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In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.
Further applications of the Cauchon algorithm to rank determination and bidiagonal factorization
(2018)
For a class of matrices connected with Cauchon diagrams, Cauchon matrices, and the Cauchon algorithm, a method for determining the rank, and for checking a set of consecutive row (or column) vectors for linear independence is presented. Cauchon diagrams are also linked to the elementary bidiagonal factorization of a matrix and to certain types of rank conditions associated with submatrices called descending rank conditions.
Assistive environments are entering our homes faster than ever. However, there are still various barriers to be broken. One of the crucial points is a personalization of offered services and integration of assistive technologies in common objects and therefore in a regular daily routine. Recognition of sleep patterns for the preliminary sleep study is one of the health services that could be performed in an undisturbing way. This article proposes the hardware system for the measurement of bio-vital signals necessary for initial sleep study in a non-obtrusive way. The first results confirm the potential of measurement of breathing and movement signals with the proposed system.
Due to the rising need for palliative care in Russia, it is crucial to provide timely and high-quality solutions for patients, relatives, and caregivers. A methodology for remote monitoring of patients in need of palliative care and the requirements will be developed for a hardware-software complex for remote monitoring of patients' health at home.
The actual task of electrocardiographic examinations is to increase the reliability of diagnosing the condition of the heart. Within the framework of this task, an important direction is the solution of the inverse problem of electrocardiography, based on the processing of electrocardiographic signals of multichannel cardio leads at known electrode coordinates in these leads (Titomir et al. Noninvasiv electrocardiotopography, 2003), (Macfarlane et al. Comprehensive Electrocardiology, 2nd ed. (Chapter 9), 2011).