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Symmetry
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Mathematical Analysis, Analytic Number Theory and Applications
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Mathematical Analysis, Analytic Number Theory and Applications

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

Deadline for manuscript submissions: closed (1 August 2019) | Viewed by 12182

Special Issue Editors

Dr. Michael Th. Rassias

E-Mail Website
Guest Editor
1. Institute of Mathematics, University of Zurich, CH-8057, Zurich, Switzerland
2. Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Institutskiy per, d. 9, Russia
3. Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USA
Interests: mathematical analysis; analytic number theory; and, more specifically, in exponential/trigonometric sums, zeta functions, approximation theory, functional equations, and analytic inequalities, the distribution of prime numbers and the analytic investigation of elliptic curves
Prof. Andrei M. Raigorodskii

E-Mail
Guest Editor
1. Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Institutskiy per, d. 9, Russia
2. Buryat State University, Ulan-Ude Russia
3. Caucasus Mathematical Center, Adyghe State University, Maykop, Russia

Special Issue Information

Dear Colleagues,
    The Special Issue Mathematical Analysis, Analytic Number Theory, and Applications will publish research as well as selected survey papers devoted to the broad, very active, and vibrant domains of Pure Mathematical Analysis as well as Analytic Number Theory, along with their various applications. Emphasis will be given to the presentation of some of the most modern results in the corresponding areas as well as to highlight properties of symmetry whenever this is applicable. Subjects that will be studied within the scope of this Special Issue are fixed point theory; operator theory; topological methods for non-linear mappings; eigenvalue problems; calculus of variations; symmetry principles; analytic inequalities; functional equations in several variables; stability theory; as well as problems associated with trigonometric/exponential sums, zeta functions, the Riemann Hypothesis, etc.
    The papers published in this Issue will deepen our knowledge of various areas of mathematical research, and hopefully be useful to a wide audience, including graduate students seeking to broaden their research horizons, as well as research mathematicians who wish to have the latest results in corresponding subjects.

Dr. Michael Th. Rassias
Prof. Andrei M. Raigorodskii
Guest Editors

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.

Keywords

  • Fixed point theory
  • Tological methods
  • Operator theory
  • Eignevalue problems
  • Functional equations
  • Analytic inequalities
  • Stability theory
  • Trigonometric/exponential sums
  • Zeta function
  • Riemann Hypothesis
  • Goldbach conjecture

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  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

13 pages, 3482 KiB  
Article
Oblique Stagnation Point Flow of Nanofluids over Stretching/Shrinking Sheet with Cattaneo–Christov Heat Flux Model: Existence of Dual Solution
by Xiangling Li, Arif Ullah Khan, Muhammad Riaz Khan, Sohail Nadeem and Sami Ullah Khan
Symmetry 2019, 11(9), 1070; https://doi.org/10.3390/sym11091070 - 22 Aug 2019
Cited by 88 | Viewed by 3977
Abstract
In the present work we consider a numerical solution for laminar, incompressible, and steady oblique stagnation point flow of Cu − water nanofluid over a stretching/shrinking sheet with mass suction S . We make use of the Cattaneo–Christov heat flux model to develop [...] Read more.
In the present work we consider a numerical solution for laminar, incompressible, and steady oblique stagnation point flow of Cu − water nanofluid over a stretching/shrinking sheet with mass suction S . We make use of the Cattaneo–Christov heat flux model to develop the equation of energy and investigate the qualities of surface heat transfer. The governing flow and energy equations are modified into the ordinary differential equations by similarity method for reasonable change. The subsequent ordinary differential equations are illuminated numerically through the function bvp4c in MATLAB. The impact of different flow parameters for example thermal relaxation parameter, suction parameter, stretching/shrinking parameter, free stream parameter, and nanoparticles volume fraction on the skin friction coefficient, local Nusselt number, and streamlines are contemplated and exposed through graphs. It turns out that the lower branch solution for the skin friction coefficient becomes singular in shrinking area, although the upper branch solution is smooth in both stretching and shrinking domain. For oblique stagnation-point flow the streamlines pattern are not symmetric, and reversed phenomenon are detected close to the shrinking surface. Also, we observed that the free stream parameter changes the direction of the oncoming flow and controls the obliqueness of the flow. The existing work mostly includes heat and mass transfer as a mechanism for improving the heat transfer rate, which is the main objective of the authors. Full article
(This article belongs to the Special Issue Mathematical Analysis, Analytic Number Theory and Applications)
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17 pages, 282 KiB  
Article
Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products
by A. C. L. Ashton and A. S. Fokas
Symmetry 2019, 11(6), 754; https://doi.org/10.3390/sym11060754 - 4 Jun 2019
Cited by 2 | Viewed by 2471
Abstract
In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean [...] Read more.
In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelöf hypothesis. Some of the above relations motivate the need for analysing the large α behaviour of the modified Hurwitz zeta function ζ 1 ( s , α ) , s ∈ C , α ∈ ( 0 , ∞ ) , which is also presented here. Full article
(This article belongs to the Special Issue Mathematical Analysis, Analytic Number Theory and Applications)
14 pages, 1542 KiB  
Article
Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method
by Azhar Iqbal, Nur Nadiah Abd Hamid and Ahmad Izani Md. Ismail
Symmetry 2019, 11(4), 469; https://doi.org/10.3390/sym11040469 - 2 Apr 2019
Cited by 10 | Viewed by 3092
Abstract
This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and [...] Read more.
This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement. Full article
(This article belongs to the Special Issue Mathematical Analysis, Analytic Number Theory and Applications)
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12 pages, 250 KiB  
Article
An Operator Method for the Stability of Inhomogeneous Wave Equations
by Ginkyu Choi, Soon-Mo Jung and Jaiok Roh
Symmetry 2019, 11(3), 324; https://doi.org/10.3390/sym11030324 - 5 Mar 2019
Cited by 5 | Viewed by 2144
Abstract
In this paper, we will apply the operator method to prove the generalized Hyers-Ulam stability of the wave equation, [...] Read more.
In this paper, we will apply the operator method to prove the generalized Hyers-Ulam stability of the wave equation, u t t ( x , t ) − c 2 ▵ u ( x , t ) = f ( x , t ) , for a class of real-valued functions with continuous second partial derivatives. Finally, we will discuss the stability more explicitly by giving examples. Full article
(This article belongs to the Special Issue Mathematical Analysis, Analytic Number Theory and Applications)
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