 ◽  
Vol 7 (12) ◽  
pp. 4357-4368 ◽  
Author(s):  
N G Theodorakis ◽  
R I Morimoto
Keyword(s):  
Protein Synthesis ◽  
Heat Shock ◽  
Posttranscriptional Regulation ◽  
High Efficiency ◽  
Hsp70 Expression ◽  
Mrna Levels ◽  
Protein Synthesis Inhibitors ◽  
Hsp70 Mrna ◽  
Infected Cells ◽  
The Stability

We have examined the posttranscriptional regulation of hsp70 gene expression in two human cell lines, HeLa and 293 cells, which constitutively express high levels of HSP70. HSP70 mRNA translates with high efficiency in both control and heat-shocked cells. Therefore, heat shock is not required for the efficient translation of HSP70 mRNA. Rather, the main effect of heat shock on translation is to suppress the translatability of non-heat shock mRNAs. Heat shock, however, has a marked effect on the stability of HSP70 mRNA; in non-heat-shocked cells the half-life of HSP70 mRNA is approximately 50 min, and its stability increases at least 10-fold upon heat shock. Moreover, HSP70 mRNA is more stable in cells treated with protein synthesis inhibitors, suggesting that a heat shock-sensitive labile protein regulates its turnover. An additional effect on posttranscriptional regulation of hsp70 expression can be found in adenovirus-infected cells, in which HSP70 mRNA levels decline precipititously late during infection although hsp70 transcription continues unabated.

Control by Mixed-Chloride Additives of the Quality and Homogeneity of Bulk Halide Perovskite upon Film Formation Process

2021 ◽  
Author(s):  
Thierry Pauporté ◽  
Daming zheng
Keyword(s):  
Solar Cells ◽  
Formation Process ◽  
High Efficiency ◽  
Film Formation ◽  
Perovskite Solar Cells ◽  
X Ray Diffraction ◽  
X Ray ◽  
Stability Issue ◽  
Halide Perovskite ◽  
The Stability

Nowadays, overcoming the stability issue of perovskite solar cells (PSCs) while keeping high efficiency has become an urgent need for the future of this technology. By using x-ray diffraction (XRD),...

scholarly journals Ligand dependent oxidation dictates the performance evolution of high efficiency PbS quantum dot solar cells

2020 ◽  
Vol 4 (1) ◽  
pp. 108-115 ◽  
Author(s):  
David Becker-Koch ◽  
Miguel Albaladejo-Siguan ◽  
Vincent Lami ◽  
Fabian Paulus ◽  
Hengyang Xiang ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Solar Cells ◽  
Lead Sulfide ◽  
High Efficiency ◽  
Photovoltaic Performance ◽  
Continuous Illumination ◽  
Quantum Dot Solar Cells ◽  
The Stability ◽  
Pbs Quantum Dots ◽  
Pbs Quantum Dot

The stability of lead sulfide (PbS) quantum dots (QD) under continuous illumination in oxygenated environments depends on the choice of ligands, determining the evolution of photovoltaic performance of high efficiency PbS QD solar cells.

scholarly journals Transient Analysis of Grout Penetration With Time-Dependent Viscosity Inside 3D Fractured Rock Mass by Unified Pipe-Network Method

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1122 ◽  
Author(s):  
Zizheng Sun ◽  
Xiao Yan ◽  
Rentai Liu ◽  
Zhenhao Xu ◽  
Shucai Li ◽  
...  
Keyword(s):  
Rock Mass ◽  
Large Scale ◽  
High Efficiency ◽  
Fractured Rock ◽  
Time Dependent ◽  
Pipe Network ◽  
Fractured Rock Mass ◽  
Network Method ◽  
The Stability ◽  
Dependent Viscosity

Grouting is widely used for mitigating the seepage of underground water and enhancing the stability of fractured rock mass. After injection, the viscosity of the grout gradually increases until solidification. Conventional multifield analysis models ignoring such effects greatly overestimate the penetration region of the grout and the stability of the grouted rock structures. Based on the 3D unified pipe-network method (UPM), we propose a novel numerical model considering the time-dependent viscosity of the grout, therein being a quasi-implicit approach of high efficiency. The proposed model is verified by comparing with analytical results and a time-wise method. Several large-scale 3D examples of fractured rock mass are considered in the numerical studies, demonstrating the effectiveness and robustness of the proposed method. The influence of the time-dependent viscosity, fracture properties, and grouting operation methods are discussed for the grout penetration process.

scholarly journals Fixed Point Root-Finding Methods of Fourth-Order of Convergence

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 769 ◽  
Author(s):  
Alicia Cordero ◽  
Lucía Guasp ◽  
Juan R. Torregrosa
Keyword(s):  
Weight Function ◽  
Dynamical Behavior ◽  
Nonlinear Problems ◽  
Dynamical Analysis ◽  
Function Technique ◽  
Weight Functions ◽  
Good Tool ◽  
Quadratic Polynomials ◽  
Root Finding ◽  
The Stability

In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different weight functions. This weight function, depending on two different evaluations of the derivative, is the unique difference between the two steps of each method, which is unusual. As it is proven that all the members of the class are optimal methods in the sense of Kung-Traub’s conjecture, the dynamical analysis is a good tool to determine the best elements of the family in terms of stability. Therefore, the dynamical behavior of this class on quadratic polynomials is studied in this work. We analyze the stability of the presented family from the multipliers of the fixed points and critical points, along with their associated parameter planes. In addition, this study enables us to select the members of the class with good stability properties.

scholarly journals Dynamics of a continued fraction of Ramanujan with random coefficients

2005 ◽  
Vol 2005 (5) ◽  
pp. 449-467 ◽  
Author(s):  
Jonathan M. Borwein ◽  
D. Russell Luke
Keyword(s):  
Dynamical Systems ◽  
Difference Equations ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Random Coefficients ◽  
Convergence Properties ◽  
Stochastic Difference Equations ◽  
Random Complex ◽  
The Stability ◽  
Complex Valued

We study a generalization of a continued fraction of Ramanujan with random, complex-valued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.

Study of Gas Production by Anaerobic Fermentation and Microbial Community Changes by In-Situ Microaerobic Desulphurization

2020 ◽  
Vol 14 (4) ◽  
pp. 517-523
Author(s):  
Yan Zhou ◽  
Hucheng Liu ◽  
Wei Kou ◽  
Lijie Shao ◽  
Peihan Liu ◽  
...  
Keyword(s):  
High Throughput Sequencing ◽  
High Efficiency ◽  
Anaerobic Fermentation ◽  
Low Cost ◽  
Total Solid ◽  
Common Species ◽  
Gas Production ◽  
High Concentration ◽  
Fermentation System ◽  
The Stability

The enhancement of biogas quality at low cost and high efficiency process was one of the purposes of biogas engineering. In this work, we designed a reactor for microaerobic desulphurization. We used this reactor to study the anaerobic fermentation in systems that used cow manure with total solid (TS) concentrations of 18.5%, 15% and 10%. The influence of anaerobic fermentation on the stability of gas production and the characteristics of the gas produced with different concentrations of fermentation materials was studied. The strain structure of the fermentation system was obtained by high-throughput sequencing and taxonomy was compared. The H2S removal results showed that the average rates of the H2S removal in concentrations of fermentation materials of 18.5%, 15%, and 10% TS were 99.2%, 97.8%, and 78.8%, respectively. 16SrRNA sequencing was performed in different fermented samples as well as a comparison between samples in order to determine the number of unique species (NUS) and the number of common species (NCS). By comparing TS 18.5 with TS 15 and TS 10 samples, it was determined that under fermentation conditions, NUS were 113 and 106, respectively. Whereas NUS were 31 and 41, respectively, when comparing TS 15 and TS 10. These demonstrated that the number of strain species in the fermentation system with TS 18.5% was far more than those found in the systems with low concentration of fermentation. Also, the ability for disturbance resistance of the microaerobic desulphurization system was stronger at high concentration of the fermentation.

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