In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a new class of multivalued solutions for an arbitrary thermodynamic state model and discuss singularities of their projections to the space of independent variables for the case of an ideal gas. Caustics and discontinuity lines are found.

From the literature, it is known that solutions of homogenous linear stable difference equations may experience large deviations, or peaks, from the nonzero initial conditions at finite time instants. In this paper we take a probabilistic standpoint to analyze these phenomena by assuming that both the initial conditions and the coefficients of the equation have random nature. Under these assumptions we find the probability for deviations to occur, which turns out very close to unity even for equations of low degree, which means that peak is typical. We also address other issues such as evaluation of the mean magnitude and maxumum value of peak.

Одной из известных теорем о неподвижной точке для отображений банаховых пространств является Теорема Канторовича о неподвижной точке (см. [1, гл. XVIII, §1.2, теорема 1]). в В статье [2] эти результаты были распространены на отображения между метрическими пространствами. Там мы вывели теоремы о существовании неподвижных точек и точек совпадения для отображений между метрические пространства. Данная работа является продолжением статьи [2] и посвящена вопросам устойчивости неподвижные точки и точки совпадения отображений между метрическими пространствами при малых возмущения соответствующих отображений. Стабильность доказана при очень общие предположения. Рассматриваются как однозначные, так и многозначные отображения.

Вычислены симметрии и дифференциальные инварианты для потоков вязких жидкостей на пространственных кривых. Найдены зависимости между алгебрами Ли симметрий, геометрией кривой и зависимостью вязкости хидкости от температуры.

Acceleration sensors allow a reduction of time-consuming visual observation. The drinking behavior of bucketfed calves has not been monitored automatically yet, although sufficient milk intake is essential for calves’ health and growth. The objectives of this pilot study were (1) to evaluate the technical and mathematical feasibility of using an acceleration sensor to detect drinking events in bucket-fed dairy calves, (2) to develop an algorithm for an acceleration sensor (SMARTBOW ear tag, Smartbow GmbH, Weibern, Austria) for monitoring drinking behavior in bucket-fed dairy calves, and (3) to validate the SMARTBOW sensor for monitoring drinking events in bucket-fed dairy calves to observations from video recordings. Three preweaned dairy calves were equipped with ear-tag accelerometers. Calves were housed in individual pens and fed milk from a teat-bucket twice a day. Acceleration data were collected and calf behavior was video-recorded for 5 d for 24 h d−1 . Based on a training data set, an algorithm was developed to predict drinking events. Further 15 d of data were generated by simulation. Video recordings were used to analyze whether drinking events (n = 174) were predicted correctly for the complete data set. Sensitivity (82.9%), specificity (96.9%), and accuracy (96.2%) were good, but precision (60.4%) was not yet optimal. Cohen’s Kappa (0.68) indicated substantial agreement between sensor and video analysis. More research based on a larger number of animals with the aim to optimize the underlying algorithm and to further increase sensitivity and precision is planned.