This paper focuses on addressing the linear quadratic (LQ) optimal control problem on an infinite time horizon for stochastic systems controlled by impulses. No constraint regarding the sign of the quadratic functional is applied. That is why our first concern is to find conditions which guarantee that the considered optimal control problem is well posed. Then, when the optimal control problem is well posed, it is natural to look for conditions which guarantee the attainability of the optimal control problem that is being evaluated. The main tool involved in the solution of the problems stated before is a backward jump matrix linear differential equation (BJMLDE) with a Riccati-type jumping operator. This is formulated using the matrix coefficients of the controlled system and the weight matrices of the performance criterion. We show that the well posedness of the optimal control problem under investigation is guaranteed by the existence of the maximal and bounded solution of the associated BJMLDE with a Riccati-type jumping operator. Further, we show that when the associated BJMLDE with a Riccati-type jumping operator has a maximal solution which satisfies a suitable sign condition, then the optimal control problem is attainable if and only if it has an optimal control in a state feedback form, or if and only if the maximal solution of the BJMLDE with a Riccati-type jumping operator is a stabilizing solution. In order to make the paper more self-contained, we present a set of conditions that correspond to the existence of the maximal solution of the BJMLDE satisfying the desired sign condition.
{"title":"The Linear Quadratic Optimal Control Problem for Stochastic Systems Controlled by Impulses","authors":"Vasile Dragan, Ioan-Lucian Popa","doi":"10.3390/sym16091170","DOIUrl":"https://doi.org/10.3390/sym16091170","url":null,"abstract":"This paper focuses on addressing the linear quadratic (LQ) optimal control problem on an infinite time horizon for stochastic systems controlled by impulses. No constraint regarding the sign of the quadratic functional is applied. That is why our first concern is to find conditions which guarantee that the considered optimal control problem is well posed. Then, when the optimal control problem is well posed, it is natural to look for conditions which guarantee the attainability of the optimal control problem that is being evaluated. The main tool involved in the solution of the problems stated before is a backward jump matrix linear differential equation (BJMLDE) with a Riccati-type jumping operator. This is formulated using the matrix coefficients of the controlled system and the weight matrices of the performance criterion. We show that the well posedness of the optimal control problem under investigation is guaranteed by the existence of the maximal and bounded solution of the associated BJMLDE with a Riccati-type jumping operator. Further, we show that when the associated BJMLDE with a Riccati-type jumping operator has a maximal solution which satisfies a suitable sign condition, then the optimal control problem is attainable if and only if it has an optimal control in a state feedback form, or if and only if the maximal solution of the BJMLDE with a Riccati-type jumping operator is a stabilizing solution. In order to make the paper more self-contained, we present a set of conditions that correspond to the existence of the maximal solution of the BJMLDE satisfying the desired sign condition.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nasser H. Sweilam, Seham M. Al-Mekhlafi, Waleed S. Abdel Kareem, Ghader Alqurishi
Two novel crossover models for breast cancer that incorporate Ψ-Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion and the crossover model for breast cancer that incorporates Atangana–Baleanu Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion are presented here, where we used a simple nonstandard kernel function Ψ(t) in the first model and a non-singular kernel in the second model. Moreover, we evaluated our models using actual statistics from Saudi Arabia. To ensure consistency with the physical model problem, the symmetry parameter ζ is introduced. We can obtain the fractal variable-order fractional Caputo and Caputo–Katugampola derivatives as special cases from the proposed Ψ-Caputo derivative. The crossover dynamics models define three alternative models: fractal variable-order fractional model, fractal fractional-order model, and variable-order fractional stochastic model over three-time intervals. The stability of the proposed model is analyzed. The Ψ-nonstandard finite-difference method is designed to solve fractal variable-order fractional and fractal fractional models, and the Toufik–Atangana method is used to solve the second crossover model with the non-singular kernel. Also, the nonstandard modified Euler–Maruyama method is used to study the variable-order fractional stochastic model. Numerous numerical tests and comparisons with real data were conducted to validate the methods’ efficacy and support the theoretical conclusions.
{"title":"Comparative Study of Crossover Mathematical Model of Breast Cancer Based on Ψ-Caputo Derivative and Mittag-Leffler Laws: Numerical Treatments","authors":"Nasser H. Sweilam, Seham M. Al-Mekhlafi, Waleed S. Abdel Kareem, Ghader Alqurishi","doi":"10.3390/sym16091172","DOIUrl":"https://doi.org/10.3390/sym16091172","url":null,"abstract":"Two novel crossover models for breast cancer that incorporate Ψ-Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion and the crossover model for breast cancer that incorporates Atangana–Baleanu Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion are presented here, where we used a simple nonstandard kernel function Ψ(t) in the first model and a non-singular kernel in the second model. Moreover, we evaluated our models using actual statistics from Saudi Arabia. To ensure consistency with the physical model problem, the symmetry parameter ζ is introduced. We can obtain the fractal variable-order fractional Caputo and Caputo–Katugampola derivatives as special cases from the proposed Ψ-Caputo derivative. The crossover dynamics models define three alternative models: fractal variable-order fractional model, fractal fractional-order model, and variable-order fractional stochastic model over three-time intervals. The stability of the proposed model is analyzed. The Ψ-nonstandard finite-difference method is designed to solve fractal variable-order fractional and fractal fractional models, and the Toufik–Atangana method is used to solve the second crossover model with the non-singular kernel. Also, the nonstandard modified Euler–Maruyama method is used to study the variable-order fractional stochastic model. Numerous numerical tests and comparisons with real data were conducted to validate the methods’ efficacy and support the theoretical conclusions.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Liping Zhou, Xu Liu, Ruiqing Tian, Wuqi Wang, Guowei Jin
The osprey optimization algorithm (OOA) is a metaheuristic algorithm with a simple framework, which is inspired by the hunting process of ospreys. To enhance its searching capabilities and overcome the drawbacks of susceptibility to local optima and slow convergence speed, this paper proposes a modified osprey optimization algorithm (MOOA) by integrating multiple advanced strategies, including a Lévy flight strategy, a Brownian motion strategy and an RFDB selection method. The Lévy flight strategy and Brownian motion strategy are used to enhance the algorithm’s exploration ability. The RFDB selection method is conducive to search for the global optimal solution, which is a symmetrical strategy. Two sets of benchmark functions from CEC2017 and CEC2022 are employed to evaluate the optimization performance of the proposed method. By comparing with eight other optimization algorithms, the experimental results show that the MOOA has significant improvements in solution accuracy, stability, and convergence speed. Moreover, the efficacy of the MOOA in tackling real-world optimization problems is demonstrated using five engineering optimization design problems. Therefore, the MOOA has the potential to solve real-world complex optimization problems more effectively.
{"title":"A Modified Osprey Optimization Algorithm for Solving Global Optimization and Engineering Optimization Design Problems","authors":"Liping Zhou, Xu Liu, Ruiqing Tian, Wuqi Wang, Guowei Jin","doi":"10.3390/sym16091173","DOIUrl":"https://doi.org/10.3390/sym16091173","url":null,"abstract":"The osprey optimization algorithm (OOA) is a metaheuristic algorithm with a simple framework, which is inspired by the hunting process of ospreys. To enhance its searching capabilities and overcome the drawbacks of susceptibility to local optima and slow convergence speed, this paper proposes a modified osprey optimization algorithm (MOOA) by integrating multiple advanced strategies, including a Lévy flight strategy, a Brownian motion strategy and an RFDB selection method. The Lévy flight strategy and Brownian motion strategy are used to enhance the algorithm’s exploration ability. The RFDB selection method is conducive to search for the global optimal solution, which is a symmetrical strategy. Two sets of benchmark functions from CEC2017 and CEC2022 are employed to evaluate the optimization performance of the proposed method. By comparing with eight other optimization algorithms, the experimental results show that the MOOA has significant improvements in solution accuracy, stability, and convergence speed. Moreover, the efficacy of the MOOA in tackling real-world optimization problems is demonstrated using five engineering optimization design problems. Therefore, the MOOA has the potential to solve real-world complex optimization problems more effectively.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Metal carbenes are widely acknowledged as a category of highly effective intermediates that facilitate otherwise inaccessible transformations. In recent decades, carbene chemistry has made considerable advances and has demonstrated remarkable abilities in the formation of diverse chemical bonds and the synthesis of structurally distinctive molecules. Nevertheless, the majority of research within this field has concentrated on α-carbon-substituted carbenes, with comparatively little investigation of carbenes that have been functionalized with a wider structural variety, particularly those that have been substituted with heteroatoms (e.g., O, N, P, S, Si, Ge, Sn and B). The objective of this review is to elucidate the advancements in enantioselective transfer reactions involving metal carbenes substituted with these elements, thereby highlighting their contribution to the expansion of the structural diversity and synthetic utility of carbenes in contemporary chemistry.
{"title":"Enantioselective Transfer Reactions of α-Heteroatom-Substituted Carbenes","authors":"Mingyao Huang, Wenjing Shi, Lu Li","doi":"10.3390/sym16091171","DOIUrl":"https://doi.org/10.3390/sym16091171","url":null,"abstract":"Metal carbenes are widely acknowledged as a category of highly effective intermediates that facilitate otherwise inaccessible transformations. In recent decades, carbene chemistry has made considerable advances and has demonstrated remarkable abilities in the formation of diverse chemical bonds and the synthesis of structurally distinctive molecules. Nevertheless, the majority of research within this field has concentrated on α-carbon-substituted carbenes, with comparatively little investigation of carbenes that have been functionalized with a wider structural variety, particularly those that have been substituted with heteroatoms (e.g., O, N, P, S, Si, Ge, Sn and B). The objective of this review is to elucidate the advancements in enantioselective transfer reactions involving metal carbenes substituted with these elements, thereby highlighting their contribution to the expansion of the structural diversity and synthetic utility of carbenes in contemporary chemistry.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maria Pia Lucia, Claudia Salera, Pierpaolo Zivi, Marco Iosa, Anna Pecchinenda
A visual stimulus that is divided in harmonic proportions is often judged as more pleasant than others. This is well known by artists that often used two main types of geometric harmonic patterns: symmetry and the golden ratio. Symmetry refers to the property of an object to have two similar halves, whereas the golden ratio consists of dividing an object in a major and a minor part so that their proportion is the same as that between the whole object and its major part. Here we investigated looking behaviour and explicit preferences for different regularities including symmetry and golden ratio. We selected four Mark Rothko’s paintings, a famous abstract expressionism artist, characterized by two main areas depicted by different colours: one symmetric (ratio between areas: 50–50%), one in golden ratio (38–62%), one in an intermediate ratio (46–54%), and one in a ratio exceeding the golden ratio (32–68%). Thirty-six healthy participants (24.75 ± 3.71 years old) completed three tasks: observation task (OT), pleasantness task (PT), and harmony task (HT). Findings for explicit ratings of pleasantness and harmony were very similar and were not significantly correlated with patterns of looking behaviour. Eye Dwell Time mainly depended on stimuli orientation (p < 0.001), but for the harmony task also by ratio and their interaction. Our results showed that the visual scanning behaviour of abstract arts primarily depends on the orientation of internal components, whereas their proportion is more important for the pleasantness and harmony explicit judgments.
{"title":"An Eye Tracking Study on Symmetry and Golden Ratio in Abstract Art","authors":"Maria Pia Lucia, Claudia Salera, Pierpaolo Zivi, Marco Iosa, Anna Pecchinenda","doi":"10.3390/sym16091168","DOIUrl":"https://doi.org/10.3390/sym16091168","url":null,"abstract":"A visual stimulus that is divided in harmonic proportions is often judged as more pleasant than others. This is well known by artists that often used two main types of geometric harmonic patterns: symmetry and the golden ratio. Symmetry refers to the property of an object to have two similar halves, whereas the golden ratio consists of dividing an object in a major and a minor part so that their proportion is the same as that between the whole object and its major part. Here we investigated looking behaviour and explicit preferences for different regularities including symmetry and golden ratio. We selected four Mark Rothko’s paintings, a famous abstract expressionism artist, characterized by two main areas depicted by different colours: one symmetric (ratio between areas: 50–50%), one in golden ratio (38–62%), one in an intermediate ratio (46–54%), and one in a ratio exceeding the golden ratio (32–68%). Thirty-six healthy participants (24.75 ± 3.71 years old) completed three tasks: observation task (OT), pleasantness task (PT), and harmony task (HT). Findings for explicit ratings of pleasantness and harmony were very similar and were not significantly correlated with patterns of looking behaviour. Eye Dwell Time mainly depended on stimuli orientation (p < 0.001), but for the harmony task also by ratio and their interaction. Our results showed that the visual scanning behaviour of abstract arts primarily depends on the orientation of internal components, whereas their proportion is more important for the pleasantness and harmony explicit judgments.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fuqiang Yang, Yue Zhang, Xuechen Zhao, Shengnan Pang
In the realm of artificial intelligence, knowledge graphs (KGs) serve as an essential structured framework, capturing intricate relationships between diverse entities and supporting a broad spectrum of AI applications. Despite their utility, the static characteristic of KGs poses challenges in dynamically evolving information landscapes. This has catalyzed the development of temporal knowledge graphs (TKGs), which introduce a temporal layer to KGs, facilitating the representation of knowledge progression through time. This study zeroes in on the critical task of TKG extrapolation, which is vital for forecasting future occurrences and offering foresight into emerging situations across a variety of fields. Most contemporary approaches to TKG extrapolation are predicated on the symmetrical encoder–decoder paradigm, wherein the processes of representation learning and reasoning are harmoniously intertwined. While the encoder often garners the most attention due to its role in capturing and encoding information, the pivotal role of the decoder, which is often overlooked, is essential for direct inference and the accurate projection of temporal dynamics. To this end, we present the Householder-transformation-based temporal knowledge graph extrapolation (HTKGE) method: a groundbreaking encoder–decoder framework that reimagines the decoder’s contribution to TKG extrapolation. Our approach spotlights an adaptive decoder propelled by Householder transformations, which engage dynamically with the temporal encoding from the encoder. This interaction fosters a nuanced comprehension of the TKG’s temporal trajectory. Our empirical evaluations across four benchmark TKG datasets substantiate HTKGE’s consistent efficacy in TKG extrapolation tasks.
{"title":"Unleashing the Power of Decoders: Temporal Knowledge Graph Extrapolation with Householder Transformation","authors":"Fuqiang Yang, Yue Zhang, Xuechen Zhao, Shengnan Pang","doi":"10.3390/sym16091166","DOIUrl":"https://doi.org/10.3390/sym16091166","url":null,"abstract":"In the realm of artificial intelligence, knowledge graphs (KGs) serve as an essential structured framework, capturing intricate relationships between diverse entities and supporting a broad spectrum of AI applications. Despite their utility, the static characteristic of KGs poses challenges in dynamically evolving information landscapes. This has catalyzed the development of temporal knowledge graphs (TKGs), which introduce a temporal layer to KGs, facilitating the representation of knowledge progression through time. This study zeroes in on the critical task of TKG extrapolation, which is vital for forecasting future occurrences and offering foresight into emerging situations across a variety of fields. Most contemporary approaches to TKG extrapolation are predicated on the symmetrical encoder–decoder paradigm, wherein the processes of representation learning and reasoning are harmoniously intertwined. While the encoder often garners the most attention due to its role in capturing and encoding information, the pivotal role of the decoder, which is often overlooked, is essential for direct inference and the accurate projection of temporal dynamics. To this end, we present the Householder-transformation-based temporal knowledge graph extrapolation (HTKGE) method: a groundbreaking encoder–decoder framework that reimagines the decoder’s contribution to TKG extrapolation. Our approach spotlights an adaptive decoder propelled by Householder transformations, which engage dynamically with the temporal encoding from the encoder. This interaction fosters a nuanced comprehension of the TKG’s temporal trajectory. Our empirical evaluations across four benchmark TKG datasets substantiate HTKGE’s consistent efficacy in TKG extrapolation tasks.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm’s effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems.
{"title":"The BiCG Algorithm for Solving the Minimal Frobenius Norm Solution of Generalized Sylvester Tensor Equation over the Quaternions","authors":"Mengyan Xie, Qing-Wen Wang, Yang Zhang","doi":"10.3390/sym16091167","DOIUrl":"https://doi.org/10.3390/sym16091167","url":null,"abstract":"In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm’s effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There is a prevailing consensus that most Computational Fluid Dynamics (CFD) frameworks can accurately predict global variables under laminar flow conditions within the Food and Drug Administration (FDA) benchmark nozzle geometry. However, variations in derived variables, such as strain rate and vorticity, may arise due to differences in numerical solvers and gradient evaluation methods, which can subsequently impact predictions related to blood damage and non-Newtonian flow behavior. To examine this, flow symmetry indices, vortex characteristics, and blood damage—were assessed using Newtonian and four non-Newtonian viscosity models with CFD codes Ansys Fluent and OpenFOAM on identical meshes. At Reynolds number (Re) 500, symmetry breakdown and complex vortex shapes were predicted with some non-Newtonian models in both OpenFOAM and Ansys Fluent, whereas these phenomena were not observed with the Newtonian model. This contradicted the expectation that employing a non-Newtonian model would delay the onset of turbulence. Similarly, at Re 2000, symmetry breakdown occurred sooner (following the sudden expansion section) with the non-Newtonian models in both Ansys Fluent and OpenFOAM. Vortex identification based on the Q-criterion resulted in distinctly different vortex shapes in Ansys Fluent and OpenFOAM. Blood damage assessments showed greater prediction variations among the non-Newtonian models at lower Reynolds numbers.
{"title":"Blood Damage Analysis within the FDA Benchmark Nozzle Geometry at Laminar Conditions: Prediction Sensitivities to Software and Non-Newtonian Viscosity Models","authors":"Gautham Krishnamoorthy, Nasim Gholizadeh","doi":"10.3390/sym16091165","DOIUrl":"https://doi.org/10.3390/sym16091165","url":null,"abstract":"There is a prevailing consensus that most Computational Fluid Dynamics (CFD) frameworks can accurately predict global variables under laminar flow conditions within the Food and Drug Administration (FDA) benchmark nozzle geometry. However, variations in derived variables, such as strain rate and vorticity, may arise due to differences in numerical solvers and gradient evaluation methods, which can subsequently impact predictions related to blood damage and non-Newtonian flow behavior. To examine this, flow symmetry indices, vortex characteristics, and blood damage—were assessed using Newtonian and four non-Newtonian viscosity models with CFD codes Ansys Fluent and OpenFOAM on identical meshes. At Reynolds number (Re) 500, symmetry breakdown and complex vortex shapes were predicted with some non-Newtonian models in both OpenFOAM and Ansys Fluent, whereas these phenomena were not observed with the Newtonian model. This contradicted the expectation that employing a non-Newtonian model would delay the onset of turbulence. Similarly, at Re 2000, symmetry breakdown occurred sooner (following the sudden expansion section) with the non-Newtonian models in both Ansys Fluent and OpenFOAM. Vortex identification based on the Q-criterion resulted in distinctly different vortex shapes in Ansys Fluent and OpenFOAM. Blood damage assessments showed greater prediction variations among the non-Newtonian models at lower Reynolds numbers.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alhanouf Ali Alhomaidhi, Sami Alabiad, Nawal A. Alsarori
Let u,v, and w be indeterminates over Fpm and let R=Fpm+uFpm+vFpm+wFpm, where p is a prime. Then, R is a ring of order p4m, and R≅Fpm[u,v,w]I with maximal ideal J=uFpm+vFpm+wFpm of order p3m and a residue field Fpm of order pm, where I is an appropriate ideal. In this article, the goal is to improve the understanding of linear codes over local non-chain rings. In particular, we investigate the symmetrized weight enumerators and generator matrices of linear codes of length N over R. In order to accomplish that, we first list all such rings up to the isomorphism for different values of the index of nilpotency l of J, 2≤l≤4. Furthermore, we fully describe the lattice of ideals of R and their orders. Next, for linear codes C over R, we compute the generator matrices and symmetrized weight enumerators, as shown by numerical examples.
设 u、v、w 是 Fpm 上的不定项，设 R=Fpm+uFpm+vFpm+wFpm ，其中 p 是素数。那么，R 是阶 p4m 的环，R≅Fpm[u,v,w]I 具有阶 p3m 的最大理想 J=uFpm+vFpm+wFpm 和阶 pm 的残差域 Fpm，其中 I 是一个适当的理想。本文旨在加深对局部非链环上线性编码的理解。为了实现这一目标，我们首先列出了在 J 的无幂指数 l 的不同值（2≤l≤4）下直到同构的所有此类环。此外，我们还完整地描述了 R 的理想晶格及其阶数。接下来，对于 R 上的线性编码 C，我们计算了生成矩阵和对称权枚举器，并通过数值示例进行了说明。
{"title":"Generator Matrices and Symmetrized Weight Enumerators of Linear Codes over Fpm + uFpm + vFpm + wFpm","authors":"Alhanouf Ali Alhomaidhi, Sami Alabiad, Nawal A. Alsarori","doi":"10.3390/sym16091169","DOIUrl":"https://doi.org/10.3390/sym16091169","url":null,"abstract":"Let u,v, and w be indeterminates over Fpm and let R=Fpm+uFpm+vFpm+wFpm, where p is a prime. Then, R is a ring of order p4m, and R≅Fpm[u,v,w]I with maximal ideal J=uFpm+vFpm+wFpm of order p3m and a residue field Fpm of order pm, where I is an appropriate ideal. In this article, the goal is to improve the understanding of linear codes over local non-chain rings. In particular, we investigate the symmetrized weight enumerators and generator matrices of linear codes of length N over R. In order to accomplish that, we first list all such rings up to the isomorphism for different values of the index of nilpotency l of J, 2≤l≤4. Furthermore, we fully describe the lattice of ideals of R and their orders. Next, for linear codes C over R, we compute the generator matrices and symmetrized weight enumerators, as shown by numerical examples.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Taher S. Hassan, Loredana Florentina Iambor, Sorin Mureşan, Khalid Alenzi, Ismoil Odinaev, Khudhayr A. Rashedi
This paper investigates second-order functional dynamic equations with mixed nonlinearities on an arbitrary unbounded above-time scale, T. We will use a unified time scale approach and the well-known Riccati technique to derive oscillation criteria of the Nehari-type for second-order dynamic equations. The findings demonstrate a significant improvement in the literature on dynamic equations. The symmetry is beneficial and influential in defining the right style of study for the qualitative behavior of solutions to dynamic equations. We include an example to demonstrate the significance of our results.
{"title":"Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations","authors":"Taher S. Hassan, Loredana Florentina Iambor, Sorin Mureşan, Khalid Alenzi, Ismoil Odinaev, Khudhayr A. Rashedi","doi":"10.3390/sym16091156","DOIUrl":"https://doi.org/10.3390/sym16091156","url":null,"abstract":"This paper investigates second-order functional dynamic equations with mixed nonlinearities on an arbitrary unbounded above-time scale, T. We will use a unified time scale approach and the well-known Riccati technique to derive oscillation criteria of the Nehari-type for second-order dynamic equations. The findings demonstrate a significant improvement in the literature on dynamic equations. The symmetry is beneficial and influential in defining the right style of study for the qualitative behavior of solutions to dynamic equations. We include an example to demonstrate the significance of our results.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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