The Convergence Region of m-Step Iterative Procedures

2021 ◽  
pp. 361-372
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Convergence Region ◽  
Iterative Procedures

scholarly journals A theory of giant vortices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Alexander A. Penin ◽  
Quinten Weller
Keyword(s):  
Asymptotic Expansion ◽  
Analytic Form ◽  
Scalar Fields ◽  
Winding Number ◽  
Asymptotic Results ◽  
Convergence Region ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Neutral Scalar ◽  
Vortex Solutions

Abstract We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number n. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-n corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.

Recognition of Moving Tracked and Wheeled Vehicles Based on Sound Analysis and Machine Learning Algorithms

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Jacek Jakubowski ◽  
Jerzy Jackowski
Keyword(s):  
Linear Prediction ◽  
Machine Learning Algorithms ◽  
Spectral Density Estimation ◽  
Power Spectral ◽  
Separable Problems ◽  
Characteristic Features ◽  
Iterative Procedures ◽  
Linear Prediction Coding ◽  
Signal Processing Methods ◽  
Wheeled Vehicles

The paper presents results of a preliminary study on verification of the possibility to establish simple methods to process acquired sound signals that were generated by a vehicle in motion; to determine its characteristic features for classification as a wheeled or tracked one. The analysis covered 220 signals acquired from real experiment and pre-processed with the use of power spectral density estimation (PSD) and linear prediction coding (LPC). The signal processing methods were used to generate features for which applicability in the classification process was assessed using a statistical method. The set of features was then optimised to reduce the dimensionality of data. Results of recognition obtained with the proposed non-iterative procedures for solving linearly separable problems were compared with results from standard methods, including SVM and k-NN. The developed features as well as selected methods of classification were proposed with respect to the possibility to implement them in low computational power computers for embedded applications.

Realistic hardening-to-softening transition effects of metals over the finite strain range up to failure

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zi-Han Xu ◽  
Lin Zhan ◽  
Si-Yu Wang ◽  
Hui-Feng Xi ◽  
Heng Xiao
Keyword(s):  
Finite Strain ◽  
Plastic Work ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Trial And Error ◽  
Content Type ◽  
Transition Effects ◽  
Iterative Procedures ◽  
First Time ◽  
Hardening And Softening

PurposeA new approach is proposed toward accurately matching any given realistic hardening and softening data from uniaxial tensile test up to failure and moreover, toward bypassing usual tedious implicit trial-and-error iterative procedures in identifying numerous unknown parameters.Design/methodology/approachFinite strain response features of metals with realistic hardening-to-softening transition effects up to eventual failure are studied for the first time based on the self-consistent elastoplastic J2-flow model with the logarithmic stress rate. As contrasted with usual approximate and incomplete treatments merely considering certain particular types of hardening effects such as power type hardening, here a novel and explicit approach is proposed to obtain a complete form of the plastic-work-dependent yield strength over the whole hardening and softening range.FindingsA new multi-axial evolution equation for both hardening and softening effects is established in an explicit form. Complete results for the purpose of model validation and prediction are presented for the finite strain responses of monotonic uniaxial stretching up to failure.Originality/valueNew finite strain elastoplastic equations are established with a new history-dependent variable equivalently in place of the usual plastic work. With these equations, a unified and accurate simulation of both gardening and softening effects up to failure is achieved for the first time in an explicit sense without involving usual tedious implicit trial-and-error iterative procedures.

Auditory-Somatosensory Multisensory Processing in Auditory Association Cortex: An fMRI Study

2002 ◽  
Vol 88 (1) ◽  
pp. 540-543 ◽  
Author(s):  
John J. Foxe ◽  
Glenn R. Wylie ◽  
Antigona Martinez ◽  
Charles E. Schroeder ◽  
Daniel C. Javitt ◽  
...  
Keyword(s):  
Auditory Cortex ◽  
Multisensory Integration ◽  
Multisensory Processing ◽  
Primary Auditory Cortex ◽  
Superior Temporal Gyrus ◽  
Brain Regions ◽  
Association Cortex ◽  
Convergence Region ◽  
Auditory Cortices ◽  
Auditory Association Cortex

Using high-field (3 Tesla) functional magnetic resonance imaging (fMRI), we demonstrate that auditory and somatosensory inputs converge in a subregion of human auditory cortex along the superior temporal gyrus. Further, simultaneous stimulation in both sensory modalities resulted in activity exceeding that predicted by summing the responses to the unisensory inputs, thereby showing multisensory integration in this convergence region. Recently, intracranial recordings in macaque monkeys have shown similar auditory-somatosensory convergence in a subregion of auditory cortex directly caudomedial to primary auditory cortex (area CM). The multisensory region identified in the present investigation may be the human homologue of CM. Our finding of auditory-somatosensory convergence in early auditory cortices contributes to mounting evidence for multisensory integration early in the cortical processing hierarchy, in brain regions that were previously assumed to be unisensory.

scholarly journals COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD

2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU
Keyword(s):  
Series Expansion ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Basis Functions ◽  
Analysis Method ◽  
Convergence Region ◽  
General Series ◽  
Homotopy Analysis ◽  
Series Expansion Method

A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

Biodegradability of wastewater – a method for COD-fractionation

2002 ◽  
Vol 45 (3) ◽  
pp. 25-34 ◽  
Author(s):  
J. Vollertsen ◽  
T. Hvitved-Jacobsen
Keyword(s):  
Oxygen Uptake ◽  
Differential Equations ◽  
Conceptual Model ◽  
Uptake Rate ◽  
Oxygen Uptake Rate ◽  
Microbial Transformations ◽  
Manual Method ◽  
Iterative Procedures

Characterization of wastewater for simulation of in-sewer transformations can be carried out by interpretation of oxygen uptake rate measurements in combination with a conceptual model of the microbial transformations involved. This interpretation can be done by iterative procedures by solving the differential equations constituting the model or by the application of a more “manual” method – the latter being the topic of this paper. Examples where different wastewaters are characterized illustrate the method.

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