This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described.
This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.
We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix. Based on the relations between the real parts of the eigenvalues and the weighted logarithmic matrix norms, we derive both lower and upper bounds of the matrix exponential, which complement and improve the existing results in the literature. Some numerical examples are also given.
A total dominating set in a graph $G$ is a subset $X$ of $V(G)$ such that each vertex of $V(G)$ is adjacent to at least one vertex of $X$. The total domination number of $G$ is the minimum cardinality of a total dominating set. A function $f\colon V(G)\rightarrow \{-1,1\}$ is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of an SDF is the sum of its function values over all vertices. The signed domination number of $G$ is the minimum weight of an SDF on $G$. In this paper we present several upper bounds on the algebraic connectivity of a connected graph in terms of the total domination and signed domination numbers of the graph. Also, we give lower bounds on the Laplacian spectral radius of a connected graph in terms of the signed domination number of the graph.
The hypergeometric distributions have many important applications, but they have not had sufficient attention in information theory. Hypergeometric distributions can be approximated by binomial distributions or Poisson distributions. In this paper we present upper and lower bounds on information divergence. These bounds are important for statistical testing and for a better understanding of the notion of exchangeability.
Let $A$ be an $n\times n$ symmetric, irreducible, and nonnegative matrix whose eigenvalues are $\lambda _1 > \lambda _2 \ge \ldots \ge \lambda _n$. In this paper we derive several lower and upper bounds, in particular on $\lambda _2$ and $\lambda _n$, but also, indirectly, on $\mu = \max _{2\le i \le n} |\lambda _i|$. The bounds are in terms of the diagonal entries of the group generalized inverse, $Q^{\#}$, of the singular and irreducible M-matrix $Q=\lambda _1 I-A$. Our starting point is a spectral resolution for $Q^{\#}$. We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected graphs, where now $Q$ becomes $L$, the Laplacian of the graph. In case the graph is a tree we find a graph-theoretic interpretation for the entries of $L^{\#}$ and we also sharpen an upper bound on the algebraic connectivity of a tree, which is due to Fiedler and which involves only the diagonal entries of $L$, by exploiting the diagonal entries of $L^{\#}$.
Jako Bouveretův syndrom je označována obstrukce v oblasti duodena impaktovaným žlučovým kamenem, který vycestuje cholecystoduodenální či cholecystogastrickou píštělí. Onemocnění je vzácné, vyskytuje se zejména u starších žen s četnými komorbiditami a vysokým operačním rizikem. K diagnóze se zpravidla dospěje endoskopicky nebo pomocí zobrazovacích metod. Pokud stav nelze řešit endoskopicky, je indikováno operační řešení. Autoři prezentují případ Bouveretova syndromu u 79leté pacientky, u níž se zdařilo zdokumentovat všechny fáze vyšetřovacího a léčebného procesu. Součástí sdělení je přehled literatury týkající se diagnostiky a terapie tohoto vzácného syndromu., Bouveret syndrome is a gastric outlet obstruction caused by impaction of a gallstone that passes through a cholecystoduodenal or cholecystogastric fistula. It is a rare disease, most common in elderly women with multiple comorbidities and high surgical risk. The diagnosis can be made either radiologically or endoscopically. Endoscopic extraction is the preferred therapeutic option. Surgical intervention is indicated when endoscopic methods fail. We describe a case of Bouveret syndrome in a 79 years old woman. The report is followed by a review of literature on the diagnostics and treatment of this rare syndrome., and P. Kocián, M. Bocková, J. Schwarz
Fourteen three-month-old rabbits spontaneously-infected with the microsporidium Encephalilozoon cuniculi Levaditi, Nicolau et Schoen, 1923 were inoculated intravenously with lymphocytes (Ly) from seropositive bovine leukemia virus infected cattle (Ly/BLV) or with fetal lamb kidney cells infected with bovine fetal leukemia (FLK/BLV). Thirteen rabbits were seropositive to BLV at least for a period of three months. Six rabbits died of pulmonary lesions. Chronic inflammatory lesions of ence-phalitozoonosis were found in six rabbits killed between 454 and 548 days of the observation period. Five animals bore subcutaneous granulomas. Immunohistochemically, E. cuniculi was demonstrated in the inflammatory lesions of rabbits studied. Control animals also spontaneously infected with E. cuniculi did not show clinical signs of encephalitozoonosis. Morphological changes were found incidentally in the form of small glial foci and focal interstitial nephritis in these animals. The combined action of BLV - E. cuniculi on the bodies of rabbits is proposed as a suitable model for the study of encephalitozoonosis in man with human immunodeficiency virus (HIV) infection.