Mediterranean Journal of Mathematics最新文献

In this paper, we give an explicit characterization of all bases of (varepsilon )-canonical number systems ((varepsilon )-CNS) with finiteness property in quadratic number fields for all values (varepsilon in [0,1)). This result is a consequence of the recent result of Jadrijević and Miletić on the characterization of quadratic (varepsilon )-CNS polynomials. Our result includes the well-known characterization of all bases of classical CNS ((varepsilon =0)) with finiteness property in quadratic number fields. It also fits into the general framework of generalized number systems (GNS) introduced by A. Pethő and J. Thuswaldner.

In previous works, Buskes and the author have made use of representations of Archimedean Riesz spaces in terms of real-valued continuous functions defined on dense open subsets of a topological space in studying tensor products. These representations may be obtained from the Ogasawara–Maeda representation by means of restriction to the set on which representing functions are real-valued, rather than infinite. In this note, we show how to obtain such a representation as a simple consequence of the Krein–Kakutani representation of an order unit space. We conclude by studying the representation of Riesz homomorphisms in this setting.

In this paper we study non-nilpotent non-Lie Leibniz (mathbb {F})-algebras with one-dimensional derived subalgebra, where (mathbb {F}) is a field with ({text {char}}(mathbb {F}) ne 2). We prove that such an algebra is isomorphic to the direct sum of the two-dimensional non-nilpotent non-Lie Leibniz algebra and an abelian algebra. We denote it by (L_n), where (n=dim _mathbb {F}L_n). This generalizes the result found in Demir et al. (Algebras and Representation Theory 19:405-417, 2016), which is only valid when (mathbb {F}=mathbb {C}). Moreover, we find the Lie algebra of derivations, its Lie group of automorphisms and the Leibniz algebra of biderivations of (L_n). Eventually, we solve the coquecigrue problem for (L_n) by integrating it into a Lie rack.

Let G be a group and N be a (pi )-solvable normal subgroup of G with (pi subsetneq pi (N)), where (pi (N)) is composed by all prime divisors of the order of N. In this paper, we determine the structure of ({N_{pi '}}{} textbf{Z}(N)/textbf{Z}(N)) if (textbf{C}_G(x)) is a maximal subgroup of group G for every (pi ')-element (xin Nsetminus textbf{Z}(N)), where (N_{pi '}) is a Hall (pi ')-subgroup of N. In particular, if (pi = {p}) is a set composed by a single prime p, we show that N is solvable, which has its own independent significance. If we assume (N=G) in the above results, then it is [8, Theorems A and B] by removing the conditions “G is p-solvable” and “with (G_{p'}) non-abelian”. We also give a detailed structure description of such groups. Further, we generalize [9, Theorem A] by removing the condition “N is p-solvable”, and also provides a positive answer to [9, Question] by giving the structure of ({N_{p'}}{} textbf{Z}(N)/textbf{Z}(N)) if (textbf{C}_G(x)) is a maximal subgroup of G for every p-regular element (xin N{setminus } textbf{Z}(N)).

A very well-covered graph is a well-covered graph without isolated vertices such that the size of its minimal vertex covers is half of the number of vertices. If G is a Cohen–Macaulay very well-covered graph, we deeply investigate some algebraic properties of the cover ideal of G via the Rees algebra associated to the ideal, and especially when G is a whisker graph.

In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus (gamma ) and degree e in ({mathbb {P}}^{e-gamma }). Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for (gamma ge 3) and (e ge 4gamma + 5), there exists a non-reduced component ({mathcal {H}}) of the Hilbert scheme of smooth curves of genus (3e + 3gamma ) and degree (3e+1) in ({mathbb {P}}^{e-gamma +1}). We show that (dim T_{[X]} {mathcal {H}} = dim {mathcal {H}} + 1 = (e - gamma + 1)^2 + 7e + 5) for a general point ([X] in {mathcal {H}}).

In this paper, we consider the Liouville-type theorems for the 3D stationary incompressible MHD equations. Using the Caccioppoli type estimate, we proved the smooth solutions (u, b) are identically equal to zero when ((u,b)in L^{p}({mathbb {R}}^{3}), pin (frac{3}{2},3).) In addition, under an additional assumption in the setting of the Sobolev space of negative order (dot{H}^{-1}({mathbb {R}}^{3}),) we can extend the index (pin (3,+infty ).) In fact, our results combine with the result of Yuan and Xiao (J Math Anal Appl 491(2):124343, 2020) that (pin [2,frac{9}{2}],) which implies a very intriguing and novel result for the 3D stationary MHD equations with ( pin (frac{3}{2},+infty ).)