journal: International Journal of Nonlinear Sciences and Numerical Simulation

Ceased

Published from March 1, 2000 to December 1, 2023

International Journal of Nonlinear Sciences and Numerical Simulation

ISSN: 2191-0294

Editor-in-chief: Björn Birnir

Editorial Board: Luiza Angheluta-Bauer, Xi Chen, Tom Chou, Rainer Grauer, Antonio Marzocchella, Govindan Rangarajan, Konstantina Trivisa, Rudi Weikard, Xu Yang

About this journal

THE JOURNAL IS CLOSED FOR SUBMISSIONS
The International Journal of Nonlinear Sciences and Numerical Simulation is closed for submissions. From 2024 onwards, the journal has been relaunched under the new title of Journal of Nonlinear, Complex and Data Science. This new chapter for the journal expands the scope to all subjects relevant to nonlinear, complex and data science and numerical simulations.

To submit to the new journal, please see the submission guidelines here.

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Publication Ethics and Malpractice Statement

Volume 24 Issue 8

December 2023

Publicly Available January 2, 2024

Frontmatter

Page range: i-ii

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Original Research Articles

January 13, 2022

Testing of logarithmic-law for the slip with friction boundary condition

Özgül İlhan, Niyazi Şahin

Page range: 2823-2837

Abstract

Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ $\bar{u}$ of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary layer theories to improve numerical boundary conditions for flow averages.

January 11, 2022

A new clique polynomial approach for fractional partial differential equations

Waleed Adel, Kumbinarasaiah Srinivasa

Page range: 2839-2851

Abstract

This paper generates a novel approach called the clique polynomial method (CPM) using the clique polynomials raised in graph theory and used for solving the fractional order PDE. The fractional derivative is defined in terms of the Caputo fractional sense and the fractional partial differential equations (FPDE) are converted into nonlinear algebraic equations and collocated with suitable grid points in the current approach. The convergence analysis for the proposed scheme is constructed and the technique proved to be uniformly convegant. We applied the method for solving four problems to justify the proposed technique. Tables and graphs reveal that this new approach yield better results. Some theorems are discussed with proof.

May 26, 2022

The modified Rusanov scheme for solving the phonon-Bose model

Kamel Mohamed, Mahmoud A. E. Abdelrahman

Page range: 2853-2864

Abstract

This paper considers the one-dimensional model of heat conduction in solids at low temperature, the so called phonon-Bose model. The nonlinear model consists of a conservation equation for the energy density e and the heat flux Q with ∣ Q ∣ < e . We present a simple and accurate class of finite volume schemes for numerical simulation of heat flow in arteries. This scheme consists of predictor and corrector steps, the predictor step contains a parameter of control of the numerical diffusion of the scheme, which modulate by using limiter theory and Riemann invariant, the corrector step recovers the balance conservation equation, the scheme can compute the numerical flux corresponding the real state of solution without relying on Riemann problem solvers and it can thus be turned to order 1 in the regions where the flow has a strong variation and to order 2 in the regions where the flow is regular. The numerical test cases demonstrate high resolution of the proposed finite volume scheme (modified Rusanov) and confirm its capability to provide accurate simulations for heat flow under flow regimes with strong shocks.

May 17, 2022

Delta-shock for a class of strictly hyperbolic systems of conservation laws

Shiwei Li

Page range: 2865-2876

Abstract

In this paper, a class of strictly hyperbolic systems of conservation laws which arises in connection with enhanced oil recovery is studied. The Riemann problem is solved analytically. The Riemann solutions with two kinds of different structures involving the delta-shock are obtained. For delta-shock, the generalized Rankine–Hugoniot relations and over-compressive delta-entropy condition are clarified. Further, the existence and uniqueness of delta-shock are established. The theoretical analysis is tested accurately by the numerical results.

May 17, 2022

The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations

Safoura Rezaei Aderyani, Reza Saadati, Donal O’Regan

Page range: 2877-2887

Abstract

In this paper, we apply the Cădariu–Radu method derived from the Diaz–Margolis theorem to investigate existence, uniqueness approximation of Ξ-Hilfer fractional differential equations, and Hypergeometric stability for both finite and infinite domains. An example is given to illustrate the main result for a fractional system.

May 20, 2022

Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method

Mahmoud Gaballah, Rehab M. El-Shiekh, Lanre Akinyemi, Hadi Rezazadeh

Page range: 2889-2897

Abstract

As Davey–Stewartson system is considered one of the most important models in optics, quantum physics, plasmas, and Bose–Einstein condensates. In this study, we have solved the Davey–Stewartson system using a modified Jacobi elliptic function methodology, and therefore many novel Jacobi elliptic wave function solutions were obtained, which degenerated to hypergeometric functions and periodic functions. The results obtained in this paper are novel in addition, contain other results achieved before in literatures. Moreover, some dynamic behavior for the periodic, kink type, and soliton wave propagation is demonstrated.

June 13, 2022

The simulation of two-dimensional plane problems using ordinary state-based peridynamics

Jingjing Zhao, Guangda Lu, Qing Zhang, Wenchao Du

Page range: 2899-2914

Abstract

The ordinary state-based peridynamics (OSB PD) model is an integral nonlocal continuum mechanics model. And the three-dimensional OSB PD model can deal with linear elastic solid problems well. But for plane problems, the calculation results of existing models have large deviations. In this paper, a set of OSB PD models for plane problems is established by theoretical derivation. First, through the strain energy density function equivalence of peridynamics and classical continuum mechanics, the equivalent coefficients of the plane strain and plane stress problems of OSB PD are deduced. Then, consider the cantilever beam deformation simulation under concentrated load. The simulation results show that the maximum displacements are in good agreement with the corresponding analytical solutions in all directions. Finally, in the simulation of the slab with a hole, the two cases of uniform displacement and uniform load are considered, respectively. The simulation results are consistent with the ANSYS analysis results, and the deviation is small, which verifies the validity of the model.

May 17, 2022

Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format

Cleophas Kweyu, Lihong Feng, Matthias Stein, Peter Benner

Page range: 2915-2935

Abstract

The Poisson–Boltzmann equation (PBE) is a fundamental implicit solvent continuum model for calculating the electrostatic potential of large ionic solvated biomolecules. However, its numerical solution encounters severe challenges arising from its strong singularity and nonlinearity. In (P. Benner, V. Khoromskaia, B. Khoromskij, C. Kweyu, and M. Stein, “Regularization of Poisson-Boltzmann type equations with singular source terms using the range-separated tensor format,” SIAM J. Sci. Comput. , vol. 43, no. 1, pp. A415–A445, 2021; C. Kweyu, V. Khoromskaia, B. Khoromskij, M. Stein, and P. Benner, “Solution decomposition for the nonlinear Poisson-Boltzmann equation using the range-separated tensor format,” arXiv:2109.14073, 2021), the effect of strong singularities was eliminated by applying the range-separated (RS) canonical tensor format (P. Benner, V. Khoromskaia, and B. N. Khoromskij, “Range-separated tensor format for many-particle modeling,” SIAM J. Sci. Comput. , vol. 40, no. 2, pp. A1034–A1062, 2018; B. N. Khoromskij, “Range-separated tensor representation of the discretized multidimensional Dirac delta and elliptic operator inverse,” J. Comput. Phys. , vol. 401, p. 108998, 2020) to construct a solution decomposition scheme for the PBE. The RS tensor format allows deriving a smooth approximation to the Dirac delta distribution in order to obtain a regularized PBE (RPBE) model. However, solving the RPBE is still computationally demanding due to its high dimension N $\mathcal{N}$ , where N $\mathcal{N}$ is always in the millions. In this study, we propose to apply the reduced basis method (RBM) and the (discrete) empirical interpolation method ((D)EIM) to the RPBE in order to construct a reduced order model (ROM) of low dimension N ≪ N $N\ll \mathcal{N}$ , whose solution accurately approximates the nonlinear RPBE. The long-range potential can be obtained by lifting the ROM solution back to the N $\mathcal{N}$ -space while the short-range potential is directly precomputed analytically, thanks to the RS tensor format. The sum of both provides the total electrostatic potential. The main computational benefit is the avoidance of computing the numerical approximation of the singular electrostatic potential. We demonstrate in the numerical experiments, the accuracy and efficacy of the reduced basis (RB) approximation to the nonlinear RPBE (NRPBE) solution and the corresponding computational savings over the classical nonlinear PBE (NPBE) as well as over the RBM being applied to the classical NPBE.

May 17, 2022

Simulation of the crystallization processes by population balance model using a linear separation method

Zehra Pinar Izgi

Page range: 2937-2944

Abstract

Crystallization problem is one of the popular problems in wide area of science. The first principles are not used to design a crystallizer in which complicated processes include nucleation, crystal growth, attrition and agglomeration of crystals. It is modeled by the population balance model, which is one of the important models of mathematical biology and engineering, is a nonlinear partial integro-differential equation and examines the exchange of particles and the production of new particles in a system of particles. For the crystallization problem, one-dimensional and multi-dimensional models are considered and semi-analytical solutions are obtained via the linear separation method.

October 11, 2022

PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria

Fatiha Bekraoui, Abdelkader Harrouz, Khayra Roummani, Ibrahim Boussaid, Amina Bekraoui

Page range: 2945-2961

Abstract

In this paper, a sliding mode controller is implemented to a permanent synchronous generator direct driven wind energy conversion system. The goal of this proposed work is to control the stator directly and quadrature axis currents to minimize the chattering phenomenon. To achieve this goal, we use two numerical techniques which are PSO (particle swarm optimization) and GWO (grey wolf optimization) algorithms to obtain gains parameters of the controller. The analysis of the recommended approach robustness and responsiveness of the system has been carried out under the real wind speed of the Adrar region (south of Algeria) and simulation results are tested under MATLAB/Simulink tool. The main result shows the effectiveness and the better performance of the PSO compared to the GWO.

October 5, 2022

Characteristics of internal flow of nozzle integrated with aircraft under transonic flow

Zijie Li, Hao Wang

Page range: 2963-2979

Abstract

To reveal how aircraft affects the internal flow of the ejector nozzle, we have constructed three model types in this article. These include the model of SR-71 aircraft, the model that only contains ejector nozzle with third auxiliary valve, and the model that integrates the previous two. The results showed that in the transonic regime ( M a = 1.2), the third auxiliary flow mainly stems from the boundary layer of the aircraft body. Indeed, a large-scale flow separation phenomenon near the third auxiliary door may require a more nuanced description. The mainstream flow is always in an overexpansion state and results in a Mach plate structure at the exit of the nozzle. However, after integration, the rates of the third auxiliary and the secondary flow are reduced by 18.15% and 5.26%, respectively. Meanwhile, the mainstream flow demonstrates higher overexpansion levels, the position of the Mach plate further downstream changes, and the thrust coefficient decreases by 1.75%. It is worthwhile noting that a strong pressure gradient occurs in the circumferential direction near the connecting structure, which induces lateral flow. This lateral flow breaks away from the wall under the reverse pressure gradient of the nozzle, thus forming three vortex pairs.

March 4, 2021

Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field

G. Nath, Arti Devi

Page range: 2981-2999

Abstract

The propagation of a cylindrical shock wave in rotating medium with azimuthal magnetic field under the action of monochromatic radiation using a method of group invariance is investigated. To derive similarity solutions as well as exact solutions, the group invariance technique is used. All classes of the solutions depending on the absorption coefficient are discussed by considering absorption coefficient to be variable or constant. A similarity solution is obtained, when the absorption coefficient is assumed to be variable. Two cases of solutions with a power law shock path are obtained by the different choices of arbitrary constants involving in the infinitesimal generators of the Lie group of transformations. To obtain the similarity solution in the case of the power law shock path, the density, magnetic field, axial and azimuthal velocity components are assumed to be varying and obeying power laws in the undisturbed medium. It is observed that with increase in the values of Alfven Mach number, adiabatic exponent and rotational parameter, shock strength decreases. The effects of variation of magnetic field strength, adiabatic exponent, rotational parameter and initial magnetic field variation index on the flow variables and on shock waves are analyzed graphically. Also, all classes of exact solutions are obtained by considering a constant absorption coefficient.

October 6, 2022

The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings

Mohammad Bavandi

Page range: 3001-3021

Abstract

Conventional earthquake-resistant systems, often experience inelastic behavior in a part of the structure during a large earthquake and eventually causing residual deformation and damage to the structure. Repairing these damages are unaffordable and often leads to structure destruction. Therefore, the use of structures with the ability to focus damage on interchangeable elements, which leads to reduced earthquake damage, is very important. Due to the importance of the performance of self-centering structures to reduce their damage against various earthquakes, in this study, the Repairability Index of Post-tensioned Self-Centering Frame for Near-Field earthquake (RIPSCF-N) has been developed. According to the 12 models of the studied building, a building that can be repaired, that the maximum rotation in its connection after the earthquake does not exceed the rotation of the immediate occupancy performance. Based on this, the output data of Incremental Dynamic Analysis (IDA) in OpenSees were drawn according to the connection of relative rotation and spectral acceleration. According to the predicted performance levels of Garlock for each acceleration level, the value of the connection opening is divided by the opening of the Design Basis Earthquake (DBE) level. The resulting curve shows the repairability index according to spectral acceleration, which if less than one, the repairability target is achieved. To evaluate the damage of angles, the Angle Failure Probability of Post-tensioned Self-Centering Frame for Near-Field earthquake (AFPPSCF-N) has been developed. This index equation is determined according to the fragility curve and the intensity of damage in each building.

January 17, 2022

Intelligent controller for maximum power extraction of wind generation systems using ANN

Driss Belkhiri, Lahoussine Elmahni, My Rachid El Moutawakil Alaoui

Page range: 3023-3038

Abstract

The generation of clean energy from wind has recently received huge attention. Thanks to the current advances of adaptive algorithms due to their benefits and flexibility. The paper introduces a new smart radial basis function (RBF) neural network to extract the optimal energy from wind for wind energy conversion systems. This scheme uses the electrical energy of the doubly fed induction-generator (DFIG) as an input in wind turbines drives a DFIG to acquire maximum energy from the available wind under uncertainties and fast-changing wind conditions. Thus, to prove the quality of our proposed intelligent scheme, a comparative study with conventional optimum power is applied to a wind turbine driving a class of 1.5 MW DFIG during the transient operation. Furthermore, the analysis and the interpretation of raw and processed real measured data using the process of linear interpolation through Matlab/Simulink illustrate the relevance and the performance of the sensorless controller for the overall wind turbine system. Briefly, the numerical simulation studies show that a good efficiency and improved tracking of the smart RBF-neural network controller when implemented online below the real wind speed despite the unknown parameters.

October 14, 2022

A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems

Cyril D. Enyi, Olaniyi S. Iyiola, Chinedu G. Ezea

Page range: 3039-3069

Abstract

Using a dynamical step size technique, a new self-adaptive CQ-algorithm is proposed in the presence of an inertial term to find the solution of convex feasibility problem and monotone inclusion problem involving a finite number of maximal monotone set valued operators. To do this, in certain Banach spaces, we construct an algorithm which converges to the fixed point of right Bregman strongly nonexpansive mappings and coincidentally solves the convex feasibility and monotone inclusion problems. Strong convergence of the algorithm is achieved without computation of the associated operator norms. Interesting numerical examples which illustrate the implementation and efficiency of our scheme are also given. Results obtained via this work improve and extend on previous results of its kind, in the literature.

October 27, 2022

Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions

Muthaiah Subramanian, Murugesan Manigandan, Akbar Zada, Thangaraj Nandha Gopal

Page range: 3071-3099

Abstract

In this paper, we analyses the existence and Hyers–Ulam stability of a coupled system of three sequential fractional differential equations with coupled integral boundary conditions. This manuscript can be categorized into three parts: The Leray–Schauder alternative is used to prove the existence of a solution in the first section. The second section emphasizes the analysis of uniqueness, which is based on the Banach fixed point theorem’s concept of contraction mapping, and the third section establishes the Hyers–Ulam stability results. In addition, we provide examples to demonstrate our findings.

October 14, 2022

A study on solvability of the fourth-order nonlinear boundary value problems

Haide Gou

Page range: 3101-3112

Abstract

The purpose of the paper is devoted to proving the solvability of the fourth order boundary value problem. Firstly, we build a maximum principle for the corresponding linear equation, by the use of this maximum principle, we develop a monotone iterative technique in the presence of lower and upper solutions to solve the nonlinear equation, secondly, the existence and uniqueness results for the problem is obtained. In addition, an example is presented to show the application of our main results.

October 19, 2022

Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays

Mehdi Pourseifi, Sara Rezaei

Page range: 3113-3132

Abstract

This paper presents a new bounded force feedback control law to improve transparency in nonlinear bilateral teleoperation systems in the presence of three problems in practical applications of teleoperation systems such as input saturation, asymmetric time varying communication delays with no restriction on their rates of variation and parametric uncertainties, simultaneously. The proposed controller is a nonlinear-proportional plus nonlinear damping (nP + nD) controller with the addition of a nonlinear adaptive term and nonlinear function of the environment force on the slave side and nonlinear function of the human force and force error on the master side. Using a novel Lyapunov–Krasovskii functional, the asymptotic stability and position and force tracking performance of the teleoperation system are established under specific conditions on the controller parameters, actuator saturation characteristics and maximum allowable time delay. The validity of the theoretical results is corroborated by the simulation results.

October 17, 2022

Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk

Ebrahem A. Algehyne, Fuad S. Alduais, Anwar Saeed, Abdullah Dawar, Muhammad Ramzan, Poom Kumam

Page range: 3133-3148

Abstract

In this article, the authors have presented the MHD hybrid nanoliquid flow comprised of CuO and Ag nanoparticles (nps) over a rotating disk under the effects of thermophoresis, Brownian motion, activation energy, heat source and chemical reaction. The flow is considered over a spinning disc with convective conditions. The proposed model is solved with the help of HAM. The convergence of the HAM is also shown in order to verify the convergence of the modeled problem. The effects of embedded parameters on the velocity, energy and mass profiles of the magnetohydrodynamic flow of hybrid nanoliquid are shown with the help of Figures. Also, the effects of embedded parameters on skin friction, heat and mass transfer rate are calculated with the help of Tables. The results showed that the velocity and energy profiles are augmented with the increasing solid volume fraction. The increasing magnetic parameter reduces both the radial and tangential velocities of the hybrid nanofluid flow. The increasing effects of heat source, thermophoresis and Brownian motion factors on energy profiles are found. The increasing influence of thermophoresis and activation energy factors on concentration profile of the hybrid nanofluid flow is found, while the increasing Brownian motion, chemical reaction and Schmidt number reduce the concentration profile.

October 17, 2022

Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium

Nepal Chandra Roy

Page range: 3149-3163

Abstract

A mathematical model is developed to analyze the free convection flow induced by catalytic surface reaction on a vertical wavy surface embedded in a non-Darcy porous medium. The governing equations are transformed using a generalized transformation which are valid near to and far from the leading edge. We then solve the resulting equations employing finite difference method. A comparison between the present solutions and the results of a past study is made which provides a good agreement. Numerical results reveal that the wall temperature and the surface concentration are enhanced for higher heat release parameter. An increase in the amplitude of the wavy surface and the reactant consumption parameter causes a decrease in the wall temperature and the surface concentration. Due to the increase of the reduced Darcy number the wall temperature substantially becomes higher whereas the surface concentration diminishes. However, a converse characteristic is observed in the case of the activation energy parameter. The momentum, thermal and concentration boundary layers are significantly increased for higher values of the reduced Darcy number and the consumption reactant parameter. Contrary to this, the larger heat release parameter reduces the thicknesses of the momentum, thermal and concentration boundary layers.

January 18, 2022

Carleman framework filtering of nonlinear noisy phase-locked loop system

Prashant G. Medewar, Shambhu N. Sharma, Hirenkumar G. Patel

Page range: 3165-3176

Abstract

In control and communications, the phase-locked loop (PLL) is regarded as the demodulator. Under the presence of small noise, the PLL system fails to accomplish the locking condition resulting in the stochastic phase difference. As a result of this, the PLL becomes a nontrivial nonlinear stochastic system. To circumvent the curse of dimensionality and nonlinearity, we exploit the method of linearization in the Carleman framework in combination with the finite closure for the stochastic system considered here. We show that the Carleman linearization has proven useful to preserve the nonlinearity via bilinearization. The Carleman setup of the nonlinear stochastic differential system has the Markov property and the terms are manageable. Then, we filter the states of the PLL using the filtering theory of the homogeneous Markov process. Finally, the numerical simulations reveal the superiority of the proposed filtering in Carleman setting in contrasts with the celebrated extended Kalman filtering framework.

Corrigendum

Publicly Available December 28, 2023

Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon

Alibek Issakhov, Berizat Omarov, Albina Mashenkova, Aizhan Abylkassymova

Page range: 3177-3177

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Volume 24 (2023)

Volume 23 (2022)

Volume 22 (2021)

Volume 21 (2020)

Volume 20 (2019)

Volume 19 (2018)

Volume 18 (2017)

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Volume 16 (2015)

Volume 15 (2014)

Volume 14 (2013)

Volume 13 (2012)

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Editorial

Editor-in-Chief

Prof. Björn Birnir
Department of Mathematics
University of California
Santa Barbara, CA 93106, USA
E-mail: ijnsns.editorial@degruyter.com
Home Page: http://www.math.ucsb.edu/~birnir

Associate Editors

Prof. Luiza Angheluta-Bauer
University of Oslo, Norway
Department of Physics, Condensed Matter Physics (CONDPHYS)
Postboks 1048
Blindern 0316 Oslo, Norway
E-mail: luiza.angheluta-bauer@fys.uio.no

Prof. Jan Awrejcewicz
Lodz University of Technology
Department of Automation, Biomechanics and Mechatronics
1/15 Stefanowski St.
90-924 Łódź, Poland
E-mail: awrejcew@p.lodz.pl

Prof. Ana Carpio
Universidad Complutense de Madrid
Departamento de Matematica Aplicada
Plaza de Ciencias 3
Madrid 28040, Spain

Dr. Liping Chen
Hefei University of Technology
Department of Automation
No.193, Tunxi Road, Hefei, Anhui, 230009,
P.R. China
Email: lip_chenhut@126.com, lip_chen@hfut.edu.cn

Ass. Prof. Alexandra Galhano
Faculdade de Ciências Naturais, Engenharias e Tecnologias
Universidade Lusófona do Porto
Rua Augusto Rosa 24
4000-098 Porto, Portugal
E-mail: amf@isep.ipp.pt

Prof. Xi Chen
Texas Tech, Mechanical Engineering
7105 Zoar Avenue, Lubbock
Texas, 79404, USA
E-mail: chenxi97@outlook.com

Prof. Elżbieta Jarzębowska
Politechnika Warszawska
Department of Mechanics and Control
24 Nowowiejska St.
00-665 Warsaw, Poland
E-mail:elajarz@meil.pw.edu.pl

Prof. Antonio Marzocchella
University of Naples UNINA
Naples, Italy
E-mail: marzocch@unina.it

Prof. Patrizia Pucci
University of Perugia - Italy
Department of Mathematics and Computer Science
E-mail: patrizia.pucci@unipg.it
Homepage: http://www.dmi.unipg.it/pucci/

Prof. Tobias Schäfer
Department of Mathematics
College of Staten Island, City University of New York
Staten Island, NY, USA
E-mail: tobias@math.csi.cuny.edu

Dr. Yuri Sobral
Universidade de Brasilia
Departamento de Matemática
Campus Universitário Darcy Ribeiro
Brasilia, DF, 70910-900, Brasil
E-mail: Y.D.Sobral@mat.unb.br

Prof. Knut Solna
University of California
Department of Mathematics
University of California, Irvine
340 Rowland Hall, Irvine, 92697-3875, California, USA
E-mail: ksolna@math.uci.edu

Prof. Xu Yang
University of California
Department of Mathematics
Santa Barbara, CA 93106, USA
E-mail: xuyang@math.ucsb.edu

Dr. Mahmoud A. Zaky
National Research Centre
Department of Applied Mathematics
Dokki, Cairo 12622, Egypt
Email: ma.zaky@yahoo.com

(Deutsch)

Online ISSN: 2191-0294
Type: Journal
Language: English
Publisher: De Gruyter
First published: March 1, 2000
Last published: December 1, 2023
Publication Frequency: 8 Issues per Year