Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.9
2.7
Journals
Symmetry
Special Issues
Symmetry and Approximation Methods II
share announcement

Symmetry and Approximation Methods II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 11906

Special Issue Editor

Dr. Simon Gluzman

E-Mail Website
Guest Editor
Materialica + Research Group, Bathurst St. 3000, Apt. 606, Toronto, ON M6B 3B4, Canada
Interests: time series; applied mathematics; computational physics; mathematical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Contributions are welcome on any subject related to Padè approximants with applications to realistic problems in addition to on any subject related to renormalization group applications in physics, finance, and geophysics.

Tentative contents (need more work!):

  1. Padè and two-point Padè—interpolation, extrapolation, and bounds;
  2. Euler-transformed, modified Padè approximants and corrected Padè approximants;
  3. Self-similarity and renormalization group as the source of roots, factors, and superexponential approximants;
  4. Nonperturbative conditions for accelerating convergence and optimization with minimal differences and sensitivity conditions;
  5. Factor and root approximants, examples of factors and roots, and interpolation as well as critical point calculations;
  6. Direct methods for critical index calculations: factors, D-Log Padè, D-Log roots, combined Log–Padè approximants, and test examples;
  7. Critical index as a control parameter and calculation with roots;
  8. Accelerated convergence of factors and D-Log Padè approximants;
  9. Additive and D-Log additive approximants for interpolation;
  10. Phase transitions, effective viscosity of suspensions, and the conductivity, elasticity, and permeability of landslides, earthquakes, and market crashes.

Dr. Simon Gluzman
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

Jump to: Review

16 pages, 7890 KiB  
Article
A Numerical Solution of Symmetric Angle Ply Plates Using Higher-Order Shear Deformation Theory
by Saira Javed
Symmetry 2023, 15(3), 767; https://doi.org/10.3390/sym15030767 - 21 Mar 2023
Viewed by 1001
Abstract
This research aims to provide the numerical analysis solution of symmetric angle ply plates using higher-order shear deformation theory (HSDT). The vibration of symmetric angle ply composite plates is analyzed using differential equations consisting of supplanting and turning functions. These supplanting and turning [...] Read more.
This research aims to provide the numerical analysis solution of symmetric angle ply plates using higher-order shear deformation theory (HSDT). The vibration of symmetric angle ply composite plates is analyzed using differential equations consisting of supplanting and turning functions. These supplanting and turning functions are numerically approximated through spline approximation. The obtained global eigenvalue problem is solved numerically to find the eigenfrequency parameter and a related eigenvector of spline coefficients. The plates of different constituent components are used to study the parametric effects of the plate’s aspect ratio, side-to-thickness ratio, assembling sequence, number of composite layers, and alignment of each layer on the frequency of the plate. The obtained results are validated by existing literature. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods II)
►▼ Show Figures

Figure 1

16 pages, 711 KiB  
Article
Regular and Intra-Regular Ternary Semirings in Terms of m-Polar Fuzzy Ideals
by Shahida Bashir, Mohammed M. Ali Al-Shamiri, Shahzeen Khalid and Rabia Mazhar
Symmetry 2023, 15(3), 591; https://doi.org/10.3390/sym15030591 - 24 Feb 2023
Viewed by 1019
Abstract
In practical applications, the basic fuzzy set is used via symmetric uncertainty variables. In the research field, it is comparatively rare to discuss two-fold uncertainty due to its complication. To deal with the multi-polar uncertainty in real life problems, m-polar (multi-polar) fuzzy [...] Read more.
In practical applications, the basic fuzzy set is used via symmetric uncertainty variables. In the research field, it is comparatively rare to discuss two-fold uncertainty due to its complication. To deal with the multi-polar uncertainty in real life problems, m-polar (multi-polar) fuzzy (m-PF) sets are put forward. The main objective of this paper is to explore the idea of m-PF sets, which is a generalization of bipolar fuzzy (BPF) sets, in ternary semirings. The major aspects and novel distinctions of this work are that it builds any multi-person, multi-period, multi-criteria, and complex hierarchical problems. The main focus of this study is to confine generalization of some important results of BPF sets to the results of m-PF sets. In this research, the notions of m-polar fuzzy ternary subsemiring (m-PFSS), m-polar fuzzy ideal (m-PFI), m-polar fuzzy generalized bi-ideal (m-PFGBI), m-polar fuzzy bi-ideal (m-PFBI), and m-polar fuzzy quasi-ideal (m-PFQI) in ternary semirings are introduced. Moreover, this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular ternary semiring in terms of these ideals. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods II)
►▼ Show Figures

Figure 1

11 pages, 265 KiB  
Article
Iterative Numerical Methods for a Fredholm–Hammerstein Integral Equation with Modified Argument
by Sanda Micula
Symmetry 2023, 15(1), 66; https://doi.org/10.3390/sym15010066 - 26 Dec 2022
Cited by 2 | Viewed by 1165
Abstract
Iterative processes are a powerful tool for providing numerical methods for integral equations of the second kind. Integral equations with symmetric kernels are extensively used to model problems, e.g., optimization, electronic and optic problems. We analyze iterative methods for Fredholm–Hammerstein integral equations with [...] Read more.
Iterative processes are a powerful tool for providing numerical methods for integral equations of the second kind. Integral equations with symmetric kernels are extensively used to model problems, e.g., optimization, electronic and optic problems. We analyze iterative methods for Fredholm–Hammerstein integral equations with modified argument. The approximation consists of two parts, a fixed point result and a quadrature formula. We derive a method that uses a Picard iterative process and the trapezium numerical integration formula, for which we prove convergence and give error estimates. Numerical experiments show the applicability of the method and the agreement with the theoretical results. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods II)
15 pages, 305 KiB  
Article
Iterative Borel Summation with Self-Similar Iterated Roots
by Simon Gluzman
Symmetry 2022, 14(10), 2094; https://doi.org/10.3390/sym14102094 - 08 Oct 2022
Cited by 3 | Viewed by 1638
Abstract
Borel summation is applied iteratively in conjunction with self-similar iterated roots. In general form, the iterative Borel summation is presented in the form of a multi-dimensional integral. It can be developed only numerically and is rarely used. Such a technique is developed in [...] Read more.
Borel summation is applied iteratively in conjunction with self-similar iterated roots. In general form, the iterative Borel summation is presented in the form of a multi-dimensional integral. It can be developed only numerically and is rarely used. Such a technique is developed in the current paper analytically and is shown to be more powerful than the original Borel summation. The self-similar nature of roots and their asymptotic scale invariance allow us to find critical indices and amplitudes directly and explicitly. The locations of poles remain the same with the uncontrolled self-similar Borel summation. The number of steps employed in the course of iterations is used as a continuous control parameter. To introduce control into the discrete version of the iterative Borel summation, instead of the exponential function, we use a stretched (compacted) exponential function. For the poles, considering inverse quantities is prescribed. The simplest scheme of the iterative Borel method, based on averaging over the one-step and two-step Borel iterations, works well when lower and upper bounds are established by making those steps. In the situations when only a one-sided bound is found, the iterative Borel summation with the number of iterations employed as the control works best by extrapolating beyond the bound. Several key examples from condensed matter physics are considered. Iterative application of Borel summation leads to an improvement compared with a conventional, single-step application of the Borel summation. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods II)
16 pages, 311 KiB  
Article
Regularized Solution of the Cauchy Problem in an Unbounded Domain
by Davron Aslonqulovich Juraev, Ali Shokri and Daniela Marian
Symmetry 2022, 14(8), 1682; https://doi.org/10.3390/sym14081682 - 12 Aug 2022
Cited by 6 | Viewed by 1038
Abstract
In this paper, using the construction of the Carleman matrix, we explicitly find a regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in a three-dimensional unbounded domain. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods II)

Review

Jump to: Research

42 pages, 658 KiB  
Review
Asymptotics and Summation of the Effective Properties of Suspensions, Simple Liquids and Composites
by Simon Gluzman
Symmetry 2022, 14(9), 1912; https://doi.org/10.3390/sym14091912 - 13 Sep 2022
Cited by 2 | Viewed by 5112
Abstract
We review the problem of summation for a very short truncation of a power series by means of special resummation techniques inspired by the field-theoretical renormalization group. Effective viscosity (EV) of active and passive suspensions is studied by means of a special algebraic [...] Read more.
We review the problem of summation for a very short truncation of a power series by means of special resummation techniques inspired by the field-theoretical renormalization group. Effective viscosity (EV) of active and passive suspensions is studied by means of a special algebraic renormalization approach applied to the first and second-order expansions in volume fractions of particles. EV of the 2D and 3D passive suspensions is analysed by means of various self-similar approximants such as iterated roots, exponential approximants, super-exponential approximants and root approximants. General formulae for all concentrations are derived. A brief introduction to the rheology of micro-swimmers is given. Microscopic expressions for the intrinsic viscosity of the active system of puller-like microswimmers are obtained. Special attention is given to the problem of the calculation of the critical indices and amplitudes of the EV and to the sedimentation rate in the vicinity of known critical points. Critical indices are calculated from the short truncation by means of minimal difference and minimal derivative conditions on the fixed points imposed directly on the critical properties. Accurate expressions are presented for the non-local diffusion coefficient of a simple liquid in the vicinity of a critical point. Extensions and corrections to the celebrated Kawasaki formula are discussed. We also discuss the effective conductivity for the classical analog of graphene and calculate the effective critical index for superconductivity dependent on the concentration of vacancies. Finally, we discuss the effective conductivity of a random 3D composite and calculate the superconductivity critical index of a random 3D composite. Full article
(This article belongs to the Special Issue Symmetry and Approximation Methods II)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop