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A real matrix is called totally nonnegative if all of its minors are nonnegative. In this paper the extended Perron complement of a principal submatrix in a matrix A is investigated. In extension of known results it is shown that if A is irreducible and totally nonnegative and the principal submatrix consists of some specified consecutive rows then the extended Perron complement is totally nonnegative. Also inequalities between minors of the extended Perron complement and the Schur complement are presented.
We consider classes of n-by-n sign regular matrices, i.e., of matrices with the property that all their minors of fixed order k have one specified sign or are allowed also to vanish, k = 1, ... ,n. If the sign is nonpositive for all k, such a matrix is called totally nonpositive. The application of the Cauchon algorithm to nonsingular totally nonpositive matrices is investigated and a new determinantal test for these matrices is derived. Also matrix intervals with respect to the checkerboard partial ordering are considered. This order is obtained from the usual entry-wise ordering on the set of the n-by-n matrices by reversing the inequality sign for each entry in a checkerboard fashion. For some classes of sign regular matrices it is shown that if the two bound matrices of such a matrix interval are both in the same class then all matrices lying between these two bound matrices are in the same class, too.
In this paper totally nonnegative (positive) matrices are considered which are matrices having all their minors nonnegative (positve); the almost totally positive matrices form a class between the totally nonnegative matrices and the totally positive ones. An efficient determinantal test based on the Cauchon algorithm for checking a given matrix for falling in one of these three classes of matrices is applied to matrices which are related to roots of polynomials and poles of rational functions, specifically the Hankel matrix associated with the Laurent series at infinity of a rational function and matrices of Hurwitz type associated with polynomials. In both cases it is concluded from properties of one or two finite sections of the infinite matrix that the infinite matrix itself has these or related properties. Then the results are applied to derive a sufficient condition for the Hurwitz stability of an interval family of polynomials. Finally, interval problems for a subclass of the rational functions, viz. R-functions, are investigated. These problems include invariance of exclusively positive poles and exclusively negative roots in the presence of variation of the coefficients of the polynomials within given intervals.
Sleep is an important aspect in life of every human being. The average sleep duration for an adult is approximately 7 h per day. Sleep is necessary to regenerate physical and psychological state of a human. A bad sleep quality has a major impact on the health status and can lead to different diseases. In this paper an approach will be presented, which uses a long-term monitoring of vital data gathered by a body sensor during the day and the night supported by mobile application connected to an analyzing system, to estimate sleep quality of its user as well as give recommendations to improve it in real-time. Actimetry and historical data will be used to improve the individual recommendations, based on common techniques used in the area of machine learning and big data analysis.
Schicksal der Freybrücke
(2016)
Karl Bernhard gilt als einer der bedeutendsten Bauingenieure in Deutschland Anfang des 20. Jahrhunderts. Seine beiden Brücken entlang der Heerstraße in Berlin, die Stößenseebrücke und die Freybrücke über die Havel, sind seit 1909 verkehrstechnisch von höchster Bedeutung für die Ost-West-Verbindung der Stadt. Die Freybrücke wurde jedoch im März 2015 abgerissen, um einem Ersatzneubau Platz zu machen. Wie kam es dazu, dass eine historisch und verkehrstechnisch derart wichtige, seit 1971 unter Denkmalschutz stehende Konstruktion so lange vernachlässigt wurde, bis sie abbruchreif war? Dieser Artikel ist eine Hommage an Bernhards Havelbrücke und geht ihrer wechselvollen Geschichte nach.
This letter introduces signal constellations based on multiplicative groups of Eisenstein integers, i.e., hexagonal lattices. These sets of Eisenstein integers are proposed as signal constellations for generalized spatial modulation. The algebraic properties of the new constellations are investigated and a set partitioning technique is developed. This technique can be used to design coded modulation schemes over hexagonal lattices.
This paper considers intervals of real matrices with respect to partial orders and the problem to infer from some exposed matrices lying on the boundary of such an interval that all real matrices taken from the interval possess a certain property. In many cases such a property requires that the chosen matrices have an identically signed inverse. We also briefly survey related problems, e.g., the invariance of matrix properties under entry-wise perturbations.