Annali dell''Universita di Ferrara最新文献

In this paper, we investigate the existence of weak solutions for the p(x)-parabolic equation with logarithmic nonlinearity of the form

where A is an elliptic operator that maps (W_{0}^{1,p(cdot )}(Omega )) into its dual space (W^{-1,p^{prime }(cdot )}(Omega )). We also obtain an upper bound for blow-up time of weak solutions under some suitable conditions. The study of such problem will be in the setting of Lebesgue-Sobolev spaces with variable exponents. Our proof is based on Galerkin approximation method and concavity method.

For a natural number n, denote by (B_n) the braid group on n strands. Y. Mikhalchishina classified all homogeneous 2-local representations of (B_n) for all (n ge 3). On the other hand, T. Mayassi and M. Nasser extended the result of Mikhalchishina by classifying all homogeneous 3-local representations of (B_n) for all (n ge 4). We consider in our work two group extensions of (B_n). The first group, denoted by (VB_n), is the virtual braid group, and the second group, denoted by (WB_n), is the welded braid group. Specifically, for (nge 2), Mikhalchishina constructed extensions of the Wada representations of (B_n) to (VB_n) and (WB_n). The Wada representations of (B_n) are known to be local representations. As a generalization of the result of Mikhalchishina, we classify all homogeneous 2-local representations for all (nge 2) and all homogeneous 3-local representations for all (nge 4) of both groups (VB_n) and (WB_n). In addition, we study the faithfulness of these local representations in some cases.

Let R be a commutative ring and (delta ) an expansion function of its ideals. A proper ideal I of R is called strongly irreducible if, for all ideals J and K of R such that (J cap K subseteq I), it follows that (J subseteq I) or (K subseteq I). In this paper, we introduce and study (delta )-irreducible ideals and several (delta )-variants by applying (delta ) in different positions within the defining condition. We then examine the relationships among them, and their connections to strongly irreducible ideals. Moreover, we establish some characterizations and provide several illustrative examples showing, in particular, the irreversibility of the strict implications. Further, we examine the structure of (delta )-irreducible ideals within product rings.

In this paper, we construct a Poincaré–type polynomial for any reduced plane curve. This polynomial is then used to decode the homological properties of plus-one generated curves. The construction presented herein offers a generalization of the results obtained in [9] for free plane curves. In accordance with the general result that has been established, combinatorial avatars of our Poincaré-type polynomial are presented for particular classes of reduced plane curves with quasi–homogeneous singularities. This phenomenon is exemplified by specific cubic-line arrangements and quartic-line arrangements.

This study examines the linear and weakly nonlinear stability of thermal convection in a fluid-saturated porous layer with couple stress, incorporating the Cattaneo heat-flux law under local thermal nonequilibrium conditions. The Cattaneo effect transforms the classical parabolic heat equation for the solid phase into a hyperbolic form, thereby enabling the propagation of temperature waves within the solid matrix. Linear instability analysis reveals that the inclusion of the Cattaneo effect induces oscillatory convection, in contrast to the stationary convection observed in its absence. The combined influences of the couple-stress parameter, interphase heat transfer coefficient, dimensionless solid thermal relaxation time, porosity-modified conductivity ratio, conductivity ratio, and the fluid's effective thermal diffusivity on system stability are systematically investigated. Critical stability parameters computed for aluminum oxide and copper oxide porous materials indicate that both the couple-stress parameter and the solid thermal relaxation time stabilize the onset of convection. A weakly nonlinear stability analysis based on a multi-scale method shows that the amplitude of linear wave motions, whether stationary or oscillatory, is governed by a first-order nonlinear evolution equation. The stationary mode may exhibit either supercritical or subcritical instability, depending on the governing parameters, whereas the overstable mode is exclusively supercritical. Notably, the transition from supercritical to subcritical instability occurs at lower interphase heat transfer coefficients for aluminum oxide porous media than for copper oxide. Overall, the results provide new physical insights into the interplay among couple-stress effects, solid thermal relaxation, conductivity ratios, the fluid's effective thermal diffusivity, and local thermal nonequilibrium effects on convection stability in porous media.

Let (B_{k,ell }(n)) count the number of ((k,ell ))-regular bipartitions of n. In this paper, we establish infinite families of congruences modulo powers of 5 for (B_{5^{2k-1}, 5^{2k}}(n)), for (k ge 1). In particular, for any integers (n ge 0), (beta ge 0) and (k ge 1), we prove that

by deriving the exact generating functions of specific arithmetic progressions in (B_{5^{2k-1}, 5^{2k}}(n)). This result substantially extends the earlier findings of Tang (Quaestiones Mathematicae 2020, 43(2): 169-183).

This study investigates the linear instability of thermohaline convection in a rotating, anisotropic porous layer saturated with a zero-order Kelvin–Voigt (or Navier–Stokes–Voigt) fluid. The flow in the porous medium is described by the Darcy–Brinkman model with Kelvin–Voigt regularization. The simultaneous presence of thermal, solutal, and rotational gradients renders the system effectively triple diffusive, with these three mechanisms jointly regulating buoyancy and momentum transport. Analytical conditions for the onset of both stationary and oscillatory convection are derived. The Kelvin–Voigt viscoelastic parameter leaves the stationary threshold unchanged but exerts a strong influence on oscillatory modes, acting either to stabilize or destabilize depending on the relative strengths of solutal buoyancy. Two novel features emerge from the analysis: (i) the appearance of disconnected, closed oscillatory neutral curves lying below the stationary branch, leading to multivalued instability thresholds that require three thermal Darcy–Rayleigh numbers for complete characterization; and (ii) parameter regimes in which rotation and a stabilizing solute gradient combine to destabilize oscillatory convection, in contrast to their generally stabilizing influence on the onset of instability. These findings offer new insight into thermo-solutal-rotational interactions in a Navier–Stokes–Voigt fluid-saturated porous medium and suggest potential pathways for manipulating transport in geophysical, filtration, and thermal-management applications.

In this article, we introduce a three-parameter family of k-Horadam sequences with arbitrary initial values and real-valued coefficient functions, extending the classical Horadam and Fibonacci sequences to third-order recurrence relations. We present several algebraic properties, including a Binet-type formula, partial sum identities, and closed-form ordinary and exponential generating functions. Moreover, we derive Catalan, d’Ocagne, and Vajda-type identities for this family of sequences. We also provide illustrative examples involving generalized Tribonacci, Perrin/Padovan, and third-order Jacobsthal sequences. The proposed results unify and generalize several known identities and properties from the literature.

The main purpose of this article is to introduce two new classes of modules, the first one is the y-duo modules, which are bigger than the class of CL-duo modules, the second one is the concept of strongly CLS module; this new class of modules lies between the strongly CCLS modules and y-duo modules. Several properties of these concepts are introduced in this paper. Furthermore, we investigate several characterizations and many relationships between certain features of the modules.

We construct the linear representation (hat{beta _ n}^{d,g,e}: SM_n rightarrow M_n(mathbb {Z}[t^{pm 1},g,d,e])), which extends the Burau representation of the braid group (B_n) to the singular braid monoid (SM_n). We show that any extension of the Burau representation to (SM_n) is of the form (hat{beta _ n}^{d,g,e}). We show that (hat{beta _ n}^{d,g,e}) is reducible to a reduced representation (hat{beta _n^r}: SM_n rightarrow M_{n-1}(mathbb {Z}[t^{pm 1},g,d,e]))). Additionally, we study whether or not extensions of the Burau representation to (SB_n), the singular braid group, exist.