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ON AN IMPORTANT OBSERVATION REGARDING SOME HYDROMAGNETIC MOTIONS OF MAXWELL FLUIDS AND ITS APPLICATIONS* 关于麦克斯韦流体的一些磁运动及其应用的一个重要观察*
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.12
C. Fetecău
{"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}
引用次数: 0
VORONOVSKAYA-TYPE THEOREM FOR POSITIVE LINEAR OPERATORS BASED ON LAGRANGE INTERPOLATION 基于Lagrange插值的正线性算子的voronovskaya型定理
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.86
S. G. Galt
{"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}
引用次数: 0
ONLINE DYNAMIC MODE DECOMPOSITION: AN ALTERNATIVE APPROACH FOR LOW RANK DATASETS 在线动态模式分解:低秩数据集的替代方法
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.229
G.H. Nedzhibov
{"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}
引用次数: 0
ON THE EQUILIBRIUM EQUATIONS OF LINEAR 6-PARAMETER ELASTIC SHELLS 线性六参数弹性壳的平衡方程
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.94
M. Blrsan
{"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}
引用次数: 0
STRONG STATIONARITY FOR THE CONTROL OF VISCOUS HISTORY-DEPENDENT EVOLUTIONARY VIS ARISING IN APPLICATIONS 强平稳性用于控制应用中产生的依赖于历史的粘性演化vis
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.250
L. Betzt
{"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}
引用次数: 1
ALGORITHMS FOR THE RICCATI EQUATION WITH A NONSINGULAR M-MATRIX 非奇异m矩阵riccati方程的算法
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.205
I Ivanov, N. Baeva
{"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}
引用次数: 0
ON THE NONLINEAR STABILITY FOR QUASI-GEOSTROPHIC FORCED ZONAL FLOWS 准地转强迫纬向流的非线性稳定性
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.73
L. Palese
{"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}
引用次数: 0
SEVERAL VARIATIONAL INCLUSIONS FOR A FRACTIONAL DIFFERENTIAL INCLUSION OF CAPUTO-FABRIZIO TYPE caputo-fabrizio型分数阶微分包体的几个变分包体
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.154
A. Cernea
{"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}
引用次数: 0
APPROXIMATING OF FIXED POINTS FOR MULTI-VALUED GENERALIZED a-NONEXPANSIVE MAPPINGS IN BANACH SPACES 巴拿赫空间中多值广义非膨胀映射不动点的逼近
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.554
S. Temir
{"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}
引用次数: 0
FROM PROPAGATION SYSTEMS TO TIME DELAYS AND BACK. CRITICAL CASES 从传播系统到时间延迟再回来。关键的情况下
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.491
V. Rasvan
{"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}
引用次数: 0
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