Image zooming based on sampling theorems

In this paper we introduce two digital zoom methods based on sampling theory and we study their mathematical foundation. The first one (usually known by the names of "sinc interpolation", "zero-padding" and "Fourier zoom") is commonly used by the image processing community

On solutions of the Fréchet functional equation

AbstractIn this paper we give a new proof of a classical result by Fréchet [M. Fréchet, Une définition fonctionnelle des polynomes, Nouv. Ann. 9 (4) (1909) 145–162]. Concretely, we prove that, if Δhk+1f=0 and f is continuous at some point or bounded at some nonempty open set, then f∈Pk. Moreover, as a consequence of the technique developed for our proof, it is possible to give a description of the closure of the graph for the solutions of the equation. Finally, we characterize some spaces of polynomials of several variables by the use of adequate generalizations of the forward differences operator Δhk+1

On the Geometric-Arithmetic Index

The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index GA1 and characterize graphs extremal with respect to them. In particular, we improve some known inequalities and we relate GA1 to other well known topological indices.Publicad

Spectral study of the Geometric-Arithmetic Index

The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reected in the algebraic properties of some matrices. The aim of this paper is to study the geometric-arithmetic index GA1 from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices.Supported in part by a grant from Ministerio de Economía y Competititvidad (MTM 2013-46374-P), Spain, and by a grant from CONACYT (CONACYT-UAG I0110/62/10), México.Publicad

Spectral properties of geometric-arithmetic index

The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reflected in the algebraic properties of some matrices. The aim of this paper is to study the geometric-arithmetic index GA(1) from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices. Moreover, using this matrix, we define a GA Laplacian matrix which determines the geometric-arithmetic index of a graph and satisfies properties similar to the ones of the classical Laplacian matrix. (C) 2015 Elsevier Inc. All rights reserved.This research was supported in part by a Grant from Ministerio de Economía y Competitividad (MTM 2013-46374-P), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México

Fast Normalized Cross-Correlation for Template Matching with Rotations

Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including rotations requires sampling the whole space of rotations, repeating the computation of the correlation each time. This article develops an alternative mathematical theory to handle efficiently, at the same time, rotations and translations. Our proposal has a reduced computational complexity because it does not require to repeatedly sample the space of rotations. To do so, we integrate the information relative to all rotated versions of the template into a unique symmetric tensor template -which is computed only once per template-. Afterward, we demonstrate that the correlation between the image to be processed with the independent tensor components of the tensorial template contains enough information to recover template instance positions and rotations. Our proposed method has the potential to speed up conventional template matching computations by a factor of several magnitude orders for the case of 3D images

New results on the harmonic index and its generalizations

In this paper we obtain new inequalities involving the harmonic index and the(general) sum-connectivity index, and characterize graphs extremal with respect tothem. In particular, we improve and generalize some known inequalities and werelate this indices to other well-known topological indices.The authors are grateful to the referees for their valuable comments which have improved this paper. This work is supported in part by two grants from Ministerio de Economía y Competititvidad (MTM2013-46374-P and MTM2015-69323-REDT), Spain, and a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México

Optimal upper bounds of the geometric-arithmetic index

The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new upper bounds of the geometric-arithmetic index and characterize graphs extremal with respect to them.This research was supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00 / AEI / 10.13039/501100011033), Spain

Alianzas en grafos

En este trabajo estudiamos propiedades matemáticas de las k-alianzas en grafos y prestamos especial interés a la relación que existe entre el número de k-alianza (defensiva, ofensiva y dual) y otros parámetros conocidos como, por ejemplo, el orden, la medida, el cuello, el diámetro, el número de independencia, el número de dominación, la conectividad algebraica y el radio espectral. En algunos casos obtenemos el valor exacto del número de k-alianza y, en general, obtenemos cotas tensas no triviales para dicho parámetro. En el caso del grafo línea, se obtienen resultados sobre el número de alianza (defensiva y ofensiva) en función de parámetros conocidos del grafo original. A lo largo de toda la memoria particularizamos al caso de grafos planares y de grafos cúbicos. Estudiamos, además, la relación entre alianzas defensivas y ofensivas, así como las principales propiedades de los conjuntos libres de k-alianzas y de los cubrimientos de k-alianzas. Otra de las aportaciones de esta memoria es el inicio del estudio de las k-alianzas conexas y de las k-alianzas independientes, as´ı como el estudio de la relación entre los conjuntos k-dominantes totales y las k-alianzas (defensivas, ofensivas y duales). Esta memoria está estructurada en tres capítulos. Los dos primeros, aunque de similar estructura, son independientes y están dedicados al estudio de las k-alianzas defensivas y de las k-alianzas ofensivas, respectivamente. En el Capítulo 3 estudiamos las k-alianzas duales, los conjuntos k-dominantes totales, así como los cubrimientos y los conjuntos libres de k-alianzas