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This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results as coefficient estimates, distortion and growth theorems, radius of starlikeness, convexity and close to convexity, extreme points, convex linear combinations, neighbourhoods, and integral transforms for a new class., Comment: 11 pages

The aim of this work is to introduced the concept of the best one-sided approximation of unbounded functions in weighted space by using algebraic operators in terms the average modulus of smoothness. We also show an estimate of the degree of best one-sided approximation of unbounded functions in the terms of average modulus of smoothness., Comment: 11 pages, Journal Article

The aim of this paper is to extend the concept of regional exponential general observability to the case of Neumann boundary conditions problem in diffusion system. More precisely, for linear distributed parameter diffusion systems, we show that the sensors characterizations allow to reconstruct the regional exponential state in a sub-region of the considered systems domain. Moreover, various interesting results associated with the choice of sensors are given and illustrated in specific situations in order regional exponential general observability notion to be achieved. Finally, we also show that, there exists a dynamical system for diffusion system is not exponential general observable in the usual sense, but it may be regional exponential general observable., Comment: 11 pages, 5 figures, regular paper

The main idea of this paper is to explore and present the original results related to the notion of regional boundary gradient strategic sensors in distributed parameter system for Neumann problem. Thus, this systems is described by parabolic state space partial differential equations where the dynamic is governed by strongly continuous semi-group in Hilbert space. In addition, we give the sufficient conditions which are guaranteed the characterizations for such sensors in order that regional boundary approximately gradient observability can be achieved and proved. The obtained results are applied to two-dimensional circular in a part of considered system domain with various cases of sensors locations are tackled and studied., Comment: 13 page, 6 figures, regular paper. arXiv admin note: text overlap with arXiv:2005.02256

In the present paper, the characterizations of regional gradient strategic sensors notions have been given for different cases of regional gradient observability. The results obtained are applied to two dimensional linear infinite distributed system in Hilbert space where the dynamic is governed by strongly continuous semi-group. Various cases of regional strategic sensors are considered and analyzed in connection with regional gradient strategic sensors concepts. Also, we show that there is a various sensors which are not gradient strategic in usual sense for the considered systems, but may be regionally gradient strategic of this system., Comment: 14 pages, 5 figures, Regular paper. arXiv admin note: text overlap with arXiv:2005.02256

The aim of this chapter is to introduce the concept of regional boundary exponential reduced observability in connection with the sensors characterizations on a sub-region on boundary of the considered domain boundary. More precisely, we explore the original results devoted to this concept in linear dynamical systems which is generated by a strongly continuous semi-group in Hilbert space of order one. Thus, the existence of sufficient conditions is presented and examined for regional boundary exponential reduced estimator in parabolic infinite dimensional systems. Finally, we apply these results to the exchange systems with various strategic sensors., Comment: Pages 18, 5 figures, regular paper

This paper, deals with the linear infinite dimensional distributed parameter systems in a Hilbert space where the dynamics of the system is governed by strongly continuous semi-groups. More precisely, for parabolic distributed systems the characterizations of regional boundary strategic sensors have been discussed and analyzed in different cases of regional boundary observability in infinite time interval. Furthermore, the results so obtained are applied in two-dimensional systems and the sensors are studied under which conditions guarantee regional boundary observability in a sub-region of the system domain boundary. Also, the authors show that, the existence of a given sensor for the diffusion system is not strategic in the usual sense, but it may be regional boundary strategic of this system., Comment: 17 Pages, 13 figures. regular paper. arXiv admin note: text overlap with arXiv:2005.02301

The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state space system of this model as mathematical model. Moreover, we present some definitions and results which is described some concepts of linear control system analysis related to this problem. More precisely, the sufficient conditions which characterize the observability notion of linear dynamical controlled system are presented and discussed. Finally, we prove that, the electrical cardiography model is completely observable system over finite time., Comment: 8 pages, 4 figures, regular paper

The main purpose of this paper is to study and characterize the existing of general asymptotic regional gradient observer which observe the current gradient state of the original system in connection with gradient strategic sensors. Thus, we give an approach based to Luenberger observer theory of linear distributed parameter systems which is enabled to determinate asymptotically regional gradient estimator of current gradient system state. More precisely, under which condition the notion of asymptotic regional gradient observability can be achieved. Furthermore, we show that the measurement structures allows the existence of general asymptotic regional gradient observer and we give a sufficient condition for such asymptotic regional gradient observer in general case. We also show that, there exists a dynamical system for the considered system is not general asymptotic gradient observer in the usual sense, but it may be general asymptotic regional gradient observer. Then, for this purpose we present various results related to different types of sensor structures, domains and boundary conditions in two dimensional distributed diffusion systems, Comment: 11 pages, 8 figures

The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and distortion theorems , radii of starlikeness and convexity for the" functions in our subclass., Comment: 9 pqges, regular paper

In this paper, a linear infinite dimensional distributed systems in a Hilbert space has been discussed and analyzed where the dynamics of system is governed by strongly continuous semi-groups. The characterizations of regional strategic sensors have been given and tackled for different cases of regional observability. Furthermore, the results so obtained are applied to two-dimensional systems. Various cases of sensors are considered and analyzed. Also, the authors show that, the existent of a sensor for the diffusion system is not strategic in the usual sense, but it may be regionally strategic of this system., Comment: 18 Pages, 6 Figures, regular paper

The purpose of this paper is to characterize regional boundary gradient strategic sensors notions for different cases of regional boundary gradient observation to be achieved. Then, the characterizations based on how to a cross from internal gradient region to the boundary gradient region. Thus, the obtained results are applied in two dimensional linear infinite distributed systems in Hilbert space where the dynamics are governed by strongly continuous semi-group. Moreover, we give the relation between the regional gradient observability on a subregion small Gama of the spatial domain Omega with the regional boundary gradient observability on a subregion Gama of the boundary Omega of. Finally, sufficient conditions of regional boundary gradient strategic sensors notions are explored, analyzed and discussed in connection with the regional boundary gradient of exact (weak) observability, positive definite observability operator and rank conditions., Comment: 17 Pages, 6 Figures, regular paper

In this study, a subclass of an univalent function with negative coefficients which is defined by a new general Linear operator have been introduced. The sharp results for coefficients estimators, distortion and closure bounds, Hadamard product, and Neighborhood, and this paper deals with the utilizing of many of the results for classical hypergeometric function, where there can be generalized to m-hypergeometric functions. A subclasses of univalent functions are presented, and it has involving operator which generalizes many well-known. Denote A the class of functions f and we have other results have been studied., Comment: 6 pages, regular paper

The purpose of this paper is to explore the concept of the regional boundary asymptotic gradient full order observer (RBAGFO-observer) in connection with the characterizations of sensors structures. Then, we present various results related to different types of measurements, domains and boundary conditions for distributed parameter systems (DPSS) in parabolic systems problem. The considered approach of this work is derived from Luenberger observer theory which is enable to estimate asymptotically the state gradient of the original system on a sub-region of the domain boundary Omega in order that the RBAGFO-observability notion to be achieved. We also show that there exists a dynamical system for the considered system is not BAGFO-observer in the usual sense, but it may be regional RBAGFO-observer., Comment: 18 pages, 9 figures. arXiv admin note: text overlap with arXiv:2004.14213

The purpose of this paper is to deals with the problem of regional boundary asymptotic gradient full order observer (regional boundary asymptotic gradient full order observer) concept by using internal regional case. Thus, we study the relation between this notion and the corresponding asymptotic detectability and sensors. More precisely, various important results have been examined and explored concern an extension of an approach which enables to reconstruct the gradient of current state from internal region. In addition, it has been shown that the characterization of regional boundary asymptotic gradient full order observability under which conditions to be achieved. Finally, we have illustrate that there is a dynamical system which does not represent the observer in the usual sense, but it could be interpreted as a regional boundary asymptotic gradient full order observer., Comment: 6 pages, 4 figures, Mathematical regular paper