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Relationship of certain rings of infinite matrices over integers

Mario Petrich, Pedro V. Silva (2000)

Bollettino dell'Unione Matematica Italiana

Sia N l'insieme degli interi non negativi e Z l'anello degli interi. Sia A l'anello delle matrici N × N su Z che hanno solo un numero finito di cifre non nulle in ogni linea ed in ogni colonna. Sia B il sottoanello generato da X e Y , dove X (rispettivamente Y ) è ottenuto dalla matrice identità muovendo gli 1 una posizione a destra (rispettivamente in giù). Sia pure C il sottoanello di A generato da 1 - X e 1 - Y . Infine sia F il sottoanello delle matrici di A che hanno solo un numero finito di cifre non nulle....

Remark on inequalities for the Laplacian spread of graphs

Igor Milovanović, Emina Milovanović (2014)

Czechoslovak Mathematical Journal

Two inequalities for the Laplacian spread of graphs are proved in this note. These inequalities are reverse to those obtained by Z. You, B. Liu: The Laplacian spread of graphs, Czech. Math. J. 62 (2012), 155–168.

Remark on properties of bases for additive logratio transformations of compositional data

Karel Hron (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The statistical analysis of compositional data, multivariate data when all its components are strictly positive real numbers that carry only relative information and having a simplex as the sample space, is in the state-of-the-art devoted to represent compositions in orthonormal bases with respect to the geometry on the simplex and thus provide an isometric transformation of the data to an usual linear space, where standard statistical methods can be used (e.g. [2], [4], [5], [9]). However, in some...

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