Ricerche di Matematica最新文献

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.

In this article, we study some properties of Ricci solitons with quarter-symmetric connection, when the soliton vector field is torse-forming. We also study some applications of quarter-symmetric connection on Riemannian submanifolds. This paper extends the results obtained by Ozgur (Filomat, 35:11(2021), 3635-3641) to the setting of quarter-symmetric connections.

Let G be a group. If the set ({mathcal {A}}(G)=lbrace alpha in {textit{Aut}}(G): xalpha (x)=alpha (x)x; textit{for all}; xin Grbrace ) forms a subgroup of ({textit{Aut}}(G)), then G is called ({mathcal {A}})-group. In this paper, we prove that a metacyclic group is an ({mathcal {A}})-group. Also, we show that, for any positive integer n and any prime number p, there exists a finite ({mathcal {A}}) p-group of nilpotency class n. Since there exist finite non ({mathcal {A}}) p-groups with (vert G/G^{prime }vert = p^{4}), we find suitable conditions implying that a finite p-group with (vert G/G^{prime }vert le p^{3}) is an ({mathcal {A}})-group. Using these results, we show that there exists a finite ({mathcal {A}}) p-group G of order (p^{n}) for all (nge 4) such that ({mathcal {A}}(G)) is equal to the central automorphisms group of G. Finally, we use semidirect product and wreath product of groups to obtain suitable examples.

Let (mathbb {P}) be the set of all prime numbers, I be a set and (sigma = lbrace sigma _i mid i in I rbrace ) be a partition of (mathbb {P}). A finite group is said to be (sigma )-primary if it is a (sigma _i)-group for some (i in I), and we say that a finite group is (sigma )-solvable if all its chief factors are (sigma )-primary. A subgroup H of a finite group G is said to be (sigma )-subnormal in G if there is a chain (H = H_0 le H_1 le dots le H_n = G) of subgroups of G such that (H_{i-1}) is normal in (H_i) or (H_i/(H_{i-1})_{H_i}) is (sigma )-primary for all (1 le i le n). Given subgroups H and A of a (sigma )-solvable finite group G, we prove two criteria for H to be (sigma )-subnormal in (langle H, A rangle ). Our criteria extend classical subnormality criteria of Fumagalli [5], which themselves generalize a classical subnormality criterion of Wielandt [13].

In the present work, we attempt to identify classes of bivariate distributions of random vector (X, Y) in which ageing concepts like increasing hazard rates, decreasing mean residual life, etc. can be inferred from univariate ageing properties of a random variable Z whose distribution specifies the dependence structure between the components of (X, Y). It is shown that a family of bivariate exponential distributions and those obtained by monotone transformations from them, and the time-transformed exponential models satisfy this property. The bivariate distributions considered here are exchangeable and the notions of ageing are interpreted in a Bayesian sense.

We show that, for any q, the pointset covered by the conic planes of a quadric Veronesean of (textrm{PG}(3,q)) is a two character set with respect to hyperplanes of (textrm{PG}(9,q)).

In this paper we investigate hyperplanes of the point-line geometry (A_{n,{1,n}}(mathbb {F})) of point-hyerplane flags of the projective geometry (textrm{PG}(n,mathbb {F})). Renouncing a complete classification, which is not yet within our reach, we describe the hyperplanes which arise from the natural embedding of (A_{n,{1,n}}(mathbb {F})), that is the embedding which yields the adjoint representation of (textrm{SL}(n+1,mathbb {F})). By exploiting properties of a particular sub-class of these hyerplanes, namely the singular hyperplanes, we shall prove that all hyperplanes of (A_{n,{1,n}}(mathbb {F})) are maximal subspaces of (A_{n,{1,n}}(mathbb {F})). Hyperplanes of (A_{n,{1,n}}(mathbb {F})) can also be contructed starting from suitable line-spreads of (textrm{PG}(n,mathbb {F})) (provided that (textrm{PG}(n,mathbb {F})) admits line-spreads, of course). Explicitly, let (mathfrak {S}) be a composition line-spread of (textrm{PG}(n,mathbb {F})) such that every hyperplane of (textrm{PG}(n,mathbb {F})) contains a sub-hyperplane of (textrm{PG}(n,mathbb {F})) spanned by lines of (mathfrak {S}). Then the set of points (p, H) of (A_{n,{1,n}}(mathbb {F})) such that H contains the member of (mathfrak {S}) through p is a hyperplane of (A_{n,{1,n}}(mathbb {F})). We call these hyperplanes hyperplanes of spread type. Many but not all of them arise from the natural embedding.