Annali dell''Universita di Ferrara最新文献

We study factorizations of HOMFLY polynomials of certain prime knots and oriented links. We begin with a computer analysis of prime knots with at most 12 crossings, finding 17 non-trivial factorizations. Next, we give an irreducibility criterion for HOMFLY polynomials of oriented links associated to 2-connected plane graphs.

In this paper we give new estimates from above and from below of the Stress Intensity Factor on an open bounded and convex domain (Omega subseteq mathbb {R}^2). This analysis is a continuation of the study that we have done in Ascenzi et al. (Appl Math Comput 158:597–617, 2004), Ascenzi (Ann Univ Ferrara Sez VII (NS) 47:41–56, 2001) and Livieri et al. (Acta Mech 176:95–105, 2005) and that started from the paper of Oore and Burns (J Press Vessel Technol 102:204–211, 1980).

There is a proposition due to Kollár as reported by Kollár (Proceedings of the summer research institute, Santa Cruz, CA, USA, July 9–29, 1995, American Mathematical Society, Providence, 1997) on computing log canonical thresholds of certain hypersurface germs using weighted blowups, which we extend to weighted blowups with non-negative weights. Using this, we show that the log canonical threshold of a convergent complex power series is at most 1/c, where ((c, ldots , c)) is a point on a facet of its Newton polyhedron. Moreover, in the case (n = 2), if the power series is weakly normalised with respect to this facet or the point (c, c) belongs to two facets, then we have equality. This generalises a theorem of Varchenko 1982 to non-isolated singularities.

This study aims to investigate a generalized version of Szász operators linked with Hermite polynomials in the Durrmeyer framework. Initially, we delve into their approximation properties employing Peetre’s K-functional, along with classical and second-order modulus of continuity. Subsequently, we evaluate the convergence speed using a Lipschitz-type function and establish a Voronovskaya-type approximation theorem. Lastly, we investigate the convergence rate for differentiable functions with bounded variation derivatives.

(1) Background: This paper is devoted to the study of a class of semilinear elliptic boundary value problems with hypoelliptic (degenerate) Robin condition that includes as particular cases the Dirichlet, Neumann and regular Robin problems. (2) Methods: We give a rigorous proof of main theorem, which is based heavily on the theory of linear elliptic boundary value problems in the framework of (L^{p}) Sobolev spaces. (3) Results: We extend earlier theorems due to Ambrosetti–Lupo and Struwe to the hypoelliptic Robin case via Morse theory. (4) Conclusions: The main purpose of this paper is to understand the essence of a modern version of the classical Lyapunov–Schmidt procedure through a concrete approach to semilinear hypoelliptic Robin problems.

Let R be a prime ring of char ((R)ne 2, 3) and L a noncentral Lie ideal of R. Let U be the Utumi quotient ring of R and (C=Z(U)) be the extended centroid of R. Suppose that F, G, H are three generalized derivations of R such that

for all (uin L). Then either R satisfies standard polynomial (s_4(x_1,x_2,x_3,x_4)) or one of the following holds:

1. 1.

   There exist (alpha , beta in C) such that (F(x)= alpha x) and (H(x)= beta x) for all ( xin R);

2. 2.

   There exists (beta in C) such that (G(x)=0), (H(x)=beta x) for all ( xin R);

3. 3.

   There exist (a,bin U) and (0ne mu in C) such that (F(x)=xa), (G(x)=mu x), (H(x)=bx) for all ( xin R) with (mu a+bin C).

My paper (Suzuki 2003) produced some computer routines in Magma (Bosma et al. J Symb Comp 24:235–265, 1997) for the numerical invariants of Fano 3-folds, and used them in particular to determine the maximum value (f=19) of the Fano index. As a byproduct of the research, extensive data associated with all possible sets of singular points of Fano 3-folds with Fano indices greater than or equal to 2 was obtained. Collaborative research with Gavin Brown developed an improved version of the Magma program. The data discussed above was added to the Graded Ring Data Base (Brown et al. 2015) at the University of Kent. Subsequently, GRDB, now located to the University of Warwick, recently modified its interface to accommodate additional conditions, facilitating a more refined selection of Fano manifolds. In this context, we focus on the inequality known as the Bogomolov stability bound. We present a list of candidates for Fano 3-folds that do not satisfy these conditions and propose the conjecture that they do not exist.This result has been independently obtained in Liu and Liu (2023).

We investigate aspects of the metric bubble tree for non-collapsing degenerations of (log) Kähler–Einstein metrics in complex dimensions one and two, and further describe a conjectural higher dimensional picture.

This paper is based on a series of talks that the author gave at the University of Edinburgh in March 2023 on surfaces in positive characteristic. In particular, infinitesimal group schemes and their actions on algebraic surfaces are discussed, the structure of the automorphism group scheme of a surface of general type and the failure of the Kodaira vanishing theorem.