Fahd Masood, Clemente Cesarano, Osama Moaaz, Sameh S. Askar, Ahmad M. Alshamrani, Hamdy El-Metwally
This paper delves into the analysis of oscillation characteristics within third-order quasilinear delay equations, focusing on the canonical case. Novel sufficient conditions are introduced, aimed at discerning the nature of solutions—whether they exhibit oscillatory behavior or converge to zero. By expanding the literature, this study enriches the existing knowledge landscape within this field. One of the foundations on which we rely in proving the results is the symmetry between the positive and negative solutions, so that we can, using this feature, obtain criteria that guarantee the oscillation of all solutions. The paper enhances comprehension through the provision of illustrative examples that effectively showcase the outcomes and implications of the established findings.
{"title":"Kneser-Type Oscillation Criteria for Half-Linear Delay Differential Equations of Third Order","authors":"Fahd Masood, Clemente Cesarano, Osama Moaaz, Sameh S. Askar, Ahmad M. Alshamrani, Hamdy El-Metwally","doi":"10.3390/sym15111994","DOIUrl":"https://doi.org/10.3390/sym15111994","url":null,"abstract":"This paper delves into the analysis of oscillation characteristics within third-order quasilinear delay equations, focusing on the canonical case. Novel sufficient conditions are introduced, aimed at discerning the nature of solutions—whether they exhibit oscillatory behavior or converge to zero. By expanding the literature, this study enriches the existing knowledge landscape within this field. One of the foundations on which we rely in proving the results is the symmetry between the positive and negative solutions, so that we can, using this feature, obtain criteria that guarantee the oscillation of all solutions. The paper enhances comprehension through the provision of illustrative examples that effectively showcase the outcomes and implications of the established findings.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136135856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The random output of renewable energy and the disorderly grid connection of electric vehicles (EV) will pose challenges to the safe and stable operation of the power system. In order to ensure the reliability and symmetry of the microgrid operation, this paper proposes a microgrid optimization scheduling strategy considering the access of EVs. Firstly, in order to reduce the impact of random access to EVs on power system operation, a schedulable model of an EV cluster is constructed based on the Minkowski sum. Then, based on the wavelet neural network (WNN), the renewable energy output is predicted to reduce the influence of its output fluctuation on the operation of the power system. Considering the operation constraints of each unit in the microgrid, the network active power loss and node voltage deviation are taken as the optimization objectives, and the established microgrid model is equivalently transformed via second-order cone relaxation to improve its solution efficiency. Based on network reconfiguration and flexible load participation in demand response, the economy and reliability of system operation are improved. Finally, the feasibility and effectiveness of the proposed method are verified based on the simulation examples.
{"title":"Research on Optimal Scheduling Strategy of Microgrid Considering Electric Vehicle Access","authors":"Zhimin Wu, Yang Zou, Feng Zheng, Ning Liang","doi":"10.3390/sym15111993","DOIUrl":"https://doi.org/10.3390/sym15111993","url":null,"abstract":"The random output of renewable energy and the disorderly grid connection of electric vehicles (EV) will pose challenges to the safe and stable operation of the power system. In order to ensure the reliability and symmetry of the microgrid operation, this paper proposes a microgrid optimization scheduling strategy considering the access of EVs. Firstly, in order to reduce the impact of random access to EVs on power system operation, a schedulable model of an EV cluster is constructed based on the Minkowski sum. Then, based on the wavelet neural network (WNN), the renewable energy output is predicted to reduce the influence of its output fluctuation on the operation of the power system. Considering the operation constraints of each unit in the microgrid, the network active power loss and node voltage deviation are taken as the optimization objectives, and the established microgrid model is equivalently transformed via second-order cone relaxation to improve its solution efficiency. Based on network reconfiguration and flexible load participation in demand response, the economy and reliability of system operation are improved. Finally, the feasibility and effectiveness of the proposed method are verified based on the simulation examples.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136232009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abdulrahman B. M. Alzahrani, Mohamed A. Abdoon, Mohamed Elbadri, Mohammed Berir, Diaa Eldin Elgezouli
This study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 method. Our primary goal is to develop effective methods for addressing symmetrical, chaotic systems. Using ABC-FD and NILM presents innovative approaches for comprehending and effectively handling intricate dynamics. The findings of this study have significant significance for addressing the occurrence of chaotic behavior in diverse scientific and engineering contexts. This research significantly contributes to fractional calculus and its various applications. The application of ABC-FD, which can identify chaotic behavior, makes our work stand out. This novel approach contributes to advancing research in nonlinear dynamics and fractional calculus. The present study not only offers a resolution to the problem of symmetric chaotic jerk systems but also presents a framework that may be applied to tackle analogous challenges in several domains. The techniques outlined in this paper facilitate the development and computational analysis of prospective fractional models, thereby contributing to the progress of scientific and engineering disciplines.
{"title":"A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods","authors":"Abdulrahman B. M. Alzahrani, Mohamed A. Abdoon, Mohamed Elbadri, Mohammed Berir, Diaa Eldin Elgezouli","doi":"10.3390/sym15111991","DOIUrl":"https://doi.org/10.3390/sym15111991","url":null,"abstract":"This study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 method. Our primary goal is to develop effective methods for addressing symmetrical, chaotic systems. Using ABC-FD and NILM presents innovative approaches for comprehending and effectively handling intricate dynamics. The findings of this study have significant significance for addressing the occurrence of chaotic behavior in diverse scientific and engineering contexts. This research significantly contributes to fractional calculus and its various applications. The application of ABC-FD, which can identify chaotic behavior, makes our work stand out. This novel approach contributes to advancing research in nonlinear dynamics and fractional calculus. The present study not only offers a resolution to the problem of symmetric chaotic jerk systems but also presents a framework that may be applied to tackle analogous challenges in several domains. The techniques outlined in this paper facilitate the development and computational analysis of prospective fractional models, thereby contributing to the progress of scientific and engineering disciplines.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136232138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider G to be a finite group and p to be a prime divisor of the order |G| in the group G. The main aim of this paper is to prove that the outcome in a recent paper of A. Laradji is true in the case of a p-constrained group. We observe that the generalization of the concept of Navarro’s vertex for an irreducible character in a p-constrained group G is generally undefined. We illustrate this with a suitable example. Let ϕ∈Irr(G) have a positive height, and let there be an anchor group Aϕ. We prove that if the normalizer NG(Aϕ) is p-constrained, then Op´(NG(Aϕ))≠{1G}, where Op´(NG(Aϕ)) is the maximal normal p´ subgroup of NG(Aϕ). We use character theoretic methods. In particular, Clifford theory is the main tool used to accomplish the results.
{"title":"On Height-Zero Characters in p-Constrained Groups","authors":"Manal H. Algreagri, Ahmad M. Alghamdi","doi":"10.3390/sym15111990","DOIUrl":"https://doi.org/10.3390/sym15111990","url":null,"abstract":"Consider G to be a finite group and p to be a prime divisor of the order |G| in the group G. The main aim of this paper is to prove that the outcome in a recent paper of A. Laradji is true in the case of a p-constrained group. We observe that the generalization of the concept of Navarro’s vertex for an irreducible character in a p-constrained group G is generally undefined. We illustrate this with a suitable example. Let ϕ∈Irr(G) have a positive height, and let there be an anchor group Aϕ. We prove that if the normalizer NG(Aϕ) is p-constrained, then Op´(NG(Aϕ))≠{1G}, where Op´(NG(Aϕ)) is the maximal normal p´ subgroup of NG(Aϕ). We use character theoretic methods. In particular, Clifford theory is the main tool used to accomplish the results.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136232258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field.
{"title":"Generation of Polynomial Automorphisms Appropriate for the Generalization of Fuzzy Connectives","authors":"Eleftherios Makariadis, Stefanos Makariadis, Avrilia Konguetsof, Basil Papadopoulos","doi":"10.3390/sym15111992","DOIUrl":"https://doi.org/10.3390/sym15111992","url":null,"abstract":"Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136232694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1
{"title":"Uniform Convexity in Variable Exponent Sobolev Spaces","authors":"Mostafa Bachar, Mohamed A. Khamsi, Osvaldo Méndez","doi":"10.3390/sym15111988","DOIUrl":"https://doi.org/10.3390/sym15111988","url":null,"abstract":"We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1<infx∈Ωp(x)≤supx∈Ωp(x)<∞ and W01,p(Ω) is uniformly convex.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space E3. Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with Bertrand curves as joint curvature lines. Consequently, the expansion to the ruled surface pencil is also designed. As demonstrations of our essential findings, we illustrate some models to emphasize the process.
{"title":"A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space","authors":"Sahar H. Nazra, Rashad A. Abdel-Baky","doi":"10.3390/sym15111986","DOIUrl":"https://doi.org/10.3390/sym15111986","url":null,"abstract":"The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space E3. Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with Bertrand curves as joint curvature lines. Consequently, the expansion to the ruled surface pencil is also designed. As demonstrations of our essential findings, we illustrate some models to emphasize the process.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study provides a scholarly examination of fundamental concepts within the field of group theory, specifically focusing on topics such as the wreath product and powerful p-groups. We examine the characteristics pertaining to the structure of the wreath product of cyclic p-groups, with a specific focus on the groups that are powerfully embedded within it. The primary discovery pertains to the construction of the powerful wreath product and the quasi-powerful wreath product. In this study, we establish that subgroups are powerful within the wreath product, specifically focusing on p-groups. The aforementioned outcome is derived from the assumption that p is a prime number and W is the standard wreath product of two nontrivial cyclic p-groups, denoted as G and H.
{"title":"The Wreath Product of Powerful p-Groups","authors":"Bashayer S. Alharbi, Ahmad M. Alghamdi","doi":"10.3390/sym15111987","DOIUrl":"https://doi.org/10.3390/sym15111987","url":null,"abstract":"This study provides a scholarly examination of fundamental concepts within the field of group theory, specifically focusing on topics such as the wreath product and powerful p-groups. We examine the characteristics pertaining to the structure of the wreath product of cyclic p-groups, with a specific focus on the groups that are powerfully embedded within it. The primary discovery pertains to the construction of the powerful wreath product and the quasi-powerful wreath product. In this study, we establish that subgroups are powerful within the wreath product, specifically focusing on p-groups. The aforementioned outcome is derived from the assumption that p is a prime number and W is the standard wreath product of two nontrivial cyclic p-groups, denoted as G and H.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we pose and solve, in tempered distribution spaces, an open problem proposed by Schrödinger in 1925. In particular, on the Schwartz distribution spaces, we define the linear continuous quantum operators associated with relativistic Hamiltonians of massive particles—particles with rest mass different from 0 and evolving in the four-dimensional Minkowski vector space M4. In other words, upon the tempered distribution state-space S′(M4,C), we have found the most natural way to introduce the free-particle relativistic Hamiltonian operator and its corresponding Schrödinger equation (together with its conjugate equation, standing for antiparticles). We have found the entire solution space of our relativistic linear continuous evolution equation by completely solving a division problem in tempered distribution space. We define the Hamiltonian (Schwartz diagonalizable) operator as the principal square root of a strictly positive, Schwartz diagonalizable second-order differential operator (linked with the “Klein–Gordon operator” on the tempered distribution space S4′). The principal square root of a Schwartz nondefective operator is defined in a straightforward way—following the heuristic fashion of some classic and greatly efficient quantum theoretical approach—in the paper itself.
{"title":"Relativistic Free Schrödinger Equation for Massive Particles in Schwartz Distribution Spaces","authors":"David Carfí","doi":"10.3390/sym15111984","DOIUrl":"https://doi.org/10.3390/sym15111984","url":null,"abstract":"In this work, we pose and solve, in tempered distribution spaces, an open problem proposed by Schrödinger in 1925. In particular, on the Schwartz distribution spaces, we define the linear continuous quantum operators associated with relativistic Hamiltonians of massive particles—particles with rest mass different from 0 and evolving in the four-dimensional Minkowski vector space M4. In other words, upon the tempered distribution state-space S′(M4,C), we have found the most natural way to introduce the free-particle relativistic Hamiltonian operator and its corresponding Schrödinger equation (together with its conjugate equation, standing for antiparticles). We have found the entire solution space of our relativistic linear continuous evolution equation by completely solving a division problem in tempered distribution space. We define the Hamiltonian (Schwartz diagonalizable) operator as the principal square root of a strictly positive, Schwartz diagonalizable second-order differential operator (linked with the “Klein–Gordon operator” on the tempered distribution space S4′). The principal square root of a Schwartz nondefective operator is defined in a straightforward way—following the heuristic fashion of some classic and greatly efficient quantum theoretical approach—in the paper itself.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By using Gronwall’s inequality and coincidence degree theory, the sufficient conditions of the globally exponential stability and existence are given for a Hebbian-type network with time-varying delays. The periodic behavior phenomenon is one of the hot topics in network systems research, from which we can discover the symmetric characteristics of certain neurons. The main theorems in the present paper are illustrated using a numerical example.
{"title":"Periodic Solution Problems for a Class of Hebbian-Type Networks with Time-Varying Delays","authors":"Mei Xu, Honghui Yin, Bo Du","doi":"10.3390/sym15111985","DOIUrl":"https://doi.org/10.3390/sym15111985","url":null,"abstract":"By using Gronwall’s inequality and coincidence degree theory, the sufficient conditions of the globally exponential stability and existence are given for a Hebbian-type network with time-varying delays. The periodic behavior phenomenon is one of the hot topics in network systems research, from which we can discover the symmetric characteristics of certain neurons. The main theorems in the present paper are illustrated using a numerical example.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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