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Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications最新文献

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A NOTE ON A CLASSICAL CONNECTION BETWEEN PARTITIONS AND DIVISORS 关于分区和除数之间的经典联系的注释
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.163
M. Mercat
{"title":"A NOTE ON A CLASSICAL CONNECTION BETWEEN PARTITIONS AND DIVISORS","authors":"M. Mercat","doi":"10.56082/annalsarscimath.2023.1-2.163","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.163","url":null,"abstract":"In this note, we consider the number of k’s in all the partitions of n in order to provide a new proof of a classical identity involving Euler’s partition function p(n) and the sum of the positive divisors function a(n). New relations connecting classical functions of multiplicative number theory with the partition function p(n) from additive number theory are introduced in this context. The fascinating feature of these relations is their common nature. A new identity for the number of 1’s in all the partitions of n is derived in this context.","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":"135009910","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":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":"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":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":"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":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":"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
STATIC OUTPUT FEEDBACK CONTROL OF LINEAR PARAMETER VARYING SYSTEMS 线性变参数系统的静态输出反馈控制
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.427
A.-M. Stoica, I. Yaesh
{"title":"STATIC OUTPUT FEEDBACK CONTROL OF LINEAR PARAMETER VARYING SYSTEMS","authors":"A.-M. Stoica, I. Yaesh","doi":"10.56082/annalsarscimath.2023.1-2.427","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.427","url":null,"abstract":"The synthesis problem of static output feedback controllers within the anisotropic-norm setup for Linear Parameter Varying system is considered. A synthesis approach involving iterations over a convex optimisation problem is suggested, leading to a gain-scheduled con¬troller. The results are formulated by a couple of Linear Matrix In¬equalities and a coupling bilinear equality, using a parameter depen¬dent Lyapunov function. Following LPVTOOL, the problem which is continuous in the gain-scheduling parameter, and hence infinite dimen¬sional, is approximated by a finite grid leading to a tractable sequence of convex optimization problems. The design method is demonstrated on a simple example from the field of flight control.","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":"135009533","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
VALIDITY OF THE QUASI STEADY STATE ASSUMPTION FOR ENZYME-CATALYSED REACTIONS WITH COMPETITIVE INHIBITION AND SUBSTRATE INPUT 具有竞争性抑制和底物输入的酶催化反应准稳态假设的有效性
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.383
A.-M. Mosneagu, I. Stolerii
{"title":"VALIDITY OF THE QUASI STEADY STATE ASSUMPTION FOR ENZYME-CATALYSED REACTIONS WITH COMPETITIVE INHIBITION AND SUBSTRATE INPUT","authors":"A.-M. Mosneagu, I. Stolerii","doi":"10.56082/annalsarscimath.2023.1-2.383","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.383","url":null,"abstract":"Enzyme-catalysed reactions are chemical reactions within cells in which the rate of the reaction is significantly increased through the action of enzymes. They are usually part of large and complex bio¬chemical networks, which form the central processing units of the living cell. Enzymatic reactions often operate on multiple time scales, which can be characterized as being either fast or slow. The quasi steady¬state approximation (QSSA) utilizes time scale separation to pro ject these complex models onto lower-dimensional slow manifolds. In this paper, we investigate the validity of a quasi steady-state assumption for enzyme-catalysed biochemical reactions with competitive inhibition that are subject to a constant substrate input. Necessary and sufficient conditions for the validity of these assumptions were derived and were shown to be dependent, among others, on the substrate input. The validity conditions are numerically verified using the classical Runge- Kutta 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":"135009538","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 DICHOTOMY WITH DIFFERENTIABLE GROWTH RATES FOR SKEW-EVOLUTION COCYCLES IN BANACH SPACES banach空间中偏演化环的生长速率可微二分法
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.473
M. Megan, A. Gaina, R. Boruga Toma
{"title":"ON DICHOTOMY WITH DIFFERENTIABLE GROWTH RATES FOR SKEW-EVOLUTION COCYCLES IN BANACH SPACES","authors":"M. Megan, A. Gaina, R. Boruga Toma","doi":"10.56082/annalsarscimath.2023.1-2.473","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.473","url":null,"abstract":"","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":"135009546","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 A NEW CLASS OF MIXED HEMIVARIATIONAL-VARIATIONAL INEQUALITIES 一类新的混合半变分-变分不等式
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.330
W. Hant
{"title":"ON A NEW CLASS OF MIXED HEMIVARIATIONAL-VARIATIONAL INEQUALITIES","authors":"W. Hant","doi":"10.56082/annalsarscimath.2023.1-2.330","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.330","url":null,"abstract":"In this paper, we study a new class of mixed hemivariational- variational inequalities in which both the non-smooth convex func­tional and the non-smooth non-convex functional can depend on two arguments. We present solution existence and uniqueness results. Then, we apply the theoretical results on a mixed hemivariational-variational inequality in the study of a stationary incompressible flow of Bingham type fluid subject to non-smooth non-monotone slip boundary condi­tion.","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":"135009551","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 HEAT DISSIPATION FUNCTION FOR MAGNETIC RELAXATION PHENOMENA IN ANISOTROPIC MEDIA 各向异性介质中磁弛豫现象的散热函数
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.119
L. Restuccia
{"title":"ON THE HEAT DISSIPATION FUNCTION FOR MAGNETIC RELAXATION PHENOMENA IN ANISOTROPIC MEDIA","authors":"L. Restuccia","doi":"10.56082/annalsarscimath.2023.1-2.119","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.119","url":null,"abstract":"Using the methods of classical irreversible thermodynamics with internal variables, the heat dissipation function for magnetizable ani­sotropic media, in which phenomena of magnetic relaxation occur, is derived. It is assumed that if different types of irreversible microscopic phenomena give rise to magnetic relaxation, it is possible to describe these microscopic phenomena splitting the total specific magnetization in two irreversible parts and introducing one of these partial specific magnetizations as internal variable in the thermodynamic state space. It is seen that, when the theory is linearized, the heat dissipation func­tion is due to the electric conduction, magnetic relaxation, viscous, magnetic irreversible phenomena. This is the case of complex media, where different kinds of molecules have different magnetic susceptibili­ties and relaxation times, present magnetic relaxation phenomena and contribute to the total magnetization. These situations arise in nuclear magnetic resonance in medicine and biology and in other fields of the applied sciences. Also, the heat conduction equation for these media is worked out and the special cases of anisotropic Snoek media and anisotropic De-Groot-Mazur media are treated.","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":"135009540","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
FIXED POINT RESULTS FOR MULTI-VALUED GRAPH CONTRACTIONS ON A SET ENDOWED WITH TWO METRICS 具有两个度量集的多值图压缩的不动点结果
Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI: 10.56082/annalsarscimath.2023.1-2.147
A. Petrușel, G. Petrușel
{"title":"FIXED POINT RESULTS FOR MULTI-VALUED GRAPH CONTRACTIONS ON A SET ENDOWED WITH TWO METRICS","authors":"A. Petrușel, G. Petrușel","doi":"10.56082/annalsarscimath.2023.1-2.147","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.147","url":null,"abstract":"In this paper we will study existence, uniqueness and data depen­dence of the fixed points of multi-valued operators on a set endowed with two metrics. The case of multi-valued graph contractions is con­sidered. Then, an extension to a more general contraction type condi­tion is also given.","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":"135009547","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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