Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.12
C. Fetecău
The problem of exact solutions for isothermal motions of nonNewtonian fluids is of interest yet and a new way to get them is welcome. In this work an important observation regarding the governing equations corresponding to some isothermal hydromagnetic unidirectional motions of incompressible Maxwell fluids is brought to light. It allows us to easily determine exact solutions for motions with shear stress or velocity on the boundary when similar solutions for motions with velocity, respectively shear stress on the boundary are know. To exemplify, the solutions of some hydromagnetic motion problems of Maxwell fluids with velocity on the boundary are used to generate exact steady state solutions for similar motions of same fluids with shear stress on the boundary. These solutions are very important for the experimental researchers who want to know the required time to reach the steady state.
{"title":"ON AN IMPORTANT OBSERVATION REGARDING SOME HYDROMAGNETIC MOTIONS OF MAXWELL FLUIDS AND ITS APPLICATIONS*","authors":"C. Fetecău","doi":"10.56082/annalsarscimath.2023.1-2.12","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.12","url":null,"abstract":"The problem of exact solutions for isothermal motions of nonNewtonian fluids is of interest yet and a new way to get them is welcome. In this work an important observation regarding the governing equations corresponding to some isothermal hydromagnetic unidirectional motions of incompressible Maxwell fluids is brought to light. It allows us to easily determine exact solutions for motions with shear stress or velocity on the boundary when similar solutions for motions with velocity, respectively shear stress on the boundary are know. To exemplify, the solutions of some hydromagnetic motion problems of Maxwell fluids with velocity on the boundary are used to generate exact steady state solutions for similar motions of same fluids with shear stress on the boundary. These solutions are very important for the experimental researchers who want to know the required time to reach the steady state.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009553","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.86
S. G. Galt
Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas, like Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorem based on Lagrange interpolation on arbitrary p + 1 simple distinct knots.
{"title":"VORONOVSKAYA-TYPE THEOREM FOR POSITIVE LINEAR OPERATORS BASED ON LAGRANGE INTERPOLATION","authors":"S. G. Galt","doi":"10.56082/annalsarscimath.2023.1-2.86","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.86","url":null,"abstract":"Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas, like Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorem based on Lagrange interpolation on arbitrary p + 1 simple distinct knots.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009892","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.229
G.H. Nedzhibov
In this study, we provide an alternative approach for computing the dynamic mode decomposition (DMD) in real-time for streaming datasets. It is a low-storage method that updates the DMD approximation of a given dynamic as new data becomes available. Unlike the standard online DMD method, which is applicable only to overconstrained and full-rank datasets, the new method is applicable for both overconstrained and underconstrained datasets. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations and is entirely data-driven. Several numerical examples are presented to demonstrate the performance of the method.
{"title":"ONLINE DYNAMIC MODE DECOMPOSITION: AN ALTERNATIVE APPROACH FOR LOW RANK DATASETS","authors":"G.H. Nedzhibov","doi":"10.56082/annalsarscimath.2023.1-2.229","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.229","url":null,"abstract":"In this study, we provide an alternative approach for computing the dynamic mode decomposition (DMD) in real-time for streaming datasets. It is a low-storage method that updates the DMD approximation of a given dynamic as new data becomes available. Unlike the standard online DMD method, which is applicable only to overconstrained and full-rank datasets, the new method is applicable for both overconstrained and underconstrained datasets. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations and is entirely data-driven. Several numerical examples are presented to demonstrate the performance of the method.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009908","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.94
M. Blrsan
We consider the linearized theory of 6-parameter elastic shells with general anisotropy. We derive the equilibrium equations from the virtual power statement and formulate the corresponding variational problem in the suitable functional framework. Then, using a Korn-type inequality for the linearized strain measures we prove the existence and uniqueness of weak solutions. Finally, we show that our general theorem can be applied to obtain existence results in the case of isotropic elastic shells. We illustrate this procedure by investigating three different linear shell models established previously in the literature, namely the simplified isotropic 6-parameter shell, the Cosserat isotropic model, and the higher-order 6-parameter Cosserat model.
{"title":"ON THE EQUILIBRIUM EQUATIONS OF LINEAR 6-PARAMETER ELASTIC SHELLS","authors":"M. Blrsan","doi":"10.56082/annalsarscimath.2023.1-2.94","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.94","url":null,"abstract":"We consider the linearized theory of 6-parameter elastic shells with general anisotropy. We derive the equilibrium equations from the virtual power statement and formulate the corresponding variational problem in the suitable functional framework. Then, using a Korn-type inequality for the linearized strain measures we prove the existence and uniqueness of weak solutions. Finally, we show that our general theorem can be applied to obtain existence results in the case of isotropic elastic shells. We illustrate this procedure by investigating three different linear shell models established previously in the literature, namely the simplified isotropic 6-parameter shell, the Cosserat isotropic model, and the higher-order 6-parameter Cosserat model.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009532","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.250
L. Betzt
This paper addresses optimal control problems governed by historydependent EVIs with viscosity. One of the prominent properties of the state system is its nonsmooth nature, so that the application of standard adjoint calculus is excluded. We extend previous results by showing that history-dependent EVIs with viscosity can be formulated as nonsmooth ODEs in Hilbert space in a general setting. The Hadamard directional differentiability of the solution map is then investigated. This allows us to establish strong stationary conditions for two different viscous damage models with fatigue.
{"title":"STRONG STATIONARITY FOR THE CONTROL OF VISCOUS HISTORY-DEPENDENT EVOLUTIONARY VIS ARISING IN APPLICATIONS","authors":"L. Betzt","doi":"10.56082/annalsarscimath.2023.1-2.250","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.250","url":null,"abstract":"This paper addresses optimal control problems governed by historydependent EVIs with viscosity. One of the prominent properties of the state system is its nonsmooth nature, so that the application of standard adjoint calculus is excluded. We extend previous results by showing that history-dependent EVIs with viscosity can be formulated as nonsmooth ODEs in Hilbert space in a general setting. The Hadamard directional differentiability of the solution map is then investigated. This allows us to establish strong stationary conditions for two different viscous damage models with fatigue.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009545","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.205
I Ivanov, N. Baeva
We consider different algorithms with linear rate of convergence for computing the minimal nonnegative solution of M-matrix algebraic Riccati equation. The performance of the considered algorithms are illustrated on numerical examples.
{"title":"ALGORITHMS FOR THE RICCATI EQUATION WITH A NONSINGULAR M-MATRIX","authors":"I Ivanov, N. Baeva","doi":"10.56082/annalsarscimath.2023.1-2.205","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.205","url":null,"abstract":"We consider different algorithms with linear rate of convergence for computing the minimal nonnegative solution of M-matrix algebraic Riccati equation. The performance of the considered algorithms are illustrated on numerical examples.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009903","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.73
L. Palese
This paper continues a series of studies providing stability crite¬ria for quasigeostrophic forced zonal flows in in the presence of lateral diffusion and bottom dissipation of the vertical vorticity. We study the Lyapunov stability of a stationary and longitude independent ba¬sic flow, obtaining linear and nonlinear stability criteria expressed in terms of the maximum shear of the basic flow and/or its meridional derivative, extending some previous results.
{"title":"ON THE NONLINEAR STABILITY FOR QUASI-GEOSTROPHIC FORCED ZONAL FLOWS","authors":"L. Palese","doi":"10.56082/annalsarscimath.2023.1-2.73","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.73","url":null,"abstract":"This paper continues a series of studies providing stability crite¬ria for quasigeostrophic forced zonal flows in in the presence of lateral diffusion and bottom dissipation of the vertical vorticity. We study the Lyapunov stability of a stationary and longitude independent ba¬sic flow, obtaining linear and nonlinear stability criteria expressed in terms of the maximum shear of the basic flow and/or its meridional derivative, extending some previous results.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010111","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.154
A. Cernea
We establish several fractional variational inclusions for solutions of a nonconvex fractional differential inclusion involving Caputo-Fabrizio fractional derivative.
{"title":"SEVERAL VARIATIONAL INCLUSIONS FOR A FRACTIONAL DIFFERENTIAL INCLUSION OF CAPUTO-FABRIZIO TYPE","authors":"A. Cernea","doi":"10.56082/annalsarscimath.2023.1-2.154","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.154","url":null,"abstract":"We establish several fractional variational inclusions for solutions of a nonconvex fractional differential inclusion involving Caputo-Fabrizio fractional derivative.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009529","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.554
S. Temir
In this paper, we study multi-valued generalized anonexpansive mappings in uniformly convex Banach spaces. We introduce a new multi-valued iterative process and prove some weak and strong convergence results in uniformly convex Banach space. We also study the stability of this iteration process. Further, we provide a numerical example of the multi-valued generalized a-nonexpansive mapping. Finally, the convergence of this iteration process to the fixed point for multi-valued generalized a-nonexpansive mapping is discussed on this numerical example.
{"title":"APPROXIMATING OF FIXED POINTS FOR MULTI-VALUED GENERALIZED a-NONEXPANSIVE MAPPINGS IN BANACH SPACES","authors":"S. Temir","doi":"10.56082/annalsarscimath.2023.1-2.554","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.554","url":null,"abstract":"In this paper, we study multi-valued generalized anonexpansive mappings in uniformly convex Banach spaces. We introduce a new multi-valued iterative process and prove some weak and strong convergence results in uniformly convex Banach space. We also study the stability of this iteration process. Further, we provide a numerical example of the multi-valued generalized a-nonexpansive mapping. Finally, the convergence of this iteration process to the fixed point for multi-valued generalized a-nonexpansive mapping is discussed on this numerical example.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009543","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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.491
V. Rasvan
The paper originates from the early ideas of A. D. Myshkis and his co-workers and of K. L. Cooke and his co-worker. These ideas send to a one-to-one correspondence between lossless and/or distortionless propagation described by nonstandard boundary value problems and a system of coupled differential and difference equations with deviated argument. In this way any property obtained for one mathematical object is automatically projected back on the other one. This approach is considered here for certain engineering applications. The common feature of these applications is the critical stability of the difference operator associated with the system with deviated argument obtained for each of the aforementioned applications. In fact the associated systems are of neutral type and, according to the assumption of Hale, only strong stability of the difference operator ensures robust asymptotic stability with respect to the delays. If the difference operator is in the critical case, the stability becomes fragile with respect to the delays. Based on some old results in the field, a conjecture concerning the (quasi)-critical modes of the system is stated; also a connection with the so called dissipative boundary conditions is suggested.
这篇论文来源于A. D. Myshkis和他的同事以及K. L. Cooke和他的同事的早期观点。这些思想将非标准边值问题描述的无损和/或无失真传播与具有偏差参数的耦合微分和差分方程系统之间的一一对应。通过这种方式，从一个数学对象获得的任何属性都会自动投影到另一个数学对象上。这种方法在这里被考虑用于某些工程应用。这些应用程序的共同特征是与上述每个应用程序获得的具有偏差参数的系统相关的差分算子的临界稳定性。事实上，相关系统是中立型的，根据Hale的假设，只有差分算子的强稳定性才能保证相对于时滞的鲁棒渐近稳定。当差分算子处于临界情况时，稳定性相对于时滞变得脆弱。在此基础上，提出了系统的准临界模态的一个猜想;还提出了与所谓耗散边界条件的联系。
{"title":"FROM PROPAGATION SYSTEMS TO TIME DELAYS AND BACK. CRITICAL CASES","authors":"V. Rasvan","doi":"10.56082/annalsarscimath.2023.1-2.491","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.491","url":null,"abstract":"The paper originates from the early ideas of A. D. Myshkis and his co-workers and of K. L. Cooke and his co-worker. These ideas send to a one-to-one correspondence between lossless and/or distortionless propagation described by nonstandard boundary value problems and a system of coupled differential and difference equations with deviated argument. In this way any property obtained for one mathematical object is automatically projected back on the other one. This approach is considered here for certain engineering applications. The common feature of these applications is the critical stability of the difference operator associated with the system with deviated argument obtained for each of the aforementioned applications. In fact the associated systems are of neutral type and, according to the assumption of Hale, only strong stability of the difference operator ensures robust asymptotic stability with respect to the delays. If the difference operator is in the critical case, the stability becomes fragile with respect to the delays. Based on some old results in the field, a conjecture concerning the (quasi)-critical modes of the system is stated; also a connection with the so called dissipative boundary conditions is suggested.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009555","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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