Mediterranean Journal of Mathematics最新文献

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 ).)

In this paper, we study real hypersurfaces of the two Kähler surfaces ({mathbb {S}}^2times {mathbb {S}}^2) and ({mathbb {H}}^2times {mathbb {H}}^2.) As the main results, amongst others, we classify all such hypersurfaces whose normal Jacobi operators are parallel with respect to either the Levi-Civita connection or the k-generalized Tanaka–Webster connection.

In this paper, we mainly study the classification of global existence and blow-up of solutions to degenerate Kirchhoff problems for the initial energy at different conditions. Firstly, under subcritical or critical conditions, we find two invariant sets and obtain the threshold results of global existence or blow-up in finite time. Furthermore, we apply (omega )-limit to prove the existence of blow-up solutions for the supercritical initial energy case. Finally, we give two-sided estimates of asymptotic behavior when the source term is controlled by the diffusion term.

In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space (H^2) and the Bergman space (A^2), meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space (A^2) and the Hardy space (H^2). We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space (H^2), on the Bergman space (A^2) and between the Bergman space (A^2) and the Hardy space (H^2), respectively. We also show that the best constant of Hyers–Ulam stability exists under different circumstances. Some results generalized the results of MacGregor and Zhu when (p=2) in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed.

We introduce and thoroughly examine a novel approach grounded in B-spline techniques to address the solution of second-kind nonlinear Volterra integral equations. Our method revolves around the application of B-spline interpolation, incorporating innovative end conditions, and delving into the associated existence and error estimation aspects. Notably, we develop this technique separately for even and odd-degree splines, leading to super-convergent approximations, particularly significant when employing even-degree splines. This paper extends its commitment to a comprehensive analysis, delving deeply into the method’s convergence characteristics and providing insightful error bounds. To empirically validate our approach, we present a series of numerical experiments. These experiments underscore the method’s efficacy and practicality, showcasing numerical approximations that closely align with the anticipated theoretical outcomes. Our proposed method thus emerges as a promising and robust tool for addressing the challenging realm of nonlinear Volterra integral equations, bridging the gap between theoretical expectations and practical applications.

Let X be a nonsingular complex projective surface. Given a semistable non isotrivial fibration (f: X rightarrow mathbb {P}^{1}) with general non-hyperelliptic fiber of genus (gge 4), we show that, if the number of singular fibers is 5, then (gle 11), thus improving the previously known bound (gle 17). Furthermore, we show that, for each possible genus, the general fiber has gonality at most 5. The corresponding fibrations are described as the resolution of concrete pencils of curves on minimal rational surfaces.