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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]

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]

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]

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]

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]

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]

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]

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]

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]

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 establish a new concentration inequality and almost complete convergence of the value of the process of autoregressive Hilbertian of order one (ARH (1)), which directly stems from works of Serge Guillas, Denis Bosq, that is defined by Xt = ρ(Xt-1) + ζt; t ε ... where the random variables are all Hilbertian, ρ is a linear operator on a space of separable Hilbert and ζt which constitute a widely orthant dependent error (WOD, in short) after recalling some results on the finite-dimensional model of this type, we introduce the mathematical and statistical tools which will be used afterwards. Then we build an estimator of the operator and we establish its asymptotic properties. [ABSTRACT FROM AUTHOR]

From the previous work, when solving the LQ optimal control problem with random coefficients (SLQ, for short), it is remarkably shown that the solution of the backward stochastic Riccati equations is not regular enough to guarantee the robustness of the feedback control. As a generalization of SLQ, interesting questions are, "how about the situation in the differential game?", "will the same phenomenon appear in SLQ?". This paper will provide the answers. In this paper, we consider a closed-loop two-person zero-sum LQ stochastic differential game with random coefficients (SDG, for short) and generalize the results of Lü–Wang–Zhang into the stochastic differential game case. Under some regularity assumptions, we establish the equivalence between the existence of the robust optimal feedback control strategy operators and the solvability of the corresponding backward stochastic Riccati equations, which leads to the existence of the closed-loop saddle points. On the other hand, the problem is not closed-loop solvable if the solution of the corresponding backward stochastic Riccati equations does not have the needed regularity. [ABSTRACT FROM AUTHOR]

In this paper, a modification of general linear positive operators introduced by Ibragimov and Gadjiev in 1970 is constructed. It is shown that this modification preserves exponential mappings and also contains modified Bernstein-, Szász- and Baskakov-type operators as special cases. The convergence properties of corresponding operators on [ 0 , ∞) and in exponentially weighted spaces are investigated. Finally, the quantitative Voronovskaja theorem in terms of modulus of continuity for functions having exponential growth is examined. [ABSTRACT FROM AUTHOR]

In this paper, we introduced double cyclic codes over Rr × Rs, where R = Z2 + uZ2 = {0, 1, u, 1 + u} is the ring with four elements and u² = 0. We first determined the generator polynomials of R-double cyclic codes for odd integers r and s, then gave the generators of duals of free double cyclic codes over Rr × Rs. By defining a linear Gray map, we looked at the binary images of R-double cyclic codes and gave several examples of optimal parameter binary linear codes obtained from R-double cyclic codes. Moreover, we studied self-dual R-double cyclic codes and presented an example of a self-dual R-double cyclic code. [ABSTRACT FROM AUTHOR]

In this paper, we study a Riemann-Liouville-type fractional Riemann-Stieltjes integral boundary value problem under some conditions regarding the spectral radius of the relevant linear operator. The existence of nontrivial solutions is obtained using topological degree, and our results improve and generalize some results in the literature. [ABSTRACT FROM AUTHOR]

The conventional approach of the local convergence analysis of an iterative method on R m , with m a natural number, depends on Taylor series expansion. This technique often requires the calculation of high-order derivatives. However, those derivatives may not be part of the proposed method(s). In this way, the method(s) can face several limitations, particularly the use of higher-order derivatives and a lack of information about a priori computable error bounds on the solution distance or uniqueness. In this paper, we address these drawbacks by conducting the local convergence analysis within the broader framework of a Banach space. We have selected an important family of high convergence order methods to demonstrate our technique as an example. However, due to its generality, our technique can be used on any other iterative method using inverses of linear operators along the same line. Our analysis not only extends in R m spaces but also provides convergence conditions based on the operators used in the method, which offer the applicability of the method in a broader area. Additionally, we introduce a novel semilocal convergence analysis not presented before in such studies. Both forms of convergence analysis depend on the concept of generalized continuity and provide a deeper understanding of convergence properties. Our methodology not only enhances the applicability of the suggested method(s) but also provides suitability for applied science problems. The computational results also support the theoretical aspects. [ABSTRACT FROM AUTHOR]

Mechanized harvesting is the key technology to solving the high cost and low efficiency of manual harvesting, and the key to realizing mechanized harvesting lies in the accurate and fast identification and localization of targets. In this paper, a lightweight YOLOv5s model is improved for efficiently identifying grape fruits and stems. On the one hand, it improves the CSP module in YOLOv5s using the Ghost module, reducing model parameters through ghost feature maps and cost-effective linear operations. On the other hand, it replaces traditional convolutions with deep convolutions to further reduce the model's computational load. The model is trained on datasets under different environments (normal light, low light, strong light, noise) to enhance the model's generalization and robustness. The model is applied to the recognition of grape fruits and stems, and the experimental results show that the overall accuracy, recall rate, mAP, and F1 score of the model are 96.8%, 97.7%, 98.6%, and 97.2% respectively. The average detection time on a GPU is 4.5 ms, with a frame rate of 221 FPS, and the weight size generated during training is 5.8 MB. Compared to the original YOLOv5s, YOLOv5m, YOLOv5l, and YOLOv5x models under the specific orchard environment of a grape greenhouse, the proposed model improves accuracy by 1%, decreases the recall rate by 0.2%, increases the F1 score by 0.4%, and maintains the same mAP. In terms of weight size, it is reduced by 61.1% compared to the original model, and is only 1.8% and 5.5% of the Faster-RCNN and SSD models, respectively. The FPS is increased by 43.5% compared to the original model, and is 11.05 times and 8.84 times that of the Faster-RCNN and SSD models, respectively. On a CPU, the average detection time is 23.9 ms, with a frame rate of 41.9 FPS, representing a 31% improvement over the original model. The test results demonstrate that the lightweight-improved YOLOv5s model proposed in the study, while maintaining accuracy, significantly reduces the model size, enhances recognition speed, and can provide fast and accurate identification and localization for robotic harvesting. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions Τ J (α i) . Further, we obtain coefficient estimates, convex linear combinations, and radii of close-to-convexity, starlikeness, and convexity for functions f ∈ Τ J (α i) . In addition, we investigate the inclusion conditions of the Hadamard product and the integral transform. Finally, we determine the second Hankel inequality for functions belonging to this subclass. [ABSTRACT FROM AUTHOR]

In this paper, the Parseval K - g -frames are constructed from a given K - g -frame by scaling the elements of the K - g -frame with the help of diagonal operators, and these frames are named scalable K - g -frames. Also, we prove some properties of scalable K - g -frames and construct new scalable K - g -frames from a given K - g -frame. The necessary and sufficient conditions for a K - g -frame to be scalable are given. Further, equivalent conditions for the scalability of K - g -frames and the K -frames induced by K - g -frames are obtained. Finally, it is shown that the direct sum of two scalable K - g -frames is again a scalable K - g -frame for some suitable bounded linear operator K. [ABSTRACT FROM AUTHOR]

Minor perturbations to a linear operator may drastically change its spectrum, and hence the difficulty of deciding whether or not a numerically computed quantity is zero causes problems in spectral theory. The purpose of this expository paper is to illustrate such instability phenomena by some examples with Toeplitz-like operators and matrices. [ABSTRACT FROM AUTHOR]

Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines. [ABSTRACT FROM AUTHOR]

Let Cp be the Schatten p-class of ℓ2 for 1

In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems ( S p CNPP ) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the hardness of the Matrix Code Equivalence (MCE) problem for matrix codes endowed with the rank metric, and provide the first algorithms for solving it. We do this by making a connection to another well-known equivalence problem from multivariate cryptography—the Isomorphism of Polynomials (IP). Under mild assumptions, we give tight reductions from MCE to the homogenous version of the Quadratic Maps Linear Equivalence (QMLE) problem, and vice versa. Furthermore, we present reductions to and from similar problems in the sum-rank metric, showing that MCE is at the core of code equivalence problems. On the practical side, using birthday techniques known for IP, we present two algorithms: a probabilistic algorithm for MCE running in time q 2 3 (n + m) up to a polynomial factor, and a deterministic algorithm for MCE with roots, running in time q min { m , n , k } up to a polynomial factor. Lastly, to confirm these findings, we solve randomly-generated instances of MCE using these two algorithms. [ABSTRACT FROM AUTHOR]

When studying the iterates of certain positive linear operators, systems of linear equations are naturally involved. The last step in investigating the limit of such iterates is represented by a special kind of system of equations. Problems of this type involving several classical operators are studied in the literature. In this paper, we investigate the iterates of new positive linear operators and the corresponding systems of equations. To solve the system we use an iterative algorithm. The approximate solution is used in order to approximate the limit of the iterates of operators. [ABSTRACT FROM AUTHOR]

This paper defines and studies the σ type mixed Morrey spaces. Furthermore, we introduce the predual spaces of σ type mixed Morrey spaces to establish the extrapolation theorem. As applications of extrapolation theory, we character the BMO space in different ways. On the one hand, we character the BMO spaces by the new John-Nirenberg inequality in terms of σ type mixed Morrey spaces. On the other hand, we establish the characterization of BMO spaces by the boundedness of commutators of the singular integral operator on σ type mixed Morrey spaces. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of Kato chaos to linear dynamics and its induced dynamics. This paper investigates some properties of Kato chaos for a continuous linear operator T and its induced operators T ¯ . The main conclusions are as follows: (1) If a linear operator is accessible, then the collection of vectors whose orbit has a subsequence converging to zero is a residual set. (2) For a continuous linear operator defined on Fréchet space, Kato chaos is equivalent to dense Li–Yorke chaos. (3) Kato chaos is preserved under the iteration of linear operators. (4) A sufficient condition is obtained under which the Kato chaos for linear operator T and its induced operators T ¯ are equivalent. (5) A continuous linear operator is sensitive if and only if its inducing operator T ¯ is sensitive. It should be noted that this equivalence does not hold for nonlinear dynamics. [ABSTRACT FROM AUTHOR]

The application of a complex fuzzy logic system based on a linear conjunctive operator represents a significant advancement in the field of data analysis and modeling, particularly for studying physical scenarios with multiple options. This approach is highly effective in situations where the data involved is complex, imprecise and uncertain. The linear conjunctive operator is a key component of the fuzzy logic system used in this method. This operator allows for the combination of multiple input variables in a systematic way, generating a rule base that captures the behavior of the system being studied. The effectiveness of this method is particularly notable in the study of phenomena in the actual world that exhibit periodic behavior. The foremost aim of this paper is to contribute to the field of fuzzy algebra by introducing and exploring new concepts and their properties in the context of conjunctive complex fuzzy environment. In this paper, the conjunctive complex fuzzy order of an element belonging to a conjunctive complex fuzzy subgroup of a finite group is introduced. Several algebraic properties of this concept are established and a formula is developed to calculate the conjunctive complex fuzzy order of any of its powers in this study. Moreover, an important condition is investigated that determines the relationship between the membership values of any two elements and the membership value of the identity element in the conjunctive complex fuzzy subgroup of a group. In addition, the concepts of the conjunctive complex fuzzy order and index of a conjunctive complex fuzzy subgroup of a group are also presented in this article and their various fundamental algebraic attributes are explored structural. Finally, the conjunctive complex fuzzification of Lagrange's theorem for conjunctive complex fuzzy subgroups of a group is demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we consider general Markov chains with discrete time in an arbitrary measurable (phase) space. Markov chains are given by a classical transition function that generates a pair of conjugate linear Markov operators in a Banach space of measurable bounded functions and in a Banach space of bounded finitely additive measures. We study sequences of Cesaro means of powers of Markov operators on the set of finitely additive probability measures. It is proved that the set of all limit measures (points) of such sequences in the weak topology generated by the preconjugate space is non-empty, weakly compact, and all of them are invariant for this operator. We also show that the well-known Doeblin condition (D) for the ergodicity of a Markov chain is equivalent to condition (∗) : all invariant finitely additive measures of the Markov chain are countably additive, i.e., there are no invariant purely finitely additive measures. We give all the proofs for the most general case. [ABSTRACT FROM AUTHOR]

This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at 0 , β and ∞ where β represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves. This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at , and where represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present Korovkin theorems for positive linear operators of two variables from Hω(K) into CB(K) via the power series method. In addition, we give an example that our new approximation result works but its classical case does not work. Furthermore, we obtain the rate of convergence of these operators. [ABSTRACT FROM AUTHOR]

Time invariant linear operators are the building blocks of signal processing. Weighted circular convolution and signal processing framework in a generalized Fourier domain are introduced by Jorge Martinez. In this paper, we prove that under this new signal processing framework, weighted circular convolution also has a generalized time invariant property. We also give an application of this property to algorithm of continuous wavelet transform (CWT). Specifically, we have previously studied the algorithm of CWT based on generalized Fourier transform with parameter 1. In this paper, we prove that the parameter can take any complex number. Numerical experiments are presented to further demonstrate our analyses. [ABSTRACT FROM AUTHOR]

In this paper we consider controlled infinite dimensional systems subjected to stochastic structured nonlinear unbounded multiperturbations. Our objective is to study the maximization of the stability radius by state feedback. We obtain conditions for the existence of suboptimal controllers. The supremal achievable stability radius is characterized via the resolution of a Riccati equation and some linear operator inequalities. Examples are given to illustrate the theory. [ABSTRACT FROM AUTHOR]

Conventionally, volcanic margins have been considered devoid of hydrocarbon, but many discoveries and research in recent past have proved the presence of hydrocarbon prospects within them. However, hydrocarbon exploration within volcanic margin is constrained by seismic imaging. Further, identification of continent to oceanic boundary (COB) is critical to hydrocarbon search as hydrocarbon is found mostly over continental crust. Seaward dipping reflectors, associated with volcano-sedimentary sequences, located along rifted continental margins and represented by highly dipping strong amplitude seismic reflectors, play an important role to study volcanic margins. Keeping in view the problems of hydrocarbon exploration within volcanics, seaward dipping reflectors (SDRs) in Indian context have been studied in detail in this paper. It facilitates mapping of continent-oceanic boundary (COB). It has impact on hydrocarbon prospectivity in volcanic margins as it can provide formidable seal and secondary induced maturity. In India, several discoveries have been made in volcanic margins along west coast, from weathered, fractured basalt and sub-basalt sediments. In the present work, long offset regional seismic data (18 dip lines and 1 cross line), along east coast, have been interpreted. SDRs help in hydrocarbon prospectivity assessment for both discrimination of interbedded sediments and preferential accumulation of hydrocarbon. Mapping of linear features not only helped to demarcate COB but also their presence at 6–10 km depth. For the first time, such comprehensive study on SDRs has been done along Indian peninsular region with indications for hydrocarbon prospectivity at deeper levels along Indian peninsular region. [ABSTRACT FROM AUTHOR]

In the previous paper Liu and Pu (2019) [17] , we proved the nonlinear Schrödinger (NLS) approximation for the Euler-Poisson system for a hot ion-acoustic plasma, where the appearance of resonances and the loss of derivatives of quadratic terms are the main difficulties. Note that when the ion-acoustic plasma is hot, the Euler-Poisson system is Friedrich symmetrizable, and the linear term can provide a derivative to compensate the loss of derivative induced by quadratic terms after diagonalizing the linearized system. When the ion-acoustic plasma is cold, as considered in the present paper, the situation is very different from that in the previous paper. The Euler-Poisson system becomes a pressureless system, so the linear operator has no regularity, and the quadratic terms still lose a derivative in the diagonalized system. This fact makes it more difficult to prove the NLS approximation of Euler-Poisson system for a cold ion-acoustic plasma. In this paper, we take advantage of the special structure of the pressureless Euler-Poisson system and the normal-form transformation to deal with the difficulties caused by resonances, especially the difficulties caused by derivative loss, in order to prove the NLS approximation. [ABSTRACT FROM AUTHOR]