Ricerche di Matematica最新文献

Let G be a finite group, (Hle G). The permutizer of H in G is defined to be (P_G(H)=langle xin G|~Hlangle xrangle =langle xrangle Hrangle ). Let (D={(g, g)|~gin G}), the main diagonal subgroup of (Gtimes G). In this paper, we use the permutizer of D in (Gtimes G) to characterize the structure of G, and the following main result is obtained. Main Theorem: Let G be a group, (D={(g, g)|~gin G}). Then the group (Gtimes G) has a chain of subgroups from D to (Gtimes G) with each contained in the permutizer of the previous subgroup if and only if all chief factors T of G have prime order or order 4 with (G/{C_G(T)}cong S_3). Finally, we also present two theorems deciding the supersolubility of finite groups.

This paper proposes interval extropy and its length-biased version to measure the uncertainty of a doubly truncated random variable. Properties and characterizations of some important life distributions in terms of the new measures are obtained. Nonparametric estimators for the proposed measures are also suggested, and their performance is verified using simulated and real data sets.

In this paper we study the additivity of multiplicative Jordan semi-derivations on rings and standard operator algebras.

Using a Caccioppoli-type inequality involving negative exponents for a directional weight we establish variants of Bernstein’s theorem for variational integrals with linear and nearly linear growth. We give some mild conditions for entire solutions of the equation

under which solutions have to be affine functions. Here f is a smooth energy density satisfying (D^2 f>0) together with a natural growth condition for (D^2 f).

This study delves into a comprehensive examination of modified three-dimensional, incompressible, anisotropic Navier–Stokes equations. The modification involves incorporating a power term in the nonlinear convection component, a particularly relevant adjustment in porous media scenarios, especially when the fluid adheres to the Darcy–Forchheimer law instead of the conventional Darcy law. Our main contributions include establishing global existence over time and demonstrating the uniqueness of solutions. Importantly, these achievements are realized without the need to assume smallness conditions on the initial data, but with the condition (beta >3). However, when (beta =3), the problem is limited to the case (0<alpha <4) as the above inequality is unsolvable for these (alpha ) values using our method. To address our statement, we will add a “slight disturbance” the function (log (e+|u|^{2})) to (|u|^{2}u). The primary objective of our research is to affirm that the solution, denoted as u in this equation, exhibits continuity in (L^{2}(mathbb {R}^{3})).

We consider a class of local rings that is properly larger than that of chain rings and investigate its properties. We show that when restricted to finite rings, elements of such rings can be factorized into a finite product of irreducible elements, and the length of such factorization is unique, although the factorization itself is far from being unique. Using these results, we determine the minimal number of generators required for each ideal. We also show that several nontrivial examples of such rings appear as a subring of a chain ring and show that such rings can be constructed using techniques commonly used in the field of multiplicative ideal theory. We choose a class of such rings and investigate the basic properties of rings induced from them (including the number of elements and ideals and the unit group structure of such a ring), which are directly associated with the structure of cyclic codes over such rings.

In this paper, we present a robust stability criterion for the one-dimensional subdiffusion equation with Caputo–Fabrizio fractional derivative. The criterion is obtained by extending a concept of stability under constant-acting perturbations that is regularly applied to systems of differential equations of integer order. We assume the existence of uncertainty in the subdiffusion equation due to the effect of external sources that are represented by Fourier series whose generalized Fourier coefficients are absolutely continuous and bounded functions. The results obtained suggest that the robust stability criterion allows us to guarantee that the solution of the subdiffusion equation, as well as its Caputo–Fabrizio fractional derivative and its first partial derivative with respect to the longitudinal axis, are bounded by a constant whose value is initially established. The results obtained are illustrated numerically.

This note provides a new simple proof of a result obtained in 2009 by Fan and Ozawa on the regularity criterion for a 3D Boussinesq equations with zero heat conductivity.

Recently, the generalized reversed aging intensity functions have been studied in the literature revealing to be a tool to characterize distributions, under suitable conditions. In this paper, some improvements on these functions are given and the relation between two cumulative distribution functions leading to the same generalization is studied. In particular, a link with the two-parameters Weibull distributions is found and a new stochastic order is defined in terms of the generalized reversed aging intensity. This order is strictly related to the definition of extropy, that is the dual measure of entropy, and some connections with well-known stochastic orders are analyzed. Finally, the possibility of introducing the concept of generalized aging intensity is studied also in terms of cumulative distribution functions with non-positive support.

Let G be a finite group and N a normal subgroup of G. We prove that the knowledge of the sizes of the conjugacy classes of G that are contained in N and of their multiplicities provides information of N in relation to the structure of G. Among other results, we obtain a criterion to determine whether a Sylow p-subgroup of N lies in the hypercentre of G for a fixed prime p, and therefore, whether the whole subgroup N is hypercentral in G.