Spectral theory for the failure of linear control in a nonlinear stochastic system

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly nonnormal evolution operators. In spatially extended systems the nonnormality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the nonnormality and the type of nonlinearity are all crucially important to understanding and describing the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong nonnormality is due to the presence of mean flow rather than the action of control.Comment: Submitted to Physical Review

Математичне моделювання руху вільної поверхні рідини при транспортуванні сільськогосподарських напівпричіпних цистерн

Mathematical modeling of the oscillatory process ofthe longitudinal motion of a machine-tractor unit with a semitrailer tank equipped with a hydraulic liquid mixer is developed. The redistribution of liquid in the tank by the characteristics of Rayleighsurface waves is taken into consideration. The influence of the mixer operation on the total vibrational motion of the liquid in the tank is given. Thespectrum of frequencies of free mechanical oscillations is determined, and the corresponding forms ofinterconnected movements of the elements of a tractor and a tank are analyzed.Виконано математичне моделювання коливального процесу поздовжнього руху машинно-тракторного агрегату з напівпричіп-цистерною, яка має гідравлічний змішувач рідини. Для перерозподілу рідини у цистерні, що викликаний коливаннями оболонки, використано характеристики поверхневих хвиль Релея. Наведено вплив роботи змішувача на загальний коливальний рух рідини в цистерні. Знайдено спектр частот вільних механічних коливань, а також проаналізовано відповідні форми взаємопов’язаних рухів елементів трактора та цистерни

Limitations of Algebraic Approaches to Graph Isomorphism Testing

We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and only if if the graphs are isomorphic, and then to (try to) decide satisfiability of the system using, for example, the Gr\"obner basis algorithm. In some cases this can be done in polynomial time, in particular, if the equations admit a bounded degree refutation in an algebraic proof systems such as Nullstellensatz or polynomial calculus. We prove linear lower bounds on the polynomial calculus degree over all fields of characteristic different from 2 and also linear lower bounds for the degree of Positivstellensatz calculus derivations. We compare this approach to recently studied linear and semidefinite programming approaches to isomorphism testing, which are known to be related to the combinatorial Weisfeiler-Lehman algorithm. We exactly characterise the power of the Weisfeiler-Lehman algorithm in terms of an algebraic proof system that lies between degree-k Nullstellensatz and degree-k polynomial calculus

The linguistic and communicative aspect of the professional communication of doctors

Implementation of the process of speaking is impossible without communication, that is, the sequence of transmission and reception of information. Approximately half of the doctor's working time is spent on meetings, telephone conversations, communication with patients and colleagues. The ability to speak is his professional duty. A doctor, who knows how to speak creates the impression of an expert in his field, inspires trust in patients, which is a guarantee of successful treatment results. A high level of development of professional communication skills will largely determine the effectiveness of a doctor's work, his ability to logically and reasonably express his opinions, establish relationships with colleagues, and create a positive social and psychological microclimate in the team. At the same time, mistakes made in professional communication can hinder the effective performance of a doctor's duties and negatively affect his career. The basis of conflicts that reduce the creative potential of medical personnel is a low level of communicative competence caused by the lack of knowledge about communication and the corresponding communicative skills. The main goal of this work is a comprehensive consideration of the linguistic and communicative aspect of the professional communication of doctors. The methods of work involve the study of the mentioned phenomenon of linguistic and communicative skills of doctors, systematization, and correction of the acquired knowledge

Methods of noninvasive electrophysiological heart examination basing on solution of inverse problem of electrocardiography

The article represents the main noninvasive methods of heart electrical activity examination, theoretical bases of solution of electrocardiography inverse problem, application of different methods of heart examination in clinical practice, and generalized achievements in this sphere in global experience

Integrative Modeling of Electrical Properties of Pacemaker Cardiac Cells

This work represents modeling of electrical properties of pacemaker (sinus) cardiac cells. Special attention is paid to electrical potential arising from transmembrane current of Na{+}, K{+} and Ca{2+} ions. This potential is calculated using the NaCaX model. In this respect, molar concentration of ions in the intercellular space which is calculated on the basis of the GENTEX model is essential. Combined use of two different models allows referring this approach to integrative modeling

Impact of filtration elements on bioelectrical signal

Filtering of the wanted signal from the noise caused by power lines, magnetic pickup, interference from body movement, etc. in the field of medical data processing is a weighty problem of cardiography. To date, different types of digital filters have been used to clear the signal from unnecessary frequency bands. This paper presents the results of the filter simulation in MATLAB package