scholarly journals New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 296 ◽  
Author(s):  
Ramandeep Behl ◽  
Alicia Cordero ◽  
Juan Torregrosa ◽  
Ali Alshomrani
Keyword(s):  
Iterative Methods ◽  
Nonlinear Models ◽  
Nonlinear Problems ◽  
Chemical Reactor ◽  
Parallel Plates ◽  
Fractional Conversion ◽  
Factor Effect ◽  
New Type ◽  
Residual Errors ◽  
Better Than

In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature.

scholarly journals Material Considerations in the Microfabrication of Grating Microstructures for use in a Laser-Powered Linear Accelerator

1986 ◽  
Vol 76 ◽  
Author(s):  
John B. Warren
Keyword(s):  
Linear Accelerator ◽  
Material Selection ◽  
Collaborative Work ◽  
Fused Silica ◽  
Image Analyzer ◽  
Metrological Analysis ◽  
Field Gradients ◽  
New Type ◽  
Specialized Form ◽  
Better Than

ABSTRACTCollaborative work between Brookhaven and Los Alamos National Laboratories is developing a new type of linear accelerator that uses a high-power, picosecond pulse CO2 laser to irradiate a specialized form of grating with a pitch of 10.6 microns. The electromagnetic field that results can be used to accelerate electrons at field gradients of several GeV/m with potential efficiencies much better than current accelerators. The grating must be conductive to minimize resistive losses, be able to withstand high fields without damage, and requires dimensional tolerances in the sub-micron range. These requirements focus attention on grating material selection, microfabrication methods, and metrological methods used for quality control. At present, several types of gratings have been manufactured by reactive ion etching of fused silica in CHF 3/Ar or etching silicon with KOH/H 2O or ethylenediamine-pyrocatechol solutions. Metrological analysis of the gratings has begun with a Tracor Northern 5700 digital image analyzer.

scholarly journals A Multi-User Schedule Method for Non-Orthogonal Multiple Access in 5G Heterogeneous Network

2019 ◽  
Vol 37 (2) ◽  
pp. 337-343
Author(s):  
Yi Xie
Keyword(s):  
Heterogeneous Network ◽  
Network Architecture ◽  
Multiple Access ◽  
Average Rate ◽  
Small Cells ◽  
Fifth Generation ◽  
Scheduling Method ◽  
New Type ◽  
Multiuser Scheduling ◽  
Better Than

Heterogeneous network is supposed to be the dominant network architecture of the fifth generation (5G) cellular network, which means small cells are overlaid on the macrocell. The beamforming (BF) and cell expansion are two important approaches to serve users in small cells. Furthermore, non-orthogonal multiple access (NOMA) is a new type of multiple access multiplexing which improves system performance without taking up extra spectrum resources. Therefore, it becomes one promising technique in 5G. In this paper, NOMA is applied in a 5G heterogeneous network with biased small cells. The BF strategy and the multiuser scheduling method are proposed. The main user in NOMA is scheduled inside the original coverage of the small cell while the side user is chosen from the biased expansion area. The BF strategy that is executed depends on the channel of main user. The multiuser scheduling method is to maximize the rate performance. The proposed method can provide performance benefits. Simulation results show that the proposed methods can be well applied in heterogeneous networks. The achieved performance gain is approximately twice better than traditional OMA and has 10% improvement to the stochastic schedule method. In addition, the average rate of cell edge users is improved.

scholarly journals Improvements on Learning Kernel Extended Dictionary for Face Recognition

2020 ◽  
Vol 34 (4) ◽  
pp. 387-394
Author(s):  
Soodabeh Amanzadeh ◽  
Yahya Forghani ◽  
Javad Mahdavi Chabok
Keyword(s):  
Sparse Representation ◽  
Face Image ◽  
Collaborative Representation ◽  
Training Images ◽  
Input Face ◽  
Proposed Model ◽  
Eigen Values ◽  
New Type ◽  
The Mean ◽  
Better Than

Kernel extended dictionary learning model (KED) is a new type of Sparse Representation for Classification (SRC), which represents the input face image as a linear combination of dictionary set and extended dictionary set to determine the input face image class label. Extended dictionary is created based on the differences between the occluded images and non-occluded training images. There are four defaults to make about KED: (1) Similar weights are assigned to the principle components of occlusion variations in KED model, while the principle components of the occlusion variations have different weights, which are proportional to the principle components Eigen-values. (2) Reconstruction of an occluded image is not possible by combining only non-occluded images and the principle components (or the directions) of occlusion variations, but it requires the mean of occlusion variations. (3) The importance and capability of main dictionary and extended dictionary in reconstructing the input face image is not the same, necessarily. (4) KED Runtime is high. To address these problems or challenges, a novel mathematical model is proposed in this paper. In the proposed model, different weights are assigned to the principle components of occlusion variations; different weights are assigned to the main dictionary and extended dictionary; an occluded image is reconstructed by non-occluded images and the principle components of occlusion variations, and also the mean of occlusion variations; and collaborative representation is used instead of sparse representation to enhance the runtime. Experimental results on CAS-PEAL subsets showed that the runtime and accuracy of the proposed model is about 1% better than that of KED.

scholarly journals RELIABLE ITERATIVE METHODS FOR SOLVING 1D, 2D AND 3D FISHER’S EQUATION

2021 ◽  
Vol 22 (1) ◽  
pp. 138-166
Author(s):  
Othman Mahdi Salih ◽  
Majeed AL-Jawary
Keyword(s):  
Iterative Methods ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Absolute Error ◽  
Fisher’S Equation ◽  
Adomian Decomposition ◽  
Fisher's Equation ◽  
2D And 3D

In the present paper, three reliable iterative methods are given and implemented to solve the 1D, 2D and 3D Fisher’s equation. Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM) and Banach contraction method (BCM) are applied to get the exact and numerical solutions for Fisher's equations. The reliable iterative methods are characterized by many advantages, such as being free of derivatives, overcoming the difficulty arising when calculating the Adomian polynomial boundaries to deal with nonlinear terms in the Adomian decomposition method (ADM), does not request to calculate Lagrange multiplier as in the Variational iteration method (VIM) and there is no need to create a homotopy like in the Homotopy perturbation method (HPM), or any assumptions to deal with the nonlinear term. The obtained solutions are in recursive sequence forms which can be used to achieve the closed or approximate form of the solutions. Also, the fixed point theorem was presented to assess the convergence of the proposed methods. Several examples of 1D, 2D and 3D problems are solved either analytically or numerically, where the efficiency of the numerical solution has been verified by evaluating the absolute error and the maximum error remainder to show the accuracy and efficiency of the proposed methods. The results reveal that the proposed iterative methods are effective, reliable, time saver and applicable for solving the problems and can be proposed to solve other nonlinear problems. All the iterative process in this work implemented in MATHEMATICA®12. ABSTRAK: Kajian ini berkenaan tiga kaedah berulang boleh percaya diberikan dan dilaksanakan bagi menyelesaikan 1D, 2D dan 3D persamaan Fisher. Kaedah Daftardar-Jafari (DJM), kaedah Temimi-Ansari (TAM) dan kaedah pengecutan Banach (BCM) digunakan bagi mendapatkan penyelesaian numerik dan tepat bagi persamaan Fisher. Kaedah berulang boleh percaya di kategorikan dengan pelbagai faedah, seperti bebas daripada terbitan, mengatasi masalah-masalah yang timbul apabila sempadan polinomial bagi mengurus kata tak linear dalam kaedah penguraian Adomian (ADM), tidak memerlukan kiraan pekali Lagrange sebagai kaedah berulang Variasi (VIM) dan tidak perlu bagi membuat homotopi sebagaimana dalam kaedah gangguan Homotopi (HPM), atau mana-mana anggapan bagi mengurus kata tak linear. Penyelesaian yang didapati dalam bentuk urutan berulang di mana ianya boleh digunakan bagi mencapai penyelesaian tepat atau hampiran. Juga, teorem titik tetap dibentangkan bagi menaksir kaedah bentuk hampiran. Pelbagai contoh seperti masalah 1D, 2D dan 3D diselesaikan samada secara analitik atau numerik, di mana kecekapan penyelesaian numerik telah ditentu sahkan dengan menilai ralat mutlak dan baki ralat maksimum (MER) bagi menentukan ketepatan dan kecekapan kaedah yang dicadangkan. Dapatan kajian menunjukkan kaedah berulang yang dicadangkan adalah berkesan, boleh percaya, jimat masa dan boleh guna bagi menyelesaikan masalah dan boleh dicadangkan menyelesaikan masalah tak linear lain. Semua proses berulang dalam kerja ini menggunakan MATHEMATICA®12.

Effects of Sintering Process on the Properties of Ti3SiC2/Cu Composite

2012 ◽  
Vol 512-515 ◽  
pp. 377-381 ◽  
Author(s):  
Jin Rong Lu ◽  
Yang Zhou ◽  
Yong Zheng ◽  
Shi Bo Li ◽  
Zhen Ying Huang ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Vickers Hardness ◽  
Hot Pressing ◽  
Sintering Temperature ◽  
Sintering Process ◽  
Vacuum Sintering ◽  
New Type ◽  
Sintering Conditions ◽  
The Relationship ◽  
Better Than

In this paper, a new type of Ti3SiC2/Cu composites with the volume fractions of 30% Ti3SiC2 particle was prepared by hot pressing and vacuum sintering respectively. The effects of sintering temperature and holding time on the density, resistance and Vickers hardness of Cu-30vol%Ti3SiC2 composite were investigated. The results show that the mechanical properties of the composites prepared by hot pressing are better than that prepared by vacuum sintering. The relative densities of Cu-30vol% Ti3SiC2 composites are rather high in suitable sintering conditions. It achieved 100% for the composites prepared by hot pressing at 930°C for 2h, and 98.4% for the composites prepared by vacuum sintering at 1250°C for 1h. At the same time, the maximum Vickers hardness reached 1735MPa at 900°C by hot pressing. The resistance and Vickers hardness of the composites decreased with an increase in sintering temperature, whereas the density increased. Scanning electron microscope (SEM) and energy-dispersive spectroscopy (EDS) were used to observe the microstructure of the composites. The relationship between microstructure and mechanical properties was discussed.

Experimental Study of Air Distribution Characteristics in Room of Stratum Ventilation under Two Kinds of Air Change Times

2013 ◽  
Vol 409-410 ◽  
pp. 668-672
Author(s):  
Yong Mei Xu ◽  
Jian Tang ◽  
Jun Han ◽  
Chu Qin Lin
Keyword(s):  
Experimental Study ◽  
Thermal Comfort ◽  
Experimental Studies ◽  
Air Distribution ◽  
Distribution Characteristics ◽  
Breathing Zone ◽  
Wind Speeds ◽  
Pollutant Concentrations ◽  
New Type ◽  
Better Than

Aimed at a new type of ventilation - stratum ventilation, air distributions at a breathing-zone in a model office were measured under kinds of air changes, the measure parameters in the experimental studies included temperatures, wind speeds and pollutant concentrations, based on which the thermal comfort at a breathing-zone were studied. Experimental results show that, the temperature, pollutant concentration and wind speeds in a breathing-zone under 5 times air changes are better than those under 6 times air changes. The calculating results of PMV and PPD indicate that the thermal comfort at a breathing-zone under 5 times air changes is better. The experimental study is instructive for the development of the ventilation.

Highly efficient family of iterative methods for solving nonlinear models

2019 ◽  
Vol 346 ◽  
pp. 110-132 ◽  
Author(s):  
Ramandeep Behl ◽  
Í. Sarría ◽  
R. González ◽  
Á.A. Magreñán
Keyword(s):  
Iterative Methods ◽  
Nonlinear Models ◽  
Highly Efficient

Simulation and Experimental Investigation of a New Type of Combined Seal Structure

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Jin Li ◽  
Xiaoli Fu ◽  
Shenglin Yan
Keyword(s):  
Numerical Simulation ◽  
Labyrinth Seal ◽  
Internal Resistance ◽  
Leakage Rate ◽  
Geometric Parameters ◽  
Inlet Flow ◽  
New Type ◽  
Leakage Characteristics ◽  
Nozzle Structure ◽  
Better Than

Abstract Based on the study of leakage characteristics of labyrinth seal structure (LSS), a new type of combined seal structure (CSS) consisting of the labyrinth structure and the nozzle structure has been proposed. The sealing characteristics of CSS and LSS are compared by means of numerical simulation and experiments, and the effects of the internal resistance of the device, structural geometric parameters and other factors on the leakage characteristics of CSS are studied. The results illustrate the following conclusions: (a) When the inlet flow is 12 m3/h and the internal resistance of the device is 2000–4000 Pa, the leakage rate of CSS decreases by 30%–40% in comparison with that of LSS, which indicates that the performance of CSS is much better than that of LSS. (b) The leakage rate increases as the internal resistance of the device increases. When the internal resistance of the device increases from 2000 Pa to 8000 Pa, the leakage rate increases from 26% to 72%. (c) When the internal resistance of the device is constant, the larger the inlet flow, the smaller the leakage rate. (d) The choice of nozzle radius in structural geometric parameters is more important for the leakage rate than the tooth height and teeth numbers. When the nozzle radius decreases, ΔPAB (pressure difference between the labyrinth structure and the nozzle structure) and the leakage rate decrease accordingly.

SAS Nonlinear Models or Artificial Higher Order Neural Network Nonlinear Models?

2021 ◽  
pp. 174-217
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Data Analysis ◽  
Learning Algorithm ◽  
Nonlinear Models ◽  
Higher Order ◽  
Model Order ◽  
Higher Order Neural Networks ◽  
Parameter Values ◽  
Better Than

This chapter delivers general format of higher order neural networks (HONNs) for nonlinear data analysis and six different HONN models. Then, this chapter mathematically proves that HONN models could converge and have mean squared errors close to zero. Moreover, this chapter illustrates the learning algorithm with update formulas. HONN models are compared with SAS nonlinear (NLIN) models, and results show that HONN models are 3 to 12% better than SAS nonlinear models. Finally, this chapter shows how to use HONN models to find the best model, order, and coefficients without writing the regression expression, declaring parameter names, and supplying initial parameter values.

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