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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":"144 1","pages":"0"},"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":"79 1","pages":"0"},"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":"30 1","pages":"0"},"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":"13 1","pages":"0"},"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":"85 1","pages":"0"},"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":"27 1","pages":"0"},"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":"7 1","pages":"0"},"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
RESULTS OF EXISTENCE OF SOLUTIONS FOR SOME VARIATIONAL CONTROL INEQUALITIES 一些变分控制不等式解的存在性结果
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.217
S. Treanta, A. Petrescu-Nil
{"title":"RESULTS OF EXISTENCE OF SOLUTIONS FOR SOME VARIATIONAL CONTROL INEQUALITIES","authors":"S. Treanta, A. Petrescu-Nil","doi":"10.56082/annalsarscimath.2023.1-2.217","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.217","url":null,"abstract":"The paper deals with the study of solutions for some weak varia­tional control inequalities of vector type, and the efficient solutions to the corresponding optimization problem. More exactly, to formulate and prove the principal results, we consider the Frechet differentia­bility, the concept of invex set, and invexity & pseudoinvexity of the curvilinear integral type functionals which are involved in the study.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009539","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 STABILITY AND MEAN SQUARE STABILIZATION OF A CLASS OF LINEAR STOCHASTIC SYSTEMS CONTROLLED BY IMPULSES 一类脉冲控制的线性随机系统的稳定性和均方镇定性
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.45
V. Dragan, S. Aberkane, I.-L. Popa, T. Morozan
{"title":"ON THE STABILITY AND MEAN SQUARE STABILIZATION OF A CLASS OF LINEAR STOCHASTIC SYSTEMS CONTROLLED BY IMPULSES","authors":"V. Dragan, S. Aberkane, I.-L. Popa, T. Morozan","doi":"10.56082/annalsarscimath.2023.1-2.45","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.45","url":null,"abstract":"This paper is devoted to the analysis of the mean-square stability of a class of linear time-varying impulsive Ito-type stochastic systems. We succeed to obtain necessary and sufficient stability conditions in the general time-varying case. This result is obtained thanks to the theory of positive operators on Hilbert spaces. The problem of state­feedback stabilization is treated as well.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009891","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
PARTIAL STABILITY IN A MODEL FOR ALLERGIC REACTIONS INDUCED BY CHEMOTHERAPY OF ACUTE LYMPHOBLASTIC LEUKEMIA 急性淋巴细胞白血病化疗致过敏反应模型的部分稳定性
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.443
R. Abdullah, A. Halanay, K. Amin, R. Mghames
{"title":"PARTIAL STABILITY IN A MODEL FOR ALLERGIC REACTIONS INDUCED BY CHEMOTHERAPY OF ACUTE LYMPHOBLASTIC LEUKEMIA","authors":"R. Abdullah, A. Halanay, K. Amin, R. Mghames","doi":"10.56082/annalsarscimath.2023.1-2.443","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.443","url":null,"abstract":"\"A new model that captures the cellular evolution of patients undergoing maintenance therapy for acute lymphoblastic leukemia in connection with al¬lergic reactions is considered. A previous model from is modified to include the cells involved in allergies induced by chemotherapy and desensitization. Delay differential equations are used to model cell evolution. General properties of solutions are deduced, eventually proving partial stability of certain equilibria with respect to some of the variables. The immune sys¬tem’s functioning, as well as the therapeutic role for cancer cure without interference of allergic reactions caused by this treatment, are also evaluated using numerical simulations.\"","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009531","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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