Annali dell''Universita di Ferrara最新文献

This paper explores the potential of local spectral theory to investigate the limit point set of the descent spectrum of upper triangular operator matrices, denoted by ({mathcal {T}}), on Banach spaces. We rigorously prove that transitioning from the accumulation set of the diagonal descent spectrum, denoted by ( hbox {Acc} sigma _{textrm{d}}({mathcal {T}}_textbf{diag})), to that of the complete descent spectrum, ( hbox {Acc} sigma _{textrm{d}}({mathcal {T}})), involves removing specific subsets within ( hbox {Acc} sigma _{textrm{d}}(A_1) cap hbox {Acc} sigma _{textrm{a}}(A_2) cap hbox {Acc} sigma _{textrm{a}}(A_3)). Additionally, we present sufficient conditions that ensure the limit points of the descent spectrum of the operator matrix encompass the combined limit points of its diagonal entry spectra. This significantly addresses a longstanding question posed by Campbell (Linear Multilinear Algebra 14:195–198, 1983) regarding the limit points for the descent spectrum of the last (3 times 3) operator matrix form. Specifically, Campbell inquired about developing new methods to analyze the spectral properties of such matrices without resorting to partitioning their entries, a challenge that has remained unresolved for decades. Our findings provide a comprehensive solution, illustrating that a deeper understanding of the spectral behavior can be achieved by considering the entire matrix structure collectively.

In this manuscript, we investigate bounds for the zeros of quaternionic polynomials with restricted coefficients. We find an annular region that contains all the zeros of a quaternionic polynomial. Moreover, we find zero-free regions thereby obtain improvement of Eneström-Kakeya theorem for quaternionic polynomials.

This work considers a one-dimensional system consisting of two identical Timoshenko beams. The model considers that an adhesive layer of small thickness joins the two surfaces, thus producing an interfacial slip under homogeneous mixed Neumann-Dirichlet-Dirichlet boundary conditions. We introduce a Kelvin-Voigt type damping into the rotation equation, and we study the well-posedness of the problem and the asymptotic behavior of the solutions using techniques from the semigroup theory of linear operators and the frequency domain method. When the wave’s propagation speeds are equal in both beams, we show that the Kelvin-Voigt dissipative term acting on the rotation equation is sufficient to obtain the exponential decay of the solutions while maintaining the structural dissipation characteristic of the model. When these propagation speeds differ, we show the lack of exponential decay and prove that the solutions decay polynomially with a decay rate of (t^{-frac{1}{2}}). We prove, finally, that this decay rate is optimal.

This paper deals with the extension of Hayman Conjecture to q-shift differential polynomials generated by meromorphic functions. We prove that the differential polynomials assumes every finite value infinitely often when sharing two Borel exceptional Values with appropriate conditions. Few examples are given to prove that the conditions are inevitable.

This paper aims to show that there exists a weak solution to the following quasilinear system driven by the M-Laplacian

where (Omega ) is a bounded open subset in ({mathbb {R}}^N) and ((-Delta _{m})) is the M-Laplacian operator. Here we consider the non-reflexive case taking into account the Orlicz and Orlicz-Sobolev Space. The non-reflexive case occurs when the N-function ({overline{M}}) does not verify the (Delta _2)-condition. We consider an approximated quasilinear elliptic problem driven by the (M_epsilon )-Laplacian and using the Mountain Pass Theorem to obtain the existence of a nontrivial and nonnegative solution for the above system in reflexive case. By tending (epsilon rightarrow 0) we get the solution in the non-reflexive case.

In this paper, we propose an inertial iterative method for approximating a common solution of generalized mixed equilibrium problem for monotone and uniformly continuous operators and fixed point of nonexpansive mapping in real Hilbert space. The strong convergence of the sequence generated by the proposed method can be guaranteed without prior knowledge of the Lipschitz constant of the operator. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method. Our result improves, extends and generalizes several of the existing results in this direction.

In this article, we present and examine a type of modules that represent appropriate generalizations of each of the singular modules, purely extending and CCLS modules. A module M is called purely CCLS module if every c-closed submodule of M is pure in M. We locate purely CCLS module with generalizations of extending modules. We present some characterizations of purely CCLS and we show that the direct summand of purely CCLS modules is again purely CCLS. Furthermore, we go over when a direct sum of purely CCLS is likewise purely CCLS. Additionally, we provide adequate circumstances under which the direct sum of purely CCLS is purely CCLS.

In 1961, Bargmann introduced the classical Segal-Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal-Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper we introduce the Dunkl-type Segal-Bargmann transform (mathscr {B}_{alpha }) associated with the Coxeter group (mathbb {Z}^d_2). Next, we investigate for this transform the main theorems of harmonic analysis (Plancherel and inversion formulas). Finally, we study some local uncertainty principles associated with the transform (mathscr {B}_{alpha }).

This paper is concerned with a thermoelastic swelling system with Coleman-Gurtin’s law, when the heat flux q is given by

where (theta ) is the temperature supposed to be known for negative times. (Psi ) is the convolution thermal kernel, a nonnegative bounded convex function on ([0, + infty )) belongs to a broad class of relaxation functions satisfying the unitary total mass, and some additional properties that will be specified later. By using the Dafermos history framework and constructing a suitable Lyapunov functional, we established a general decay result, from which the exponential and polynomial decay rates are only special cases. The stability result in this manuscript is obtained without imposing any stability number, and extends and improves many earlier results in the literature.

Motivated by the recent work of Park on the analogue of the Ramanujan’s function (k(tau )=r(tau )r^2(2tau )) for the Ramanujan’s cubic continued fraction, where (r(tau )) is the Rogers–Ramanujan continued fraction, we use the methods of Lee and Park to study the modularity and arithmetic of the function (w(tau ) = X(tau )X(3tau )), which may be considered as an analogue of (k(tau )) for the continued fraction (X(tau )) of order six introduced by Vasuki, Bhaskar and Sharath. In particular, we show that (w(tau )) can be written in terms of the normalized generator (u(tau )) of the field of all modular functions on (Gamma _0(18)), and derive modular equations for (u(tau )) of smaller prime levels. We also express (j(dtau )) for (din {1,2,3,6,9,18}) in terms of (u(tau )), where j is the modular j-invariant.