In this study, the synchronization challenge of fractional-order competitive neural networks (FOCNNs) with additive time-varying delays is examined within the framework of quantized sampled-data control (QSDC). To achieve this, a novel Lyapunov–Krasovskii functional (LKF) is developed by fully incorporating the effects of fractional derivatives, time-varying delays, and sampling instants. Then, by employing inequality-based analysis in conjunction with a QSDC scheme, the asymptotic stability of the error system is guaranteed, and the derived conditions are presented as linear matrix inequalities (LMI). This exhibits that synchronization between the fractional-order master and slave systems is achieved by the proposed QSDC. The validity of the method is verified through a numerical example, while its practical applicability is demonstrated in the context of image encryption, emphasizing its potential for secure communication.
Following the geometric theory of generalized inverses, the image-kernel (P,Q)-inverse is investigated in the context of the algebra of bounded linear operators on Banach spaces. We present several results using matrix representation techniques.
In this paper, according to the classification of linear fractional self-mappings, we characterize disjoint hypercyclic composition operators on the weighted Dirichlet space when the induced mappings have the same attractive fixed point.
The aim of this work is to exhibit a collection of results due to the author in the area of moment problems, accompanied by inspiring or inspired results of other authors, emphasizing his standpoint of operator theorist on this important branch of mathematics.
In this paper, we study the products of two self-adjoint weighted composition operators on the Hardy space. In particular, we provide necessary and sufficient conditions for such products to be self-adjoint, unitary, or normal. Finally, we show that if T is a product of two self-adjoint weighted composition operators, then T is similar to T^* .
This paper examines a new class of stochastic FitzHugh–Nagumo system with the Rosenblatt process, and Poisson jumps. Firstly, the proposed problem is reformulated in the abstract space, and solvability results are investigated by using the successive approximation technique, and Bihari inequality. Moreover, sufficient conditions are derived to establish the mean-square stability and exponential mean-square stability of the proposed system, thereby ensuring the stable generation and transmission of electrical signals in neurons. Finally, an illustrative example is given to demonstrate the obtained results.
The paper studies the distortion of the chordal (spherical) distance under ring Q-homeomorphisms in the complex plane. Assuming that the majorant Q has finite mean l-oscillation at a point, we obtain power-type estimates for the distortion of the chordal distance near this point. The results are then applied, via the corresponding distortion quotient, to Beltrami equations with two characteristics.
The linear canonical boostlet transform is developed as a chirp-preconditioned extension of continuous boostlet analysis for functions on two-dimensional space–time. A unitary quadratic-phase multiplier is applied before the boostlet transform, yielding analyzing atoms obtained by pulling ordinary boostlet atoms through the inverse chirp operator. The construction preserves translation, dilation, and Lorentz-rapidity parameters while incorporating a prescribed canonical phase. An exact factorization in the linear canonical transform domain is derived, together with convolution and covariance formulas. For a two-window Calderón-admissible system, the transform satisfies a Plancherel identity, admits a bounded synthesis operator, and provides stable reconstruction in the square-integrable setting. An explicit admissible window pair supported on the four open Minkowski frequency cones is constructed, and its Calderón constant is evaluated directly. Heisenberg, logarithmic, Pitt, and Nazarov uncertainty inequalities are obtained with constants consistent with the chosen two-dimensional Fourier normalization and canonical-frequency scaling. A closed-form anisotropic Gaussian calculation describes the dependence of the coefficients on translation, scale, Lorentz rapidity, and chirp mismatch. Numerical illustrations confirm joint localization, scale selectivity, rapidity dependence, and exact recovery under matched chirp compensation.
In this brief note, we obtain a recurrence relation for the average singular value α (d) of a complex valued d× d matrix 1/√(d)X with Gaussian entries, of the form: α _ℂ( d+1) =α _ℂ( d) +R(d), where R(d) can be written as the linear combination of two integrals involving Laguerre polynomials. This reduces to showing that R(d)<0 (a non-trivial analysis problem) a 2016 conjecture of Bandeira, Kennedy and Singer, where it is predicted that α (d) decreases monotonically with d, from α _ℂ( 1) =√(π/4) , to the d→∞ limit 8/3π provided by the Marchenko-Pastur distribution. While this may point to a possible path to solving the conjecture, it is still far from a solution, since the two integrals R(d) are non-summable hypergeometric functions, and showing that R(d)<0 is a non-trivial analysis problem.
This paper tackles the challenging issue of synchronization problem for quaternion-valued inertial neural networks (QVINNs) with mixed delays, encompassing both time-varying discrete and distributed delays. A hybrid control strategy combining sampled-data control and quantized control is proposed to integrates a semi-Markovian jump process to model random structural transitions, enabling a more flexible and realistic representation of stochastic switching behavior compared to conventional Markovian models. Leveraging a non-decomposition approach to retain the full algebraic structure of quaternion matrices, a rigorous synchronization error system is formulated. An advanced input delay approach and Lyapunov-Krasovskii functional(LKF) construction are utilized to derive new synchronization criteria in terms of quaternion-valued linear matrix inequalities (LMIs), which are then transformed into equivalent complex-valued LMIs for easier analysis. Furthermore, synchronization criteria under the event-triggered (ET) scheme are derived in a straightforward manner. Numerical simulations validate the effectiveness and performance of the proposed synchronization strategies, demonstrating their potential for practical applications.
Abstract In this paper we consider a two–dimensional Hamiltonian integral system on an interval $$[ a,b )$$ [ a , b ) . We investigate the definiteness and surjectivity properties and define associated with this system the maximal $$S_{\max }$$ S max and minimal $$S_{\min }$$ S min linear relations. For an improper gauge $${\mathfrak L}$$ L , we calculate the $${\mathfrak L}$$ L -resolvent matrix and describe the set of $${\mathfrak L}$$ L -resolvents of the linear relation $$S_{\min }$$ S min in the cases when the system is either quasiregular, limit circle, or limit point at b .
In the present work, we establish that a Parseval identity for the Bessel wavelet transform holds under certain assumptions on the functions and their transforms. Furthermore, we derive Tauberian and sharp remainder Tauberian theorems for the Bessel wavelet transform by exploiting the Wiener-Ganelius method in conjunction with the Parseval identity.
We study the discrete spectrum of fiber Hamiltonians H_μ _1μ _2(K) for a two-boson lattice model on ℤ^3 with on-site and nearest-neighbour interactions. The operators depend on the total quasi-momentum K∈𝕋^3 and the real coupling constants μ _1,μ _2, and act on the Hilbert space L^2,e(𝕋^3) of even square-integrable functions. Each fiber Hamiltonian is a self-adjoint rank-four perturbation of the multiplication operator by the two-particle fiber dispersion relation, so its essential spectrum is explicitly determined. For K=0, the space L^2,e(𝕋^3) decomposes into three orthogonal invariant subspaces. In one subspace, the (μ _1,μ _2) -plane is divided by smooth hyperbolic curves into regions where the number of eigenvalues below the lower edge of the essential spectrum is constant and equal to 0, 1 or 2. On these curves, eigenvalues reach the lower threshold of the essential spectrum and generate threshold resonances. In each of the remaining two subspaces, a unique critical point on the μ _2 -axis separates the parameter regimes with 0 and 1 eigenvalue below the essential spectrum; at this point, the lower threshold becomes an eigenvalue. An analogous description holds for the number of eigenvalues above the upper edge of the essential spectrum, together with the corresponding threshold phenomena at the upper spectral edge. In addition, we obtain a complete classification of the discrete spectrum of H_μ _1μ _2(0) describing the exact number of eigenvalues lying below and above the essential spectrum in each region of the parameter plane. Moreover, we establish stability of these eigenvalues under perturbations of the total quasi-momentum K∈𝕋^3 : for K 0 , the operator H_μ _1μ _2(K) has at least as many eigenvalues below and above the essential spectrum as H_μ _1μ _2(0). If the lower edge of the essential spectrum is a threshold resonance of H_μ _1μ _2(0) , then H_μ _1μ _2(K) has at least one more eigenvalue below the essential spectrum than H_μ _1μ _2(0). If the lower edge is a threshold eigenvalue of multiplicity two then H_μ _1μ _2(K) has at least two more such eigenvalues. Analogous statement holds for the upper edge of the essential spectrum.
We conduct a systematic study of Hausdorff operators H_ϕ on weighted Fock spaces ℱ_β(ℂ) . We establish boundedness, compactness, and Schatten class properties, and investigate commutators with multiplication and derivation operators. Classical examples, including the Cesáro, truncated power, Pólya, and de la Vallée–Poussin operators, are analyzed in detail, illustrating the richness of the theory.
We study the class of weighted Hadamard–Bergman operators 𝕂_g,a^(λ ) with general holomorphic kernels g∈ℋ(𝔻) and radial symbols a∈ L_λ^1(𝔻) acting on general holomorphic function spaces 𝒳 . By imposing a set of natural assumptions on 𝒳 , together with the boundedness of the maximal Bergman projection, we derive a sufficient condition for the boundedness of 𝕂_g,a^(λ ) . This condition relates the behavior of certain derivatives of the holomorphic kernel to specific integral averages of the symbol a. Furthermore, we establish the validity of our results for mixed-norm spaces and Orlicz spaces
We study several spectral sets of Hausdorff operators on Fock spaces of entire functions. We show that the Hausdorff operators can be expressed via the Hille-Phillips functional calculus of an operator semigroup, and we compute the different spectral sets of the Hausdorff operators from those of the infinitesimal generator of the semigroup by means of spectral mapping theorems.
This paper investigates several sharp versions of Bohr-type inequalities for the class of operator-valued holomorphic functions f defined on a simply connected domain Ω⊆ℂ that contains the unit disk 𝔻 . By introducing a new constant λ _ℋ^* related to the operator-valued Taylor coefficients, we establish improved Bohr inequalities that incorporate the planar integral S_r^* (related to the area of the image disk). Furthermore, we generalize the classical Bohr and Bohr-Rogosinski radius results for functions mapping into the space of bounded linear operators ℒ(ℋ) on a complex Hilbert space H. We provide a refined version of these inequalities using non-negative continuous sequences and demonstrate that our results generalize several known theorems for scalar-valued functions and specific domain geometries, such as the disk Ω _γ . Sharpness of the constants and equality conditions are also discussed.
