Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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ON SPECTRUM OF I-GRAPHS AND ITS ORDERING WITH RESPECT TO SPECTRAL MOMENTS
Full text linkSuppose is a graph, its adjacency matrix, and are eigenvalues of . The numbers , , are said to be the k−th spectral moment of and the sequenceS(G) = (S_0(G), S_1(G), \sdots, S_{n−1}(G)) is called the spectral moments sequence of . For two graphs and , we define , if there exists an integer, , such that for each , , andS_k(G_1) < S_k(G_2).The I−graph is a graph of order with the vertex and edge sets,,respectively. The aim of this paper is to compute the spectrum of an arbitraryI−graph and the extremal I−graphs with respect to the S−order
Square roots and n-th roots in pseudo-Michael algebras
Full text linkThe purpose of this paper is to study the existence of square roots and more generally n-th roots in pseudo-Michael algebras. We examine several conditions that imply the existence of n-th roots and hermitian n-th roots. We also simplify the proofs of the results given by D. Sterbova
Covering of Elliptic Curves and the Kernel of the Prym Map
Full text linkMotivated by a conjecture of Xiao, we study families of coverings of elliptic curves and their corresponding Prym map . More precisely, we describe the codi↵erential of the period map P associated to in terms of the residue of meromorphic 1-forms and then we use it to give a characterization for the coverings for which the dimension of Ker(dP) is the least possibile. This is useful in order to exclude the existence of non isotrivial fibrations with maximal relative irregularity and thus also in order to give counterexamples to the Xiao’s conjecture mentioned above. The first counterexample to the original conjecture, due to Pirola, is then analysed in our framework. 
2-absorbing and strongly 2-absorbing secondary submodules of modules
Full text linkIn this paper, we will introduce the concept of 2-absorbing (resp. strongly 2-absorbing) secondary submodules of modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of these classes of modules
On the codimension of subalgebras of the algebra of matrices over a field
Full text linkIn this paper we provide an elementary and easy proof that a proper subalgebra of the matrix algebra K^n,n, with n>=3 and K an arbitrary field, has dimension strictly less than n^2-
Solvability of Curves on Surfaces
Full text linkIn this article, we study subloci of solvable curves in Mg which are contained in either a K3-surface or a quadric or a cubic surface. We give a bound on the dimension of such subloci. In the case of complete intersection genus g curves in a cubic surface, we show that a general such curve is solvable. 
Remarks on hyponormal operators and almost normal operators.
Full text linkIn 1984 M. Putinar proved that hyponormal operators are sub-scalar operators of order two. The proof provided a concrete structure of such operators. We will use this structure to give a sufficient condition for hyponormal operators T with trace-class commutator to admit a direct summand S, so that T\oplus S is the sum of a normal operator and a Hilbert-Schmidt operator. We will investigate what this sufficient condition amounts to in the case of a weighted shift operator
Some new estimates of Hermite-Hadamard inequalities via harmonically r-convex functions
Full text linkIn this paper, we introduce the class of harmonically r-convex functions. We derive some Hermite-Hadamard type inequalities for this class of convex functions
On nodal and conodal ideals in MV-algebras
Full text linkIn this paper, we introduce the notions of nodes and nodal ideals in an MV-algebra and we define the notions of conodes and conodal ideals in an MV-algebra. We state some examples and theorems. In addition, we investigate some relations between the nodal (conodal) ideals and some the other ideals of an MV-algebra. Also, we show that if I is a non principal nodal ideal, then A/I is an MV-chain. Moreover, we prove that if I is a conodal ideal of an MV-algebra A, then A/I is a semi-simple MV-algebra.Finally, we construct algorithm for studing the structure of the nodal (conodal) ideals in finite MV-algebras
Functional continuity of unital B_{0}-algebras with orthogonal bases
Full text linkLet A be a unital B_{0}-algebra with an orthogonal basis, then every multiplicative linear functional on A is continuous. This gives an answer to a problem posed by Z. Sawon and Z. Wronski