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Let ℓ be a Banach sequence space with a monotone norm in which the canonical system (en) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between ℓ -Köthe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Köthe matrices when every continuous linear operator between ℓ -Köthe spaces is bounded. As an application, we observe that the existence of an unbounded operator between ℓ -Köthe spaces, under a splitting condition, causes the existence of a common basic subspace. [ABSTRACT FROM AUTHOR]

This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by reducing them to different but isomorphic interpretations of an abstract notion, viz. the universal property, which is based on a pair of axioms. [ABSTRACT FROM AUTHOR]

In this short note we indicate some improvement of an article published in this journal by Crespo, Ivorra and Ramos 6. The techniques used are connected with several smoothing effects associated with linear partial differential operators which give rise to some accretive operators in L¹(Ω), as well as with some H²(Ω) estimates independent on time. [ABSTRACT FROM AUTHOR]

The abstract results and applications presented in 'Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941-959, are not correct. Moreover, the class of differential control problems studied in [1] is not H-controllable. [ABSTRACT FROM AUTHOR]

We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of [ABSTRACT FROM AUTHOR]

In this paper, we studied the stability of the Cauchy problem for a class of first-order linear quasi-periodically forced PDEs on the m-dimensional torus: {∂tu + (ξ + f(x, ωt, ξ)) · ∂xu = 0, u(x, 0) = u0(x), where ξ ∈ ℝm, x ∈ Tm, ω ∈ ℝd, in the case of multidimensional Liouvillean forced frequency. We proved that for each compact set O ∈ ℝm there exists a Cantor subset Oγ of O with positive Lebesgue measure such that if ξ ∈ Oγ, then for a perturbation f being small in some analytic Sobolev norm, there exists a bounded and invertible quasi-periodic family of linear operator Ψ(ωt), such that the above PDEs are reduced by the transformation v := Ψ(ωt)−1 [u] into the following PDE: ∂tv + (ξ + m∞(ωt)) · ∂xv = 0, provided that the forced frequency ω ∈ ℝd possesses finite uniform Diophantine exponent, which allows Liouvillean frequency. The reducibility can immediately cause the stability of the above Cauchy problem, that is, the analytic Sobolev norms of the Cauchy problem are controlled uniformly in time. The proof is based on a finite dimensional Kolmogorov-Arnold-Moser (KAM) theory for quasi-periodically forced linear vector fields with multidimensional Liouvillean forced frequency. As we know, the results on Liouvillean frequency existing in the literature deal with two-dimensional frequency and exploit the theory of continued fractions to control the small divisor problem. The results in this paper partially extend the analysis to higher-dimensional frequency and impose a weak nonresonance condition, i.e., the forced frequency ω possesses finite uniform Diophantine exponent. Our result can be regarded as a generalization of analytic cases in the work [R. Feola, F. Giuliani, R. Montalto and M, Procesi, Reducibility of first order linear operators on tori via Moser’s theorem, J. Funct. Anal., 2019] from Diophantine frequency to Liouvillean frequency. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide new results on the Wolf and Schechter essential pseudospectra of bounded linear operators on a Banach space. More precisely, we characterize the Wolf and Schechter essential pseudospectra by using the notion of Fredholm perturbation. Also, we state the condition under which the Wolf (respectively, Schechter) essential pseudospectrum of two different bounded linear operators coincides. Furthermore, we give some characterizations of the Wolf and Schechter essential pseudospectra of 3 × 3 upper triangular block operator matrices. [ABSTRACT FROM AUTHOR]

Let X be a complex Banach space, and denote by \mathcal {B}(X) the algebra of all bounded linear operators on X. Let C,D\in \mathcal {B} \left (X\right) be fixed operators. In this paper, we characterize linear, continuous and bijective maps \varphi and \psi on \mathcal {B}\left (X\right) for which there exist invertible operators T_0, W_0 \in \mathcal { B}(X) such that \varphi (T_0), \psi (W_0) \in \mathcal {B}(X) are both invertible, having the property that \varphi \left (A\right) \psi \left (B\right) =D in \mathcal {B}(X) whenever AB=C in \mathcal {B}(X). As a corollary, we deduce the form of linear, bijective and continuous maps \varphi on \mathcal {B}(X) having the property that \varphi \left (A\right) \varphi \left (B\right) =D in \mathcal {B}(X) whenever AB=C. [ABSTRACT FROM AUTHOR]

Abstract: In this note, we will modify several gaps in Gurudwan and Sharma [N. Gurudwan, B.K. Sharma, Convergence theorem for the common solution for a finite family of -strongly accretive operator equations, Appl. Math. Comput. 217 (2011) 6748–6754]. [Copyright &y& Elsevier]

In this paper, we investigate various stabilisation problems of a hybrid system of elasticity, consisting of a thin tape, which moves axially between two sets of rollers. We present a control solution, which works simultaneously, for three variants of the tape model. In particular, we design boundary feedback control laws via Lyapunov's second method. The resulting closed-loop system for the general case is then analysed, where we prove the existence and uniqueness of solution using the semigroup theory of linear operators; furthermore, we prove the exponential decay of the solution via a frequency domain theorem. The stabilisation of the two other special cases is derived implicitly from the general case proofs presented in the paper. Finally, the paper is concluded by presenting computer simulations to support the theoretical results. [ABSTRACT FROM AUTHOR]

Our paper introduces a new linear operator using the convolution between a Mittag Leffler Function and basic hypergeometric function. Use of the linear operator creates a new class of meromorphic functions defined in the punctured open unit disk. Consequently, the paper examines different aspects Apps and assets like, extreme points, coefficient inequality, growth and distortion. In conclusion, the work discusses modified Hadamard product and closure theorems. [ABSTRACT FROM AUTHOR]

The present paper deals with the approximation properties of the linear positive operators, including Δh -Gould-Hopper Appell polynomials. We investigate some theorems for convergence of the operators and their approximation degrees with the help of the classical approach, Peetre's K-functional, Lipschitz class and Voronovskajatype theorem. In the last section of the paper, we introduce the Kantorovich form of the operators and examine the approximation degree. [ABSTRACT FROM AUTHOR]

The present paper continues investigation of narrow operators on complex vector lattices started in a recent paper by Dzhusoeva, Huang, Pliev and Sukochev. We answer their questions and strengthen one of their main results by proving that the extension T_{\Bbb {C}}\colon E_{\Bbb {C}}\to F_{\Bbb {C}} of a linear operator T \colon E \to F acting from a Dedekind complete real Riesz space E to a real Banach lattice F to their complexifications is narrow if and only if T is. [ABSTRACT FROM AUTHOR]

In this paper, we study a connection between the operator Riccati equation S′(x) = KS(x) + S(x)K - 2S(x)KS(x), x ∈ R, and the set of reflectionless Schr¨odinger operators with operator-valued potentials. Here K ∈ B(H), K > 0 and S: R → B(H), where B(H) is the Banach algebra of all linear continuous operators acting in a separable Hilbert space H. Let S+(K) be the set of all solutions S of the Riccati equation satisfying the conditions 0 < S(0) < I and S′(0) ≥ 0, with I being the identity operator in H. We show that every solution S ∈ S+(K) generates a reflectionless Schr¨odinger operator with some potential q that is an analytic function in the strip... [ABSTRACT FROM AUTHOR]

Consider an infinite-dimentional Banach space denoted as X, and designate ∂(X) as the algebra of all bounded linear operators on X. Moreover, let s (A) denote the spectrum of ..., and ...(A)) indicate the boundary of s (A). A map ... is termed a ρ-spectrum if ... (A) for all A ... In this paper, we characterize all surjective maps f1 and f2 on ρ(X) satisfying ... = (AB) for all A,B(X). [ABSTRACT FROM AUTHOR]

Mapping Travel: The Origins and Conventions of Western Journey Maps: By Jordana Dym. Journey maps are distinct from road maps, Dym argues, because they attend primarily to 'the personal and individual rather than the permanent and collective'. She highlights William Wey as a crucial figure here, not because he made maps - although he did annotate a map of Palestine with his list of places - but rather because he began to imagine the relationship between personal travel and the map. [Extracted from the article]

Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor's formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas. These include Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorems based on Hermite interpolation on two double knots. [ABSTRACT FROM AUTHOR]

This paper studies several problems related to quadratic matrix inequalities (QMIs), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, or bounded or has a nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of "structured"" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMIs can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller and also leads to explicit formulas for data-guided feedback gains. [ABSTRACT FROM AUTHOR]

A study of the class \Delta consisting of topological \Delta-spaces was originated by Jerzy Ka̧kol and Arkady Leiderman [Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 86–99; Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 267–280]. The main purpose of this paper is to introduce and investigate new classes \Delta _2 \subset \Delta _1 properly containing \Delta. We observe that for every first-countable X the following equivalences hold: X\in \Delta _1 iff X\in \Delta _2 iff each countable subset of X is G_{\delta }. Thus, new proposed concepts provide a natural extension of the family of all \lambda-sets beyond the separable metrizable spaces. We prove that (1) A pseudocompact space X belongs to the class \Delta _1 iff countable subsets of X are scattered. (2) Every regular scattered space belongs to the class \Delta _2. We investigate whether the classes \Delta _1 and \Delta _2 are invariant under the basic topological operations. Similarly to \Delta, both classes \Delta _1 and \Delta _2 are invariant under the operation of taking countable unions of closed subspaces. In contrast to \Delta, they are not preserved by closed continuous images. Let Y be l-dominated by X, i.e. C_p(X) admits a continuous linear map onto C_p(Y). We show that Y \in \Delta _1 whenever X \in \Delta _1. Moreover, we establish that if Y is l-dominated by a compact scattered space X, then Y is a pseudocompact space such that its Stone–Čech compactification \beta Y is scattered. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the algebraic structure of 2 r 8 s -additive codes, where r and s are nonnegative integers, 2 (respectively, 8 ) denotes the finite field of order 2 (respectively, 8). We first give the generator polynomials of additive cyclic codes over 8 and then the generator polynomials of additive cyclic codes over 2 8 is also given. In addition, we introduce a linear map W : 2 8 → 2 , and study its properties. What's more, the dual of additive cyclic codes over 2 8 are investigated as well. And we get that the duals of any additive cyclic codes over 2 8 are also additive cyclic codes. Finally, separable 2 8 -additive cyclic codes are investigated. [ABSTRACT FROM AUTHOR]

In this article, the symmetric operator L corresponding to the boundary value problem is represented as the difference of two commuting operators A and  B.  The uniqueness of the solution is guaranteed if the spectra of the operators A and B do not intersect and the domain of the operator B is given by non-degenerate boundary conditions. In contrast to the existing papers, the criterion for the uniqueness of the boundary value problem formulated in this paper is satisfied even when the system of root functions of the operator B does not form a basis in the corresponding space. At the same time, only the closedness of the linear operator A is required. [ABSTRACT FROM AUTHOR]

In this paper we give an explicit description of linear maps preserving the Cullis determinant of rectangular matrices of the size (n+1)×n. Unlike the result about the ordinary determinant, it appears that linear preservers of Cullis determinant can be singular. We provide the corresponding examples and characterize the case when these maps are non-singular. [ABSTRACT FROM AUTHOR]

In this paper we obtain several operator inequalities providing upper bounds for the Davis-Choi-Jensen's Difference Φ(f (A)) -- f (Φ (A)) for any convex function f : I → R, any selfadjoint operator A in H with the spectrum Sp (A) ⊂ I and any linear, positive and normalized map Φ : B (H) → B (K), where H and K are Hilbert spaces. Some examples of convex and operator convex functions are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we show that the cover ideals of Jahangir's graphs are normal, and also satisfy the (symbolic) (strong) persistence property. In addition, we determine when the unique homogeneous maximal ideal appears in the set of associated primes of powers of the cover ideals of Jahangir's graphs. [ABSTRACT FROM AUTHOR]

The emergence of deep learning has not only brought great changes in the field of image recognition, but also achieved excellent node classification performance in graph neural networks. However, the existing graph neural network framework often uses methods based on spatial domain or spectral domain to capture network structure features. This process captures the local structural characteristics of graph data, and the convolution process has a large amount of calculation. It is necessary to use multi-channel or deep neural network structure to achieve the goal of modeling the high-order structural characteristics of the network. Therefore, this paper proposes a linear graph neural network framework [Linear Graph Neural Network (LGNN)] with superior performance. The model first preprocesses the input graph, and uses symmetric normalization and feature normalization to remove deviations in the structure and features. Then, by designing a high-order adjacency matrix propagation mechanism, LGNN enables nodes to iteratively aggregate and learn the feature information of high-order neighbors. After obtaining the node representation of the network structure, LGNN uses a simple linear mapping to maintain computational efficiency and obtain the final node representation. The experimental results show that the performance of the LGNN algorithm in some tasks is slightly worse than that of the existing mainstream graph neural network algorithms, but it shows or exceeds the machine learning performance of the existing algorithms in most graph neural network performance evaluation tasks, especially on sparse networks. [ABSTRACT FROM AUTHOR]

Let D be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space. In this paper, we characterize the linear maps δ, τ: AlgD → AlgD satisfying δ(A)B+ Aτ(B) = 0 for any A, B ∈ AlgD with AB = 0. This result can be used to characterize linear maps derivable (centralized) at zero point and local centralizers on AlgD, respectively. [ABSTRACT FROM AUTHOR]

Let esv be the extended Schrödinger-Virasoro Lie algebra. In this paper, we consider the skew-symmetric biderivations of the extended Schrödinger-Virasoro Lie algebra. We prove that all biderivations of esv are inner. Based on this result, we show that all linear commuting maps on esv, which have the form ψ(x) = λx, are standard. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate some inequalities for positive linear maps on matrices. Moreover, we discuss lower bounds for the spread of nonnegative matrices which provides improvement over the existing bounds. [ABSTRACT FROM AUTHOR]

We propose necessary and sufficient conditions for the negativity of the two-point boundary value problem in the form of the Vallée-Poussin theorem about differential inequalities for the Hadamard fractional functional differential problem ... Here, the operator T:C→L∞ can be an operator with deviation (of delayed or advanced type), an integral operator or various linear combinations and superpositions. For example, the operator can be of the forms (Tx)(t)=q(t)x(t-τ(t)), (Tx)(t)=∫e1Q(t,s)x(θ(s))ds or (Tx)(t)=∫e1x(s)dsQ(t,s). We obtain explicit tests of negativity of Green's function in the form of algebraic inequalities. Our paper is the first one where a general form of the operator is considered with Hadamard fractional derivatives. [ABSTRACT FROM AUTHOR]

Let n ∈ N 0 , ψ be an analytic self-map on D and u be an analytic function on D. The single operator D u , ψ n acting on various spaces of analytic functions has been a subject of investigation for many years. It is defined as (D u , ψ n f) (z) = u (z) f (n) (ψ (z)) , f ∈ H (D) . However, the study of the operator P u → , ψ k , which represents a finite sum of these operators with varying orders, remains incomplete. The boundedness, compactness and essential norm of the operator P u → , ψ k on the Bloch space are investigated in this paper, and several characterizations for these properties are provided. [ABSTRACT FROM AUTHOR]

In this paper, we have established Cosine Trigonometric Operational Law (CTOL) and constructed Cosine Trigonometric Neutrosophic Weighted Averaging (CT-NWA) operator in the domain of generalized neutrosophic environment, which has been endorsed in a Multi-Criteria Group Decision Making (MCGDM) technique to select the best Anti-Pegasus software. In this study, the expertize recommendations and public opinion are well taken in context of debatable Pegasus issue in the Indian political, bureaucratic and democratic aspects. The problem has been addressed and resolved by using the integrated methodology of Analytical Network Process (ANP) and Evaluation based on Distance from Average Solution (EDAS) strategies. Here, we have optimized the weight factors and the gradation values of the decision makers as well as the sub-criteria of each criterion using Linear Programming (LP) model. Finally, we have performed the comparative analysis from various aspects to justify the reliability of our results. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study a sequence of linear and positive operators which was introduced by A. Lupas. First, we obtain estimate of moments of the operators and then prove a basic convergence theorem for simultaneous approximation. Further, we find error in approximation in terms of modulus of continuity of function. Finally, we establish a Voronovskaja asymptotic formula for linear combination of the above operators. [ABSTRACT FROM AUTHOR]

This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails safely and fails due to the malfunction of the robot. Using the C 0 – semigroups theory of linear operators, we first show that the system has a unique non-negative, time-dependent solution. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution. In addition, we study the asymptotic behavior of some time-dependent reliability indices and present a numerical example demonstrating the effects of different parameters on the system. [ABSTRACT FROM AUTHOR]

Let $ n \geq ~2 $ n ≥ 2 be a natural number, and denote by $ \mathcal {M}_{n} $ M n the algebra of all $ n \times n $ n × n matrices over an algebraically closed field $ \mathbb {F} $ F of zero characteristic. Let also $ K_{1} $ K 1 and $ K_{2} $ K 2 be two non-empty proper subsets of $ \mathbb {F} $ F . In this paper, we characterize linear maps φ on $ \mathcal {M}_{n} $ M n having the property that, for every $ T \in \mathcal {M}_{n} $ T ∈ M n , the spectrum of T is a subset of $ K_1 $ K 1 if and only if the spectrum of $ \varphi (T) $ φ (T) is a subset of $ K_2 $ K 2 . We obtain a similar caracterization for the case when $ K_{1} $ K 1 and $ K_{2} $ K 2 have both at most n elements, working with the equality of the spectrum to the fixed subsets instead of the inclusion. [ABSTRACT FROM AUTHOR]

Let $ (X, T) $ (X , T) be a linear dynamical system defined on a Banach space X and $ {L_T}:{K_{{X^ * }}} \to {K_{{X^ * }}} $ L T : K X ∗ → K X ∗ be defined by $ {L_T}S = TS $ L T S = TS , where $ {K_{{X^ * }}} = \overline {span\{ \langle \cdot,{y^ * } \rangle x:{y^ * } \in {X^ * },x \in X\} } $ K X ∗ = span { 〈 ⋅ , y ∗ 〉 x : y ∗ ∈ X ∗ , x ∈ X } ¯ . This paper first obtains the equivalence of the (syndetically) weak multi-sensitive compactness between $ (X, T) $ (X , T) and $ ({K_{{X^ * }}},{L_T}) $ (K X ∗ , L T). Then, it is shown that (1) there exists a non-mean-sensitive linear dynamical system $ (X ,T) $ (X , T) satisfying that $ ({K_{{X^ * }}},{L_T}) $ (K X ∗ , L T) is mean sensitive; (2) There exists a non-topologically-transitive and weakly multi-sensitive compact system, which is not syndetically weakly multi-sensitive compact. Besides, it is proved that every weakly mixing linear dynamical system defined on a separable Banach space is weakly multi-sensitive compact. [ABSTRACT FROM AUTHOR]

Collage Theorem provides a bound for the distance between an element of a given space and a fixed point of a self-map on that space, in terms of the distance between the point and its image. We give in this paper some results of Collage type for Reich mutual contractions in b-metric and strong b-metric spaces. We give upper and lower bounds for this distance, in terms of the constants of the inequality involved in the definition of the contractivity. Reich maps contain the classical Banach contractions as particular cases, as well as the maps of Kannan type, and the results obtained are very general. The middle part of the article is devoted to the invertibility of linear operators. In particular we provide criteria for invertibility of operators acting on quasi-normed spaces. Our aim is the extension of the Casazza-Christensen type conditions for the existence of inverse of a linear map defined on a quasi-Banach space, using different procedures. The results involve either a single map or two operators. The latter case provides a link between the properties of both mappings. The last part of the article is devoted to study the construction of fractal curves in Bochner spaces, initiated by the first author in a previous paper. The objective is the definition of fractal curves valued on Banach spaces and Banach algebras. We provide further results on the fractal convolution of operators, defined in the same reference, considering in this case the nonlinear operators. We prove that some properties of the initial maps are inherited by their convolutions, if some conditions on the elements of the associated iterated function system are satisfied. In the last section of the paper we use the invertibility criteria given before in order to obtain perturbed fractal spanning systems for quasi-normed Bochner spaces composed of Banach-valued integrable maps. These results can be applied to Lebesgue spaces of real valued functions as a particular case. [ABSTRACT FROM AUTHOR]

In this paper, we prove some q-numerical radius power inequalities for a product of operators on a complex Hilbert space. We introduce also the notion of the q-center for bounded operators, and we give the relationship between this q-center, the q-numerical radius and the center of the q -numerical range. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the problem of stabilization of a degenerate parabolic equation with a Dirichlet control, evolving in bounded domain 퓞 ⊂ ℝd, d ≥ 2. We apply the proportional control design technique based on the spectrum of the linear operator which governs the evolution equation. The stabilizing feedback control, we design here, is linear, of finite-dimensional structure, easily manageable from the computational point of view. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some Korovkin type approximation theorems for double sequences of positive linear operators on two-dimensional weighted spaces via statistical type convergence method with respect to power series method. Additionally, we calculate the rate of convergence. As an application, we provide an approximation using the generalization of Gadjiev-Ibragimov operators for Pp-statistical convergence. Our results are meaningful and stronger than those previously given for two-dimensional weighted spaces. [ABSTRACT FROM AUTHOR]

This paper concerns with the existence of radial solutions of the biharmonic elliptic equation ▵ 2 u = f (| x | , u , | ∇ u | , ▵ u) in an annular domain Ω = { x ∈ R N : r 1 < | x | < r 2 } ( N ≥ 2 ) with the boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : [ r 1 , r 2 ] × R × R + × R → R is continuous. Under certain inequality conditions on f involving the principal eigenvalue λ 1 of the Laplace operator − ▵ with boundary condition u | ∂ Ω = 0 , an existence result and a uniqueness result are obtained. The inequality conditions allow for f (r , ξ , ζ , η) to be a superlinear growth on ξ , ζ , η as | (ξ , ζ , η) | → ∞ . Our discussion is based on the Leray–Schauder fixed point theorem, spectral theory of linear operators and technique of prior estimates. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions for a changing-sign perturbation tempered fractional model with weak singularity which arises from the sub-diffusion study of anomalous diffusion in Brownian motion. By two-step substitution, we first transform the higher-order sub-diffusion model to a lower-order mixed integro-differential sub-diffusion model, and then introduce a power factor to the non-negative Green function such that the linear integral operator has a positive infimum. This innovative technique is introduced for the first time in the literature and it is critical for controlling the influence of changing-sign perturbation. Finally, an a priori estimate and Schauder's fixed point theorem are applied to show that the sub-diffusion model has at least one positive solution whether the perturbation is positive, negative or changing-sign, and also the main nonlinear term is allowed to have singularity for some space variables. [ABSTRACT FROM AUTHOR]

This study takes a detailed look at various inequalities related to the Euclidean operator radius. It examines groups of n-tuple operators, studying how they add up and multiply together. It also uncovers a unique power inequality specific to the Euclidean operator radius. The research broadens its scope to analyze how n-tuple operators, when used as parts of 2 × 2 operator matrices, illustrate inequalities connected to the Euclidean operator radius. By using the Euclidean numerical radius and Euclidean operator norm for n-tuple operators, the study introduces a range of new inequalities. These inequalities not only set limits for the addition, multiplication, and Euclidean numerical radius of n-tuple operators but also help in establishing inequalities for the Euclidean operator radius. This process involves carefully examining the Euclidean numerical radius inequalities of 2 × 2 operator matrices with n-tuple operators. Additionally, a new inequality is derived, focusing specifically on the Euclidean operator norm of 2 × 2 operator matrices. Throughout, the research keeps circling back to the idea of finding and understanding symmetries in linear operators and matrices. The paper highlights the significance of symmetry in mathematics and its impact on various mathematical areas. [ABSTRACT FROM AUTHOR]

The Foguel operator is defined as FT = [ S* T 0 S ], where S is the right shift on a Hilbert space H and T is an arbitrary bounded linear operator acting on H. Obviously, the numerical range W(F0) of FT with T = 0 is the open unit disk, and it was suggested by Gau, Wang and Wu in their Linear Algebra and Applications (2021) paper that W(FaI) for non-zero a ∈ C might be an elliptical disk. In this paper, we described W(FaI) explicitly and, as it happens, it is not. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the non-autonomous stochastic evolution equations of parabolic type with nonlinear noise and nonlocal initial conditions in Hilbert spaces, where the operators in linear part depend on time tt and generate an noncompact evolution family. New existence result of mild solutions is established under some weaker growth and measure of noncompactness conditions on nonlinear functions and nonlocal term. The discussions are based on Sadovskii's fixed-point theorem as well as the theory of evolution family. At last, as a sample of application, the obtained abstract result is applied to a class of non-autonomous stochastic partial differential equations of parabolic type with nonlocal initial conditions. The result obtained in this paper is a supplement to the existing literature and essentially extends some existing results in this area. [ABSTRACT FROM AUTHOR]

In this paper, we show that every continuous linear map between unital C*-algebras is skew Lie triple derivable at the identity is a C*-derivation and that every continuous linear map between unital C*-algebras which is a skew Lie triple homomorphism at the identity is a Jordan *-homomorphism. [ABSTRACT FROM AUTHOR]

According to the Weierstrass Approximation Theorem, any continuous function on the closed and bounded interval can be approximated by polynomials. A constructive proof of this theorem uses the so-called Bernstein polynomials. For the approximation of integrable functions, we may consider Kantorovich operators as certain modifications for Bernstein polynomials. In this paper, we investigate the behaviour of Kantorovich operators in Lebesgue spaces. We first give an alternative proof of the uniform boundedness of Kantorovich operators in Lebesgue spaces by using the Riesz-Thorin Interpolation Theorem. In addition, we examine the convergence of Kantorovich operators in the space of essentially bounded functions. We also give an example related to the rate of convergence of Kantorovich operators in a subspace of Lebesgue spaces. [ABSTRACT FROM AUTHOR]

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq equations that also has application to numerical methods. The phase averaging technique, well-known in dynamical systems theory, relies on a mapping using the exponential operator, and then an averaging over the phase. The exponential operator has connections to the Craya–Herring basis pioneered by Jack Herring to study the fluid dynamics of oscillatory, nonlinear fluid dynamics. In this paper, we perform numerical experiments to study the effect of this averaging technique on the time evolution of the solution. We explore its potential as a definition for mean flows. We also show that, as expected from theory, the phase-averaging method can reduce the magnitude of the time rate of change in the PDEs, making them potentially suitable for time stepping methods. [ABSTRACT FROM AUTHOR]

The authors of the present paper previously proved the Ulam stability for the n-th-order linear differential operator with constant coefficients. They obtained its best Ulam constant for the case of distinct roots of the characteristic equation. However, a complete answer to the problem of the best Ulam constant was later obtained only for the second-order linear differential operator. This paper deals with the Ulam stability of the third-order linear differential operator with constant coefficients acting in a Banach space. The paper's main purpose is to obtain the best Ulam constant of this operator, thus completing the previous research in the field. [ABSTRACT FROM AUTHOR]

In this paper, we present some further refinements of the Tan-Xie inequality for sector matrices and its applications due to Nasiri and Furuichi [J. Math. Inequal., 15 (2021), 1425-1434]. [ABSTRACT FROM AUTHOR]

In this paper, we characterize bounded linear operators A,B on a complex Hilbert space such that inf λ∈C ||A+B-λ I|| = inf λ∈C ||A-λ I||+ inf λ∈C ||B-λ I||, where I is the identity operator. We also establish some inequalities satisfied by the distance from scalar operators for products of two complex Hilbert space operators. [ABSTRACT FROM AUTHOR]