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Publications Influence

Young-type inequalities and their matrix analogues

- H. Alzer, Carlos M. da Fonseca, A. Kovacec
- Mathematics
- 4 March 2015

We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers , and , with and , we prove the… Expand

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The singular acyclic matrices with the second largest number of P-vertices

- Zhibin Du, Carlos M. da Fonseca
- Mathematics
- 3 October 2015

Suppose that the nullity of the submatrix obtained from the deletion of a row and a column of the same index of a real symmetric matrix goes up by one. Such an index is called a P-vertex of the given… Expand

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Vertex types in some lexicographic products of graphs

- M. Andelic, F. Ashraf, Carlos M. da Fonseca, S. Simic
- Mathematics
- 2 November 2019

ABSTRACT Let be a symmetric matrix, or equivalently, a weighted graph whose edge ij has the weight . The eigenvalues of are the eigenvalues of M. We denote by the principal submatrix of M obtained by… Expand

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A matrix approach to some second-order difference equations with sign-alternating coefficients

- M. Anđelić, Z. Du, Carlos M. da Fonseca, E. Kilic
- Mathematics
- 7 January 2020

ABSTRACT In this paper, we analyse and unify some recent results on the double sequence , for , defined by the second-order difference equation with and , in terms of matrix theory and orthogonal… Expand

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The μ-permanent revisited

- Carlos M. da Fonseca
- 3 August 2019

This letter aims to correct and clarify several results appearing in [2]. It is clear that, under similarity, the -permanent does not keep the same value, in general, i.e. the polynomial P (A) is not… Expand

Comment on "Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs".

- M. Anđelić, Carlos M. da Fonseca
- Physics, Medicine
- Physical review. E
- 1 May 2019

In this Comment we recall the notion of a tridiagonal 2-Toeplitz matrix and its spectrum, confronting these results with others obtained recently on exact solutions of thermal transport in dimerized… Expand

A new type of Sylvester–Kac matrix and its spectrum

- Carlos M. da Fonseca, E. Kilic
- Mathematics
- 27 May 2019

ABSTRACT The Sylvester–Kac matrix, sometimes known as Clement matrix, has many extensions and applications throughout more than a century of its existence. The computation of the eigenvalues or even… Expand

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A Short Note on the Determinant of a Sylvester–Kac Type Matrix

- Carlos M. da Fonseca
- 19 February 2020

Abstract The Sylvester–Kac matrix, also known as Clement matrix, has many extensions and applications. The evaluation of determinant and spectra of many of its generalizations sometimes are hard to… Expand

On a conjecture about a tridiagonal matrix

- Carlos M. da Fonseca
- 16 November 2020

Abstract In this note we answer to a recent conjecture posed by Q.M. Al-Hassan on a factorization for the characteristic polynomial of the tridiagonal matrix with zero main diagonal and all 1’s sub-… Expand

Tridiagonal Matrices and Spectral Properties of Some Graph Classes

- M. Anđelić, Zhibin Du, Carlos M. da Fonseca, S. Simic
- Mathematics
- 23 April 2020

A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula for… Expand

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