Articles de revues : « Do operator »

1

Rooin, Jamal, Akram Alikhani et Mohammad Sal Moslehian. « Operator m-convex functions ». Georgian Mathematical Journal 25, n^o 1 (1 mars 2018) : 93–107. http://dx.doi.org/10.1515/gmj-2017-0045.

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AbstractThe aim of this paper is to present a comprehensive study of operatorm-convex functions. Let{m\in[0,1]}, and{J=[0,b]}for some{b\in\mathbb{R}}or{J=[0,\infty)}. A continuous function{\varphi\colon J\to\mathbb{R}}is called operatorm-convex if for any{t\in[0,1]}and any self-adjoint operators{A,B\in\mathbb{B}({\mathscr{H}})}, whose spectra are contained inJ, we have{\varphi(tA+m(1-t)B)\leq t\varphi(A)+m(1-t)\varphi(B)}. We first generalize the celebrated Jensen inequality for continuousm-convex functions and Hilbert space operators and then use suitable weight functions to give some weighted refinements. Introducing the notion of operatorm-convexity, we extend the Choi–Davis–Jensen inequality for operatorm-convex functions. We also present an operator version of the Jensen–Mercer inequality form-convex functions and generalize this inequality for operatorm-convex functions involving continuous fields of operators and unital fields of positive linear mappings. Employing the Jensen–Mercer operator inequality for operatorm-convex functions, we construct them-Jensen operator functional and obtain an upper bound for it.

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Li, Xiaochun, et Fugen Gao. « On Properties of ClassA(n)andn-Paranormal Operators ». Abstract and Applied Analysis 2014 (2014) : 1–5. http://dx.doi.org/10.1155/2014/629061.

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Letnbe a positive integer, and an operatorT∈B(ℋ)is called a classA(n)operator ifT1+n2/1+n≥|T|2andn-paranormal operator ifT1+nx1/1+n≥||Tx||for every unit vectorx∈ℋ, which are common generalizations of classAand paranormal, respectively. In this paper, firstly we consider the tensor products for classA(n)operators, giving a necessary and sufficient condition forT⊗Sto be a classA(n)operator whenTandSare both non-zero operators; secondly we consider the properties forn-paranormal operators, showing that an-paranormal contraction is the direct sum of a unitary and aC.0completely non-unitary contraction.

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Wong, M. W. « Minimal and Maximal Operator Theory With Applications ». Canadian Journal of Mathematics 43, n^o 3 (1 juin 1991) : 617–27. http://dx.doi.org/10.4153/cjm-1991-036-7.

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AbstractLetXbe a complex Banach space andAa linear operator fromXintoXwith dense domain. We construct the minimal and maximal operators of the operatorAand prove that they are equal under reasonable hypotheses on the spaceXand operatorA. As an application, we obtain the existence and regularity of weak solutions of linear equations on the spaceX. As another application we obtain a criterion for a symmetric operator on a complex Hilbert space to be essentially self-adjoint. An application to pseudo-differential operators of the Weyl type is given.

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Rosales, Edixo. « Operadores de riesz en el Alglat(T)∩{T} ». Revista Bases de la Ciencia. e-ISSN 2588-0764 6, n^o 1 (30 avril 2021) : 49. http://dx.doi.org/10.33936/rev_bas_de_la_ciencia.v6i1.2515.

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En este trabajo X es un espacio de Banach y B(X) denota los operadores acotados. Si T∈B(X), por lat(T) entenderemos los subespacios invariantes por T. Se dice que T es lleno, si (T(M)) ̅=M, para todo M∈lat(T) (la barra indica la clausura en la topología inducida por la norma). Se prueba principalmente el siguiente resultado: Sean X un espacio de Banach y T ∈B(X) acotado por abajo. Sea K ∈Alglat(T)∩{T}' un operador de Riesz. Si K es lleno, entonces T es lleno. Aquí Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} y {T}^'={S∈B(X):S∘T=T∘S}. Palabras clave: Operador lleno, operador de Riesz, operador acotado por abajo. Abstract In this work X is a Banach space and B(X) denotes the bounded operators. If T ∈B(X), for lat(T) we will understand the invariant subspaces for T. An operator T is full, if (T(M)) ̅=M, for all M∈ latT (the bar indicates the closure in the topology induced by the norm). The following result is true: Let X be a Banach space, T ∈B(X) a bounded below operator and K ∈Alglat(T)∩{T}' a Riesz operator: If K is a full operator, then T is a full operator. Here Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} and {T}^'={S∈B(X):S∘T=T∘S}. Keywords: full operator, Riesz operator, bounded below operator.

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Harjule, Priyanka, Manish Bansal et Serkan Araci. « An investigation of incomplete H−functions associated with some fractional integral operators ». Filomat 36, n^o 8 (2022) : 2695–703. http://dx.doi.org/10.2298/fil2208695h.

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Arbitrary-order integral operators find variety of implementations in different science disciplines as well as engineering fields. The study presented as part of this research paper derives motivation from the fact that applications of fractional operators and special functions demonstrate a huge potential in understanding many of physical phenomena. Study and investigation of a fractional integral operator containing an incomplete H? functions (IHFs) as the kernel is the primary objective of the research work presented here. Specifically, few interesting relations involving the new fractional operator with IHFs in its kernel and classical Riemann Liouville(R-L) fractional integral and derivative operators, the Hilfer fractional derivative operator, the generalized composite fractonal derivate operaor are established. Results established by the authors in [1-3] follow as few interesting and significant special cases of our main results.

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Miloslova, A. A., et T. A. Suslina. « Averaging of Higher-Order Parabolic Equations with Periodic Coefficients ». Contemporary Mathematics. Fundamental Directions 67, n^o 1 (15 décembre 2021) : 130–91. http://dx.doi.org/10.22363/2413-3639-2021-67-1-130-191.

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In L2(Rd;Cn), we consider a wide class of matrix elliptic operators A of order 2p (where p2) with periodic rapidly oscillating coefficients (depending on x/). Here 0 is a small parameter. We study the behavior of the operator exponent e-A for 0 and small . We show that the operatore-A converges as 0 in the operator norm in L2(Rd;Cn) to the exponent e-A0 of the effective operator A0. Also we obtain an approximation of the operator exponent e-A in the norm of operators acting from L2(Rd;Cn) to the Sobolev space Hp(Rd; Cn). We derive estimates of errors of these approximations depending on two parameters: and . For a fixed 0 the errors have the exact order O(). We use the results to study the behavior of a solution of the Cauchy problem for the parabolic equation u(x,)= -(A u)(x,)+F(x,) in Rd.

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Gunawan, Gunawan, et Erni Widiyastuti. « KARAKTERISTIK OPERATOR PARANORMAL- * QUASI ». Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 3, n^o 1 (30 avril 2022) : 256–73. http://dx.doi.org/10.46306/lb.v3i1.114.

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Given Hilbert space H over the fields of . This study aimed to investigate the paranormal- * quasi operators and their properties in Hilbert space. The study resulted the properties of paranormal- * quasi operators, hyponormal operator, class A operator, Class A- * operator, p- hyponormal operator for p > 0, - paranormal operators, compact operator, and the relationship between them

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Alomari, Mohammad W., Christophe Chesneau et Ahmad Al-Khasawneh. « Operator Jensen’s Inequality for Operator Superquadratic Functions ». Axioms 11, n^o 11 (6 novembre 2022) : 617. http://dx.doi.org/10.3390/axioms11110617.

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In this work, an operator superquadratic function (in the operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. A general Bohr’s inequality for positive operators is thus deduced. A Jensen-type inequality is proved. Equivalent statements of a non-commutative version of Jensen’s inequality for operator superquadratic function are also established. Finally, several trace inequalities for superquadratic functions (in the ordinary sense) are provided as well.

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Rosales, Edixo. « RESULTADOS SOBRE OPERADORES LLENOS EN ESPACIOS DE HILBERT ». Revista Bases de la Ciencia. e-ISSN 2588-0764 5, n^o 1 (30 avril 2020) : 51. http://dx.doi.org/10.33936/rev_bas_de_la_ciencia.v5i1.1686.

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Se prueba, entre otros, el siguiente resultado: Sea T:H→H un operador autoadjunto inyectivo, y K:H→H un operador de Riesz, tal que K∈Alglat(T)∩{T}'. Si K:H→H es lleno, entonces T:H→H es lleno. Palabras clave: Operador de Riesz, operador autoadjunto, operador lleno. Abstract It is proved here, among other results, the following: Let T:H→H be a self-adjoint injective operator, and K:H→H a Riesz operator, such that K∈Alglat(T)∩{T}'. If K:H→H is a full operator, then T:H→H is a full operator. Keywords: Riesz operator, self-adjoint operator, full operator. Resumo O siguiente resultado, entre outros, está provado: Seja T:H→H um operador autoadjunto limitado abaixo, e K:H→H um operador de Riesz, tal qual K∈AlglatT⋂{T}^'. Se K:H→H é um operador completo, então T:H→H é um operador completo. Palavras-chave: operador Riesz, operador autoadjunto completo.

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Chetverikov, V. N. « Linear Differential Operators Invertible in the Integro-differential Sense ». Mathematics and Mathematical Modeling, n^o 4 (13 décembre 2019) : 20–33. http://dx.doi.org/10.24108/mathm.0419.0000195.

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The paper studies linear differential operators in derivatives with respect to one variable. Such operators include, in particular, operators defined on infinite prolongations of evolutionary systems of differential equations with one spatial variable. In this case, differential operators in total derivatives with respect to the spatial variable are considered. In parallel, linear differential operators with one independent variable are investigated. The known algorithms for reducing the matrix to a stepwise or diagonal form are generalized to the operator matrices of both types. These generalizations are useful at points, where the functions, into which the matrix components are divided when applying the algorithm, are nonzero.In addition, the integral operator is defined as a multi-valued operator that is the right inverse of the total derivative. Linear operators that involve both the total derivatives and the integral operator are called integro-differential. An invertible operator in the integro-differential sense is an operator for which there exists a two-sided inverse integro-differential operator. A description of scalar differential operators that are invertible in this sense is obtained. An algorithm for checking the invertibility in the integro-differential sense of a differential operator and for constructing the inverse integro-differential operator is formulated.The results of the work can be used to solve linear equations for matrix differential operators arising in the theory of evolutionary systems with one spatial variable. Such operator equations arise when describing systems that are integrable by the inverse scattering method, when calculating recursion operators, higher symmetries, conservation laws and symplectic operators, and also when solving some other problems. The proposed method for solving operator equations is based on reducing the matrices defining the operator equation to a stepwise or diagonal form and solving the resulting scalar operator equations.

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Wei, Guiwu. « Uncertain Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making ». International Journal of Decision Support System Technology 10, n^o 2 (avril 2018) : 40–64. http://dx.doi.org/10.4018/ijdsst.2018040103.

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This article utilizes Hamacher operations to develop some uncertain aggregation operators: uncertain Hamacher weighted average (UHWA) operator, uncertain Hamacher weighted geometric (UHWG) operator, uncertain Hamacher ordered weighted average (UHOWA) operator, uncertain Hamacher ordered weighted geometric (UHOWG) operator, uncertain Hamacher hybrid average (UHHA) operator, uncertain Hamacher hybrid geometric (UHHG) operator and some uncertain Hamacher correlate aggregation operators and uncertain induced Hamacher aggregation operators. The prominent characteristics of these proposed operators are studied. Then, the article utilizes these operators to develop some approaches to solve the uncertain multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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Wang, Li Yuan, et Kai Kang. « Research and Analysis of Edge-Detection of Digital Images ». Applied Mechanics and Materials 263-266 (décembre 2012) : 2538–41. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.2538.

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Edge-detection is the basic characteristic of images. Edge-detection plays an important role in computer vision and image analysis, it is the key link of image analysis and recognition. In this paper, we mainly analyze several edge-detection operators, research the processing results. The edge-detection operators mainly include Roberts operator, Prewitt operator, Sobel operator, Canny operator and LoG operator. Finally we discuss the advantage and disadvantage of the edge-detection operators.

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Journal, Baghdad Science. « Quasi-posinormal operators ». Baghdad Science Journal 7, n^o 3 (5 septembre 2010) : 1282–87. http://dx.doi.org/10.21123/bsj.7.3.1282-1287.

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In this paper, we introduce a class of operators on a Hilbert space namely quasi-posinormal operators that contain properly the classes of normal operator, hyponormal operators, M–hyponormal operators, dominant operators and posinormal operators . We study some basic properties of these operators .Also we are looking at the relationship between invertibility operator and quasi-posinormal operator .

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Liu, Lanzhe. « Estimates of multilinear singular integral operators and mean oscillation ». Publications de l'Institut Math?matique (Belgrade) 95, n^o 109 (2014) : 201–14. http://dx.doi.org/10.2298/pim1409201l.

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We prove the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces. The operators include Calder?n-Zygmund singular integral operator, Littlewood-Paley operator and Marcinkiewicz operator.

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Liu, Lanzhe. « Weighted boundedness for Toeplitz type operator associated to general integral operators ». Asian-European Journal of Mathematics 07, n^o 02 (juin 2014) : 1450026. http://dx.doi.org/10.1142/s1793557114500260.

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In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

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Berkani, M., et N. Castro-González. « UNBOUNDED B-FREDHOLM OPERATORS ON HILBERT SPACES ». Proceedings of the Edinburgh Mathematical Society 51, n^o 2 (juin 2008) : 285–96. http://dx.doi.org/10.1017/s0013091505001574.

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AbstractThis paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space $H$ and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index $0$ is given in terms of the sum of a Drazin closed operator and a finite-rank operator. We analyse the properties of the powers $T^m$ of a closed B-Fredholm operator and we establish a spectral mapping theorem.

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Fomin, Vasiliy I. « About a complex operator resolvent ». Russian Universities Reports. Mathematics, n^o 138 (2022) : 183–97. http://dx.doi.org/10.20310/2686-9667-2022-27-138-183-197.

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A normed algebra of bounded linear complex operators acting in a complex normed space consisting of elements of the Cartesian square of a real Banach space is constructed. In this algebra, it is singled out a set of operators for each of which the real and imaginary parts commute with each other. It is proved that in this set, any operator for which the sum of squares of its real and imaginary parts is a continuously invertible operator, is invertible itself; a formula for the inverse operator is found. For an operator from the indicated set, the form of its regular points is investigated: conditions under which a complex number is a regular point of the given operator are found; a formula for the resolvent of a complex operator is obtained. The set of unbounded linear complex operators acting in the above complex normed space is considered. In this set, a subset of those operators for each of which the domains of the real and imaginary parts coincide is distinguished. For an operator from the specified subset, conditions on a complex number under which this number belongs to the resolvent set of the given operator are found; a formula for the resolvent of the operator is obtained. The concept of a semi-bounded complex operator as an operator in which one component is a bounded and the other is an unbounded operator is introduced. It is noted that the first and second resolvent identities for complex operators can be proved similarly to the case of real operators.

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Čatipović, Marija, et Saša Krešić-Jurić. « Sturm-Liouvilleov problem ». Acta mathematica Spalatensia. Series didactica 4, n^o 4 (11 décembre 2021) : 97–111. http://dx.doi.org/10.32817/amssd.4.4.7.

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Klasična Sturm-Liouvilleova jednadžba, nazvana po Jacquesu Sturmu i Josephu Liouvilleu, je obična diferencijalna jednadžba drugog reda posebnog oblika u ovisnosti o parametru lambda. Pronalaženje te vrijednosti za koju postoje netrivijalna rješenja jednadžbe i koja zadovoljavaju rubne uvjete je dio problema kojeg nazivamo Sturm-Liouvilleov problem. Pokazat ćemo da se proizvoljni linearni operator drugog reda može transformirati u Sturm-Liouvilleov operator tj. da je Sturm-Liouvilleov operator kanonski oblik diferencijalnog operatora drugog reda. Vlastite vrijednosti regularnog Sturm-Liouvilleovog problema su realne, prebrojive i tvore strogo rastući neomeđeni niz. Također, za svaku vlastitu vrijednost postoji odgovarajuća vlastita funkcija jedinstveno određena do na multiplikativnu konstantu koja ima točno n nultočki u intervalu [a; b]. Ovo je jedan od fundamentalnih rezlutata za Sturm-Liouvilleove operatore.

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Dakheel, Shireen O., et Buthainah A. Ahmed. « C₁ C₂- symmetric operators for some types of operators ». Journal of Physics : Conference Series 2322, n^o 1 (1 août 2022) : 012051. http://dx.doi.org/10.1088/1742-6596/2322/1/012051.

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Abstract In this paper, we give some new properties of C1C2-symmetric operators and discuss some results about these kind of operators. Also, we describe the conditions that a binormal operator becomes normal operator and give necessary and sufficient conditions that C1C2- symmetric operators becomes a binormal operator. Finally, we solve the problem that a binormal operator is not closed under addition.

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Mahmoud, Sid Ahmed Ould Ahmed, El Moctar Ould Beiba, Sidi Hamidou Jah et Maawiya Ould Sidi. « Structure of k -Quasi- m , n -Isosymmetric Operators ». Journal of Mathematics 2022 (26 septembre 2022) : 1–13. http://dx.doi.org/10.1155/2022/8377463.

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The investigation of new operators belonging to some specific classes has been quite fashionable since the beginning of the century, and sometimes it is indeed relevant. In this study, we introduce and study a new class of operators called k -quasi- m , n -isosymmetric operators on Hilbert spaces. This new class of operators emerges as a generalization of the m , n -isosymmetric operators. We give a characterization for any operator to be k -quasi- m , n -isosymmetric operator. Using this characterization, we prove that any power of an k -quasi- m , n -isosymmetric operator is also an k -quasi- m , n -isosymmetric operator. Furthermore, we study the perturbation of an k -quasi- m , n -isosymmetric operator with a nilpotent operator. The product and tensor products of two k -quasi- m , n -isosymmetries are investigated.

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Yang, Yixuan, Yuchao Tang et Chuanxi Zhu. « Iterative Methods for Computing the Resolvent of Composed Operators in Hilbert Spaces ». Mathematics 7, n^o 2 (1 février 2019) : 131. http://dx.doi.org/10.3390/math7020131.

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The resolvent is a fundamental concept in studying various operator splitting algorithms. In this paper, we investigate the problem of computing the resolvent of compositions of operators with bounded linear operators. First, we discuss several explicit solutions of this resolvent operator by taking into account additional constraints on the linear operator. Second, we propose a fixed point approach for computing this resolvent operator in a general case. Based on the Krasnoselskii–Mann algorithm for finding fixed points of non-expansive operators, we prove the strong convergence of the sequence generated by the proposed algorithm. As a consequence, we obtain an effective iterative algorithm for solving the scaled proximity operator of a convex function composed by a linear operator, which has wide applications in image restoration and image reconstruction problems. Furthermore, we propose and study iterative algorithms for studying the resolvent operator of a finite sum of maximally monotone operators as well as the proximal operator of a finite sum of proper, lower semi-continuous convex functions.

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Fomin, Vasiliy I. « About unbounded complex operators ». Russian Universities Reports. Mathematics, n^o 129 (2020) : 57–67. http://dx.doi.org/10.20310/2686-9667-2020-25-129-57-67.

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The concept of an unbounded complex operator as an operator acting in the pull-back of a Banach space is introduced. It is proved that each such operator is linear. Linear operations of addition and multiplication by a number and also the operation of multiplication are determined on the set of unbounded complex operators. The conditions for commutability of operators from this set are indicated. The product of complex conjugate operators and the properties of the conjugation operation are considered. Invertibility questions are studied: two contractions of an unbounded complex operator that have an inverse operator are proposed, and an explicit form of the inverse operator is found for one of these restrictions. It is noted that unbounded complex operators can ﬁnd application in the study of a linear homogeneous diﬀerential equation with constant unbounded operator coeﬃcients in a Banach space.

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Wang, Rui, Jie Wang, Hui Gao et Guiwu Wei. « Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk ». Symmetry 11, n^o 1 (21 décembre 2018) : 6. http://dx.doi.org/10.3390/sym11010006.

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In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the PFWMM and PFWDMM operators to build a decision-making model to handle picture fuzzy MADM problems. In the end, we take a concrete instance of appraising a financial investment risk to demonstrate our defined model and to verify its accuracy and scientific merit.

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Lupaş, Alina Alb, et Loriana Andrei. « Certain Integral Operators of Analytic Functions ». Mathematics 9, n^o 20 (14 octobre 2021) : 2586. http://dx.doi.org/10.3390/math9202586.

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In this paper, two new integral operators are defined using the operator DRλm,n, introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators are used for introducing several new classes of functions, and properties of the integral operators on these classes are investigated. Subordination results for the differential operator DRλm,n are also obtained.

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Bracic, Janko. « Arens regularity andweakly compact operators ». Filomat 32, n^o 14 (2018) : 4993–5002. http://dx.doi.org/10.2298/fil1814993b.

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We explore the relation between Arens regularity of a bilinear operator and the weak compactness of the related linear operators. Since every bilinear operator has natural factorization through the projective tensor product a special attention is given to Arens regularity of the tensor operator. We consider topological centers of a bilinear operator and we present a few results related to bilinear operators which can be approximated by linear operators.

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Chen, Dazhao, et Hui Huang. « Sharp function estimates and boundedness for Toeplitz-type operators associated with general fractional integral operators ». Open Mathematics 19, n^o 1 (1 janvier 2021) : 1554–66. http://dx.doi.org/10.1515/math-2021-0122.

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Abstract In this paper, we establish some sharp maximal function estimates for certain Toeplitz-type operators associated with some fractional integral operators with general kernel. As an application, we obtain the boundedness of the Toeplitz-type operators on the Lebesgue, Morrey and Triebel-Lizorkin spaces. The operators include the Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

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Sharma, Poonam, Ravinder Krishna Raina et Janusz Sokół. « On a Generalized Convolution Operator ». Symmetry 13, n^o 11 (10 novembre 2021) : 2141. http://dx.doi.org/10.3390/sym13112141.

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Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.

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Hiai, Fumio, Yuki Seo et Shuhei Wada. « Ando–Hiai-type inequalities for operator means and operator perspectives ». International Journal of Mathematics 31, n^o 01 (17 décembre 2019) : 2050007. http://dx.doi.org/10.1142/s0129167x2050007x.

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We improve the existing Ando–Hiai inequalities for operator means and present new ones for operator perspectives in several ways. We also provide the operator perspective version of the Lie–Trotter formula and consider the extension problem of operator perspectives to non-invertible positive operators.

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Beanland, Kevin, et Ryan M. Causey. « Genericity and Universality for Operator Ideals ». Quarterly Journal of Mathematics 71, n^o 3 (17 juin 2020) : 1081–129. http://dx.doi.org/10.1093/qmathj/haaa018.

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Abstract A bounded linear operator $U$ between Banach spaces is universal for the complement of some operator ideal $\mathfrak{J}$ if it is a member of the complement and it factors through every element of the complement of $\mathfrak{J}$. In the first part of this paper, we produce new universal operators for the complements of several ideals, and give examples of ideals whose complements do not admit such operators. In the second part of the paper, we use descriptive set theory to study operator ideals. After restricting attention to operators between separable Banach spaces, we call an operator ideal $\mathfrak{J}$ generic if whenever an operator $A$ has the property that every operator in $\mathfrak{J}$ factors through a restriction of $A$, then every operator between separable Banach spaces factors through a restriction of $A$. We prove that many classical operator ideals (such as strictly singular, weakly compact, Banach–Saks) are generic and give a sufficient condition, based on the complexity of the ideal, for when the complement does not admit a universal operator. Another result is a new proof of a theorem of M. Girardi and W. B. Johnson, which states that there is no universal operator for the complement of the ideal of completely continuous operators.

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Albeverio, Sergio, Konstantin A. Makarov et Alexander K. Motovilov. « Graph Subspaces and the Spectral Shift Function ». Canadian Journal of Mathematics 55, n^o 3 (1 juin 2003) : 449–503. http://dx.doi.org/10.4153/cjm-2003-020-7.

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AbstractWe obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept we express the spectral shift function arising in a perturbation problem for block operator matrices in terms of the angular operators associated with the corresponding perturbed and unperturbed eigenspaces.

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Miura, Hiroaki. « A Fourth-Order-Centered Finite-Volume Scheme for Regular Hexagonal Grids ». Monthly Weather Review 135, n^o 12 (1 décembre 2007) : 4030–37. http://dx.doi.org/10.1175/2007mwr2075.1.

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Abstract Fourth-order-centered operators on regular hexagonal grids with the ZM-grid arrangement are described. The finite-volume method is used and operators are defined at hexagonal cell centers. The gradient operator is calculated from 12 surrounding cell center scalars. The divergence operator is defined from 12 surrounding cell corner vectors. A linear combination of local or interpolated values generates cell corner values used to calculate the operators. The flux-divergence operator applies the same cell corner values as those used in the gradient and divergence operators. The fourth-order convergence of the gradient and divergence operators is obtained in numerical tests using sufficiently smooth and differentiable test functions. The flux-divergence operator is formally second-order accurate. However, the results from a cone advection test show that the flux-divergence operator performs better than a commonly used second-order flux-divergence operator. Numerical dispersion and phase error are small because mean wind advection is computed with fourth-order accuracy.

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Yang, Wei, Jiarong Shi, Yong Liu, Yongfeng Pang et Ruiyue Lin. « Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Application in Multiple-Attribute Decision-Making ». Complexity 2018 (1 novembre 2018) : 1–25. http://dx.doi.org/10.1155/2018/3606245.

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The aim of this paper is to develop partitioned Pythagorean fuzzy interaction Bonferroni mean operators based on the Pythagorean fuzzy set, Bonferroni mean, and interaction between membership and nonmembership. Several new aggregation operators are developed including the Pythagorean fuzzy interaction partitioned Bonferroni mean (PFIPBM) operator, the Pythagorean fuzzy weighted interaction partitioned Bonferroni mean (PFWIPBM) operator, the Pythagorean fuzzy interaction partitioned geometric Bonferroni mean (PFIPGBM) operator, and the Pythagorean fuzzy weighted interaction partitioned geometric Bonferroni mean (PFWIPGBM) operator. Some main properties and some special particular cases of the new operators are studied. Many existing operators are the special cases of new aggregation operators. Moreover, a multiple-attribute decision-making method based on the proposed operator has been developed and the investment company selection problem is presented to illustrate feasibility and practical advantages of the new method.

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Park, Jin Han, Jong Jin Seo, Young Chel Kwun et Ja Hong Koo. « An Approach Based on Power Generalized Aggregation Operator to Decision Making ». Advanced Materials Research 542-543 (juin 2012) : 198–203. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.198.

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The power average (PA) operator and power generalized mean (PGM) operator, proposed by Yager [15], are the nonlinear weighted aggregation tools whose weighting vectors depend on input arguments. In this paper, we study the power generalized mean (PGM) operator and its weighted form, and develop a power ordered weighted generalized mean (POWGM) operator, and study some properties of these operators. The relationship between the PGM operator and other existing operators is also discussed. Moreover, we utilize the weighted PGM operator to develop an approach to group decision making.

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Momenzadeh, M., et N. I. Mahmudov. « Study of new class of q-fractional integral operator ». Filomat 33, n^o 17 (2019) : 5713–21. http://dx.doi.org/10.2298/fil1917713m.

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In this paper, we study on the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied tp f(t) in these integrals and a new class of q-fractional integral operator with parameter p, is introduced. Recently, the q-analogue of fractional differential integral operator is studied and all of the operators defined in these studies are q-analogue of Riemann fractional differential operator. We show that our new class of operator generalize all the operators in use, and additionally, it can cover the q-analogue of Hadamard fractional differential operator, as well. Some properties of this operator are investigated.

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Kittaneh, Fuad. « On the commutants modulo Cp of A2 and A3 ». Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, n^o 1 (août 1986) : 47–50. http://dx.doi.org/10.1017/s1446788700028056.

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AbstractWe prove the following statements about bounded linear operators on a complex separable infinite dimensional Hilbert space. (1) Let A and B* be subnormal operators. If A2X = XB2 and A3X = XB3 for some operator X, then AX = XB. (2) Let A and B* be subnormal operators. If A2X – XB2 ∈ Cp and A3X – XB3 ∈ Cp for some operator X, then AX − XB ∈ C8p. (3) Let T be an operator such that 1 − T*T ∈ Cp for some p ≥1. If T2X − XT2 ∈ Cp and T3X – XT3 ∈ Cp for some operator X, then TX − XT ∈ Cp. (4) Let T be a semi-Fredholm operator with ind T < 0. If T2X − XT2 ∈ C2 and T3X − XT3 ∈ C2 for some operator X, then TX − XT ∈ C2.

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Rong, Yuan, Zheng Pei et Yi Liu. « Hesitant Fuzzy Linguistic Hamy Mean Aggregation Operators and Their Application to Linguistic Multiple Attribute Decision-Making ». Mathematical Problems in Engineering 2020 (19 février 2020) : 1–22. http://dx.doi.org/10.1155/2020/3262618.

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Linguistic aggregation operator is a paramount appliance to fix linguistic multiple attribute decision-making (MADM) issues. In the article, the Hamy mean (HM) operator is utilized to fuse hesitant fuzzy linguistic (HFL) information and several novel HFL aggregation operators including the hesitant fuzzy linguistic Hamy mean (HFLHM) operator, weighted hesitant fuzzy linguistic Hamy mean (WHFLHM) operator, hesitant fuzzy linguistic dual Hamy mean (HFLDHM) operator, and weighted hesitant fuzzy linguistic dual Hamy mean (WHFLDHM) operator are proposed. Besides, several paramount theorems and particular cases of these aggregation operators are investigated in detail, and then a novel MADM approach is presented by using the proposed aggregation operators. Ultimately, a practical example is utilized to manifest the effectiveness and practicability of the propounded method.

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Bachir, Ahmed, et Abdelkader Segres. « Asymmetric Putnam-Fuglede Theorem for (n,k)-Quasi-∗-Paranormal Operators ». Symmetry 11, n^o 1 (8 janvier 2019) : 64. http://dx.doi.org/10.3390/sym11010064.

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T ∈ B ( H ) is said to be ( n , k ) -quasi-∗-paranormal operator if, for non-negative integers k and n, ∥ T ∗ ( T k x ) ∥ ( 1 + n ) ≤ ∥ T ( 1 + n ) ( T k x ) ∥ ∥ T k x ∥ n ; for all x ∈ H . In this paper, the asymmetric Putnam-Fuglede theorem for the pair ( A , B ) of power-bounded operators is proved when (i) A and B ∗ are n-∗-paranormal operators (ii) A is a ( n , k ) -quasi-∗-paranormal operator with reduced kernel and B ∗ is n-∗-paranormal operator. The class of ( n , k ) -quasi-∗-paranormal operators properly contains the classes of n-∗-paranormal operators, ( 1 , k ) -quasi-∗-paranormal operators and k-quasi-∗-class A operators. As a consequence, it is showed that if T is a completely non-normal ( n , k ) -quasi-∗-paranormal operator for k = 0 , 1 such that the defect operator D T is Hilbert-Schmidt class, then T ∈ C 10 .

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Yang, Wei, et Yongfeng Pang. « T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making ». Mathematics 10, n^o 6 (19 mars 2022) : 988. http://dx.doi.org/10.3390/math10060988.

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To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the T-spherical fuzzy interaction geometric Bonferroni mean operator are first defined. Then, the T-spherical fuzzy interaction weighted Bonferroni mean operator and the T-spherical fuzzy weighted interaction geometric Bonferroni mean operator are defined. Based on the Dombi mean and the Bonferroni mean operator, some T-Spherical fuzzy Dombi Bonferroni mean operators are proposed, including the T-spherical fuzzy Dombi Bonferroni mean operator, T-spherical fuzzy geometric Dombi Bonferroni mean operator, T-spherical fuzzy weighted Dombi Bonferroni mean operator and the T-spherical fuzzy weighted geometric Dombi Bonferroni mean operator. The properties of these proposed operators are studied. An attribute weight determining method based on the T-spherical fuzzy entropy and symmetric T-spherical fuzzy cross-entropy is developed. A new decision making method based on the proposed T-Spherical fuzzy Bonferroni mean operators is proposed for partly known or completely unknown attribute weight situations. The furniture procurement problem is presented to illustrate the new algorithm, and some comparisons are made.

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Yao, Tianxiang, et Hong Gao. « Studies on the properties of buffer operators ». Grey Systems : Theory and Application 8, n^o 1 (5 février 2018) : 14–24. http://dx.doi.org/10.1108/gs-08-2017-0030.

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Purpose Buffer operators can be utilized to improve the smooth degree of the raw data sequence, and to increase the simulation accuracy of the model. The purpose of this paper is to analyze the cause of increase in the simulation accuracy of the buffer operator. Design/methodology/approach This paper probed into the modeling mechanism of several typical buffer operators such as the arithmetic buffer operators, the buffer operators with monotonic function and weighted buffer operators. The paper also gives an example of the buffer operator sequence. Findings The results indicate that after applying an infinite buffer operator, whether the authors adopt a weakening buffer operator or a strengthen buffer operator, the raw sequence can be changed into a constant sequence. Because the discrete GM(1,1) model can completely simulate constant sequence, the simulation accuracy is 100 percent. Because the discrete GM(1,1) model is the accurate form of the GM(1,1) model, after applying an infinite buffer operator, the GM(1,1) model can have a very high simulation accuracy. The buffer operator model can increase the simulation accuracy of both the GM(1,1) model and the discrete GM(1,1) model. Originality/value The paper analyses the cause of increasing simulation accuracy of the buffer operator model. The paper may indicate that possible results can be studied in the future. All the buffer operator models have similar properties. After applying an infinite buffer operator, the raw sequence can be changed into a constant sequence. A fixed-point axiom may be the basic cause.

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MERIGÓ, JOSÉ M., et MONTSERRAT CASANOVAS. « THE UNCERTAIN GENERALIZED OWA OPERATOR AND ITS APPLICATION TO FINANCIAL DECISION MAKING ». International Journal of Information Technology & ; Decision Making 10, n^o 02 (mars 2011) : 211–30. http://dx.doi.org/10.1142/s0219622011004300.

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We introduce the uncertain generalized OWA (UGOWA) operator. This operator is an extension of the OWA operator that uses generalized means and uncertain information represented as interval numbers. By using UGOWA, it is possible to obtain a wide range of uncertain aggregation operators such as the uncertain average (UA), the uncertain weighted average (UWA), the uncertain OWA (UOWA) operator, the uncertain ordered weighted geometric (UOWG) operator, the uncertain ordered weighted quadratic averaging (UOWQA) operator, the uncertain generalized mean (UGM), and many specialized operators. We study some of its main properties, and we further generalize the UGOWA operator using quasi-arithmetic means. The result is the Quasi-UOWA operator. We end the paper by presenting an application to a decision-making problem regarding the selection of financial strategies.

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Kanguzhin, Baltabek, et Bakytbek Koshanov. « Uniqueness Criteria for Solving a Time Nonlocal Problem for a High-Order Differential Operator Equation l(·)—A with a Wave Operator with Displacement ». Symmetry 14, n^o 6 (14 juin 2022) : 1239. http://dx.doi.org/10.3390/sym14061239.

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This article presents a criterion for the uniqueness of the solution of a problem nonlocal in time for a differential-operator equation with a symmetric operator part on space variables. The symmetry of the operator part of the operator-differential equation guarantees the existence of good basic properties of its system of root elements. The spectral properties of the symmetric operator part make it possible not only to prove the necessity of the criterion formulated by us, but also to substantiate their sufficiency. In contrast to previously known works, in this work the semiboundedness of the symmetric part of the differential-operator equation can be violated. In this article, the differential-operator equation is represented as the difference of two commuting operators. The uniqueness of the solution is guaranteed when the spectra of the commuting operators do not intersect. It is important that only one of the operators should be symmetrical.

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Gu, Juan. « Infinite Matrix Transformation of a Class of Operator ». Advanced Materials Research 542-543 (juin 2012) : 1371–75. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.1371.

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On the basis of the uniform convergence theory, this paper discusses the infinite matrix transformation of a class of operator which includes the whole linear operators、homogeneous operator and the many nonlinear operators, and then has obtained the conclusion of the summability of nonlinear operator.

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Kalidolday, A. H., et E. D. Nursultanov. « Interpolation of nonlinear integral Urysohn operators in net spaces ». BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 105, n^o 1 (30 mars 2022) : 66–73. http://dx.doi.org/10.31489/2022m1/66-73.

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In this paper, we study the interpolation properties of the net spaces N_p,q(M), in the case when M is a sufficiently general arbitrary system of measurable subsets from R^n. The integral Urysohn operator is considered. This operator generalizes all linear, integral operators, and non-linear integral operators. The Urysohn operator is not a quasilinear or subadditive operator. Therefore, the classical interpolation theorems for these operators do not hold. A certain analogue of the Marcinkiewicz-type interpolation theorem for this class of operators is obtained. This theorem allows to obtain, in a sense, a strong estimate for Urysohn operators in net spaces from weak estimates for these operators in net spaces with local nets. For example, in order for the Urysohn integral operator in a net space, where the net is the set of all balls in R^n, it is sufficient for it to be of weak type for net spaces, where the net is concentric balls.

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Khan, Qaisar, Nasruddin Hassan et Tahir Mahmood. « Neutrosophic Cubic Power Muirhead Mean Operators with Uncertain Data for Multi-Attribute Decision-Making ». Symmetry 10, n^o 10 (28 septembre 2018) : 444. http://dx.doi.org/10.3390/sym10100444.

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The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) operator, the power Muirhead mean (PMM) operator is developed and is scrutinized under NC information. To manage the problems upstretched, some new NC aggregation operators, such as the NC power Muirhead mean (NCPMM) operator, weighted NC power Muirhead mean (WNCPMM) operator, NC power dual Muirhead mean (NCPMM) operator and weighted NC power dual Muirhead mean (WNCPDMM) operator are proposed and related properties of these proposed aggregation operators are conferred. The important advantage of the developed aggregation operator is that it can remove the effect of awkward data and it considers the interrelationship among aggregated values at the same time. Furthermore, a novel multi-attribute decision-making (MADM) method is established over the proposed new aggregation operators to confer the usefulness of these operators. Finally, a numerical example is given to show the effectiveness of the developed approach.

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Benson, N., P. Sugiono et P. Youderian. « DNA sequence determinants of lambda repressor binding in vivo. » Genetics 118, n^o 1 (1 janvier 1988) : 21–29. http://dx.doi.org/10.1093/genetics/118.1.21.

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Abstract The critical operator determinants for lambda repressor recognition have been defined by analyzing the binding of wild-type repressor to a set of mutant operators in vivo. Base pair substitutions at six positions within the lambda operator half-site impair binding severely, and define these base pairs as critical for operator function. One mutant operator binds repressor better than the consensus operator, and is a superoperator. The model proposed by M. Lewis in 1983 for the binding of lambda repressor to its operator accurately predicts the observed operator requirements for binding in vivo, with several minor exceptions. The order of affinities of the six natural lambda operators has also been determined.

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Wei, Guiwu, et Mao Lu. « Pythagorean Hesitant Fuzzy Hamacher Aggregation Operators in Multiple-Attribute Decision Making ». Journal of Intelligent Systems 28, n^o 5 (17 octobre 2017) : 759–76. http://dx.doi.org/10.1515/jisys-2017-0106.

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Abstract The Hamacher product is a t-norm and the Hamacher sum is a t-conorm. They are good alternatives to the algebraic product and the algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average operator, Pythagorean hesitant fuzzy Hamacher weighted geometric operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric operator, Pythagorean hesitant fuzzy Hamacher hybrid average operator, and Pythagorean hesitant fuzzy Hamacher hybrid geometric operator. The prominent characteristics of these proposed operators are studied. Then, we utilize these operators to develop some approaches for solving the Pythagorean hesitant fuzzy multiple-attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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WEI, GUI-WU. « UNCERTAIN LINGUISTIC HYBRID GEOMETRIC MEAN OPERATOR AND ITS APPLICATION TO GROUP DECISION MAKING UNDER UNCERTAIN LINGUISTIC ENVIRONMENT ». International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, n^o 02 (avril 2009) : 251–67. http://dx.doi.org/10.1142/s021848850900584x.

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In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the special case of the ULHGM operator. The ULHGM operator generalizes both the ULWGM and ULOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWGM and ULHGM operators, we propose a practical method for multiple attribute group decision making with uncertain linguistic preference relations. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method.

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Ameen, Zanyar A., Tareq M. Al-shami, Abdelwaheb Mhemdi et Mohammed E. El-Shafei. « The Role of Soft θ -Topological Operators in Characterizing Various Soft Separation Axioms ». Journal of Mathematics 2022 (7 juillet 2022) : 1–7. http://dx.doi.org/10.1155/2022/9073944.

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This manuscript begins with an introduction to a soft θ -kernel operator. Then, the main properties and connections of this soft topological operator with other known soft topological operators are examined. We show that soft θ -kernel operator is weaker than soft kernel operator but stronger than soft θ -closure. Both soft θ -closure and soft θ -kernel operators are equivalent on soft compact sets. Furthermore, the stated operators are utilized to obtain several new characterizations of soft R i -topologies and soft T j -topologies, for i = 0,1 and j = 0,1,2 .

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Park, Jin Han, Jung Mi Park, Young Chel Kwun et Ja Hong Koo. « Induced Power Aggregation Operators and their Applications in Group Decision Making ». Applied Mechanics and Materials 404 (septembre 2013) : 672–77. http://dx.doi.org/10.4028/www.scientific.net/amm.404.672.

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The power ordered weighted average (POWA) operator and the power ordered weighted geometric (POWG) operator are the two nonlinear weighted average aggregation tools whose weighting vectors depend on their input arguments. In this paper, as a more general type of POWA and POWG operators, respectively, we develop two induced power aggregation operators called the induced POWA (IPOWA) operator and the induced POWG (IPOWG) operator, respectively, and establish various properties of these induced power aggregation operators, and then apply them, respectively, to develop an approach to multiple attribute group decision making.

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Finta, Zoltan. « A generalization of the Lupaș $q$-analogue of the Bernstein operator ». Journal of Numerical Analysis and Approximation Theory 45, n^o 2 (9 décembre 2016) : 147–62. http://dx.doi.org/10.33993/jnaat452-1090.

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We introduce a Stancu type generalization of the Lupaș $q$-analogue of the Bernstein operator via the parameter $\alpha$. The construction of our operator is based on the generalization of Gauss identity involving $q$-integers. We establish the convergence of our sequence of operators in the strong operator topology to the identity, estimating the rate of convergence by using the second order modulus of smoothness. For $\alpha$ and $q$ fixed, we study the limit operator of our sequence of operators taking into account the relationship between two consecutive terms of the constructed sequence of operators.

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