Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.163
M. Mercat
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.
{"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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.217
S. Treanta, A. Petrescu-Nil
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.
{"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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.45
V. Dragan, S. Aberkane, I.-L. Popa, T. Morozan
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.
{"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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.443
R. Abdullah, A. Halanay, K. Amin, R. Mghames
"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."
{"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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.427
A.-M. Stoica, I. Yaesh
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.
{"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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.383
A.-M. Mosneagu, I. Stolerii
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.
{"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}
Pub Date : 2023-01-01DOI: 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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.330
W. Hant
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.
{"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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.119
L. Restuccia
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.
{"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}
Pub Date : 2023-01-01DOI: 10.56082/annalsarscimath.2023.1-2.147
A. Petrușel, G. Petrușel
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.
{"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}
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