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Table Of Integrals Series And Products

Mathematica--A System for Doing Mathematics by Computer.

Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.

An Introduction to the Theory of Graph Spectra: Spectral techniques

Topology and Geometry

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An Introduction To The Theory Of Graph Spectra

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 inequalitieswhere and are, respectively, the (weighted) arithmetic and geometric means of the positive real numbers and with . In addition, we show that both bounds are sharp. An example of a matrix analogue for the case is the double-inequalityfor positive definite matrices . Our results extend some fresh inequalities established by Kittaneh, Manasrah, Hirzallah and Feng. Estimates for the quotient and its matrix analogues given by Furuichi and Minculete are also improved.

Young-type inequalities and their matrix analogues

On structural properties of trees with minimal atom-bond connectivity index III

Some comments on k-tridiagonal matrices

On a family of trees with minimal atom-bond connectivity index

We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivation of generating functions and to the number of the closed walks on a path and in a cycle.

Carlos M. da Fonseca

Papers

Young-type inequalities and their matrix analogues

On structural properties of trees with minimal atom-bond connectivity index III

Some comments on k-tridiagonal matrices

On a family of trees with minimal atom-bond connectivity index

Basic trigonometric power sums with applications