Symmetry

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14 pages, 308 KB

Open AccessArticle

Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator

by Feng Xiong and Zhan Zhou

Symmetry 2021, 13(7), 1207; https://doi.org/10.3390/sym13071207 - 5 Jul 2021

Cited by 6 | Viewed by 2099

Abstract

In this paper, we consider a perturbed partial discrete Dirichlet problem with the

(p, q)

-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the [...] Read more.

In this paper, we consider a perturbed partial discrete Dirichlet problem with the

(p, q)

-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the origin on the nonlinear term f, we obtain the sufficient conditions for the existence of infinitely many small solutions. As far as we know, this is the study of perturbed partial discrete boundary value problems. Finally, the results are exemplified by an example. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

18 pages, 1091 KB

Open AccessArticle

Vibration Properties of a Concrete Structure with Symmetries Used in Civil Engineering

by Sorin Vlase, Marin Marin and Ovidiu Deaconu

Symmetry 2021, 13(4), 656; https://doi.org/10.3390/sym13040656 - 12 Apr 2021

Cited by 3 | Viewed by 3114

Abstract

The paper aims to study a concrete structure, currently used in civil engineering, which has certain symmetries. This type of problem is common in engineering practice, especially in civil engineering. There are many reasons why structures with identical elements or certain symmetries are [...] Read more.

The paper aims to study a concrete structure, currently used in civil engineering, which has certain symmetries. This type of problem is common in engineering practice, especially in civil engineering. There are many reasons why structures with identical elements or certain symmetries are used in industry, related to economic considerations, shortening the design time, for constructive, simplicity, cost or logistical reasons. There are many reasons why the presence of symmetries has benefits for designers, builders, and beneficiaries. In the end, the result of these benefits materializes through short execution times and reduced costs. The paper studies the eigenvalue and eigenmode properties of vibration for components of the constructions’ structure, often encountered in current practice. The identification of such properties allows the simplification and easing of the effort necessary for the dynamic analysis of such a structure. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

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20 pages, 2360 KB

Open AccessArticle

Evaluating the Impact of Different Symmetrical Models of Ambient Assisted Living Systems

by Wael Alosaimi, Md Tarique Jamal Ansari, Abdullah Alharbi, Hashem Alyami, Adil Hussain Seh, Abhishek Kumar Pandey, Alka Agrawal and Raees Ahmad Khan

Symmetry 2021, 13(3), 450; https://doi.org/10.3390/sym13030450 - 10 Mar 2021

Cited by 19 | Viewed by 3484

Abstract

In recent years, numerous attempts have been made to enhance the living standard for old-aged people. Ambient Assisted Living (AAL) is an evolving interdisciplinary field aimed at the exploitation of knowledge and communication technology in health and tele-monitoring systems to combat the impact [...] Read more.

In recent years, numerous attempts have been made to enhance the living standard for old-aged people. Ambient Assisted Living (AAL) is an evolving interdisciplinary field aimed at the exploitation of knowledge and communication technology in health and tele-monitoring systems to combat the impact of the growing aging population. AAL systems are designed for customized, responsive, and predictive requirements, requiring high performance of functionality to ensure interoperability, accessibility, security, and consistency. Standardization, continuity, and assistance of system development have become an urgent necessity to meet the increasing needs for sustainable systems. In this article, we examine and address the methods of the different AAL systems. In addition, we analyzed the acceptance criteria of the AAL framework intending to define and evaluate different AAL-based symmetrical models, leveraging performance characteristics under the integrated fuzzy environment. The main goal is to provide an understanding of the current situation of the AAL-oriented setups. Our vision is to investigate and evaluate the potential symmetrical models of AAL systems and frameworks for the implementation of effective new installations. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

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14 pages, 893 KB

Open AccessArticle

Dynamical Simulation of Effective Stem Cell Transplantation for Modulation of Microglia Responses in Stroke Treatment

by Awatif Jahman Alqarni, Azmin Sham Rambely and Ishak Hashim

Symmetry 2021, 13(3), 404; https://doi.org/10.3390/sym13030404 - 2 Mar 2021

Cited by 4 | Viewed by 2234

Abstract

Stem cell transplantation therapy may inhibit inflammation during stroke and increase the presence of healthy cells in the brain. The novelty of this work, is to introduce a new mathematical model of stem cells transplanted to treat stroke. This manuscript studies the stability [...] Read more.

Stem cell transplantation therapy may inhibit inflammation during stroke and increase the presence of healthy cells in the brain. The novelty of this work, is to introduce a new mathematical model of stem cells transplanted to treat stroke. This manuscript studies the stability of the mathematical model by using the current biological information on stem cell therapy as a possible treatment for inflammation from microglia during stroke. The model is proposed to represent the dynamics of various immune brain cells (resting microglia, pro-inflammation microglia, and anti-inflammation microglia), brain tissue damage and stem cells transplanted. This model is based on a set of five ordinary differential equations and explores the beneficial effects of stem cells transplanted at early stages of inflammation during stroke. The Runge–Kutta method is used to discuss the model analytically and solve it numerically. The results of our simulations are qualitatively consistent with those observed in experiments in vivo, suggesting that the transplanted stem cells could contribute to the increase in the rate of ant-inflammatory microglia and decrease the damage from pro-inflammatory microglia. It is found from the analysis and simulation results that stem cell transplantation can help stroke patients by modulation of the immune response during a stroke and decrease the damage on the brain. In conclusion, this approach may increase the contributions of stem cells transplanted during inflammation therapy in stroke and help to study various therapeutic strategies for stem cells to reduce stroke damage at the early stages. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

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10 pages, 267 KB

Open AccessArticle

Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

by Osama Moaaz, Amany Nabih, Hammad Alotaibi and Y. S. Hamed

Symmetry 2021, 13(2), 318; https://doi.org/10.3390/sym13020318 - 14 Feb 2021

Cited by 4 | Viewed by 2019

Abstract

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the [...] Read more.

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

12 pages, 5878 KB

Open AccessArticle

Generalized Attracting Horseshoe in the Rössler Attractor

by Karthik Murthy, Ian Jordan, Parth Sojitra, Aminur Rahman and Denis Blackmore

Symmetry 2021, 13(1), 30; https://doi.org/10.3390/sym13010030 - 27 Dec 2020

Cited by 1 | Viewed by 2777

Abstract

We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations—realizable by a rather simple electronic circuit—capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincaré section yielding the desired map is described, but [...] Read more.

We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations—realizable by a rather simple electronic circuit—capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincaré section yielding the desired map is described, but not pursued due to its complexity, which makes the construction of a circuit realization exceedingly difficult. Instead, the generalized attracting horseshoe and its trapping region is obtained by using a carefully chosen Poincaré map of the Rössler attractor. Novel numerical techniques are employed to iterate the map of the trapping region to approximate the chaotic strange attractor contained in the generalized attracting horseshoe, and an electronic circuit is constructed to produce the map. Several potential applications of the idea of a generalized attracting horseshoe and a physical electronic circuit realization are proposed. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

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13 pages, 253 KB

Open AccessArticle

Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems

by Longfei Lin, Yansheng Liu and Daliang Zhao

Symmetry 2020, 12(12), 1989; https://doi.org/10.3390/sym12121989 - 2 Dec 2020

Cited by 4 | Viewed by 2007

Abstract

This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The [...] Read more.

This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions

(u (t), v (t))

is that the solution

u (t)

is positive, and the other solution

v (t)

may change sign. Finally, two examples with continuous function

f_{1}

being positive and

f_{2}

being semipositone are worked out to illustrate the main results. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

13 pages, 791 KB

Open AccessArticle

Existence of Three Solutions for a Nonlinear Discrete Boundary Value Problem with ϕ_c-Laplacian

by Yanshan Chen and Zhan Zhou

Symmetry 2020, 12(11), 1839; https://doi.org/10.3390/sym12111839 - 6 Nov 2020

Cited by 10 | Viewed by 2206

Abstract

In this paper, based on critical point theory, we mainly focus on the multiplicity of nontrivial solutions for a nonlinear discrete Dirichlet boundary value problem involving the mean curvature operator. Without imposing the symmetry or oscillating behavior at infinity on the nonlinear term [...] Read more.

In this paper, based on critical point theory, we mainly focus on the multiplicity of nontrivial solutions for a nonlinear discrete Dirichlet boundary value problem involving the mean curvature operator. Without imposing the symmetry or oscillating behavior at infinity on the nonlinear term f, we respectively obtain the sufficient conditions for the existence of at least three non-trivial solutions and the existence of at least two non-trivial solutions under different assumptions on f. In addition, by using the maximum principle, we also deduce the existence of at least three positive solutions from our conclusion. As far as we know, our results are supplements to some well-known ones. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

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23 pages, 842 KB

Open AccessArticle

On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations

by Allaberen Ashyralyev, Evren Hınçal and Suleiman Ibrahim

Symmetry 2020, 12(6), 1033; https://doi.org/10.3390/sym12061033 - 19 Jun 2020

Cited by 4 | Viewed by 2925

Abstract

The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on [...] Read more.

The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on the Taylor’s decomposition method on three and two points. The theorem on the stability of the presented difference scheme is proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations are obtained. Finally, in order to ensure the coincidence between experimental and theoretical results and to clarify how efficient the proposed scheme is, some numerical experiments are tested. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

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