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Let G be a connected graph with adjacency matrix $ A(G) $ A (G) and distance matrix $ \mathcal {D}(G) $ D (G). The adjacency-distance matrix of G is defined as $ S(G) = \mathcal {D}(G) + A(G) $ S (G) = D (G) + A (G). In this paper, $ S(G) $ S (G) is generalized by the convex linear combinations \[ S_{\alpha}(G)=\alpha \mathcal{D}(G)+(1-\alpha)A(G) \] S α (G) = α D (G) + (1 − α) A (G) where $ \alpha \in [0,1] $ α ∈ [ 0 , 1 ]. Let $ \rho (S_{\alpha }(G)) $ ρ (S α (G)) be the spectral radius of $ S_{\alpha }(G) $ S α (G). This paper presents results on $ S_{\alpha }(G) $ S α (G) with emphasis on $ \rho (S_{\alpha }(G)) $ ρ (S α (G)) and some results on $ S(G) $ S (G) are extended to all α in some subintervals of $ [0,1] $ [ 0 , 1 ]. For $ \alpha \in [1/2,1] $ α ∈ [ 1 / 2 , 1 ] , the trees attaining the largest and the smallest $ \rho (S_{\alpha }(G)) $ ρ (S α (G)) among trees of fixed order are determined and it is proved that $ \rho (S_{\alpha }(G)) $ ρ (S α (G)) is a branching index. Moreover, for $ \alpha \in (1/2,1] $ α ∈ (1 / 2 , 1 ] , the graphs that uniquely minimize $ \rho (S_{\alpha }(G)) $ ρ (S α (G)) : among all connected graphs of fixed order and fixed connectivity, and among all connected graphs of fixed order and fixed chromatic number are characterized. [ABSTRACT FROM AUTHOR]

This paper studies two inverse eigenvalue problems for two kinds of acyclic matrices whose graphs are caterpillars. The spectral data of the first problem considers the minimal and maximal eigenvalues of all leading principal submatrices of the matrix. The second consists of an extremal eigenvalue of each leading principal submatrix and one eigenpair of the matrix. In the main results, we give sufficient conditions for the existence of such matrices, and their proofs provide algorithmic procedures for their construction. Finally, we present some numerical examples that illustrate the applicability of the solutions obtained. [ABSTRACT FROM AUTHOR]

Introduction: Foreign body ingestion (FBI) is common in pediatrics and can lead to complications. The aim of the present study is to review the experience of our center in the management of these patients and to propose a treatment protocol. Material and Method: Retrospective, observational and descriptive cross-sectional study, in which the endoscopic reports and records of patients diagnosed with IFB managed by the Pediatric Endoscopy Unit of the Regional Clinical Hospital of Concepción between January 2013 and June 2017 (53 months) were reviewed, with a total of 40 cases. Data recording and analysis was performed with Microsoft® Excel 2016® for MacOS®. Results: The average age was 3,96 ± 3,24 years. The statistical fashion was 2 years. All patients underwent a upper gastrointestinal endoscopy. The most frequent FB was the coin (61,9%). In 6 opportunities (14,2%) was a button batery. FB retention was in the proximal third of the esophagus (30,9%), the gastric body (26,2%) and the distal third of the esophagus (14,2%), being extracted mainly with foreign body clamp (90,4%). The 57,5% showed some injury related to the location of the FB, being the most serious the produced by button batery. Conclusion: FBI in children is a potentially dangerous entity, so it becomes necessary to have a pediatric endoscopy unit and treatment protocols to avoid complications, especially with high-risk objects. [ABSTRACT FROM AUTHOR]

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