Ricerche di Matematica最新文献

We investigate the zero sets of complex exponential polynomials in one variable with only one iteration. We characterize when such polynomials have the same zero set in terms of the radical ideals. Moreover we give a bound on the multiplicity of zeros.

Let G be a finite group. A group G is called a T group if its every subnormal subgroup is normal. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of (H^G), where (H^G) is the normal closure of H in G. Using the notion of Hall normally embedded subgroups, we characterize supersolvable groups and solvable T-group. First, we prove that if every cyclic subgroup of G of order prime or 4 is Hall normally embedded in G, then G is supersolvable with a well defined structure. Second, we prove that an A-group G is supersolvable if and only if its Sylow subgroups are products of cyclic Hall normally embedded subgroups of G. Final, we show that G is a solvable T-group if and only if every p-subgroup of G is Hall normally embedded in G, for all primes (pin pi (G)).

Let ({mathfrak {Nil}}) be the class of nilpotent groups and G be a group. We call G a meta-({mathfrak {Nil}})-Hamiltonian group if any of its non-({mathfrak {Nil}}) subgroups is normal. Also, we call G a para-({mathfrak {Nil}})-Hamiltonian group if G is a non-({mathfrak {Nil}}) group and every non-normal subgroup of G is either a ({mathfrak {Nil}})-group or a minimal non-({mathfrak {Nil}}) group. In this paper we investigate the class of finitely generated meta-({mathfrak {Nil}})-Hamiltonian and para-({mathfrak {Nil}})-Hamiltonian groups.

Martingale optimal transportation has gained significant attention in mathematical finance due to its applications in pricing and hedging. A key distinguishing factor between martingale optimal transportation and traditional optimal transportation is the concept of a peacock, which refers to a sequence of measures satisfying the convex order property. In the realm of traditional optimal transportation, the Wasserstein geometry, induced by a transportation problem with the p-th power of distance as the cost, provides valuable geometric insights. This motivates us to investigate the differences between Wasserstein geometries with and without the martingale constraint. As a first step, this paper focuses on studying the topological properties of convex order, with the aim of establishing a foundational understanding for further exploration of the geometric properties of martingale Wasserstein geometry.

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.