As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker-Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge-Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black-Scholes two-dimensional model are used. To illustrate the stochastic "predator-prey" type model is used. The utility of the combined numerical-analytical approach is demonstrated.

The article is an overview. We carry out the comparison of actual machine learning libraries that can be used the neural networks development. The first part of the article gives a brief description of TensorFlow, PyTorch, Theano, Keras, SciKit Learn libraries, SciPy library stack. An overview of the scope of these libraries and the main technical characteristics, such as performance, supported programming languages, the current state of development is given. In the second part of the article, a comparison of five libraries is carried out on the example of a multilayer perceptron, which is applied to the problem of handwritten digits recognizing. This problem is well known and well suited for testing different types of neural networks. The study time is compared depending on the number of epochs and the accuracy of the classifier. The results of the comparison are presented in the form of graphs of training time and accuracy depending on the number of epochs and in tabular form.

This paper discusses stochastic numerical methods of Runge-Kutta type with weak and strong convergences for systems of stochastic differential equations in Itô form. At the beginning we give a brief overview of the stochastic numerical methods and information from the theory of stochastic differential equations. Then we motivate the approach to the implementation of these methods using source code generation. We discuss the implementation details and the used programming languages and libraries

When modeling such phenomena as population dynamics, controllable flows, etc., a problem arises of adapting the existing models to a phenomenon under study. For this purpose, we propose to derive new models from the first principles by stochastization of one-step processes. Research can be represented as an iterative process that consists in obtaining a model and its further refinement. The number of such iterations can be extremely large. This work is aimed at software implementation (by means of computer algebra) of a method for stochastization of one-step processes. As a basis of the software implementation, we use the SymPy computer algebra system. Based on a developed algorithm, we derive stochastic differential equations and their interaction schemes. The operation of the program is demonstrated on the Verhulst and Lotka-Volterra models.

In the special theory of relativity (SR) it is usual to highlight so-called paradoxes. One of these paradoxes is the formal appearance of speed values grater then the light speed. In this paper we show that most of these paradoxes arise due to the incompleteness of relativistic calculus over velocities. Namely, operation over speeds form a group by composition. In this case, the extension to the field is usually carried out using non-relativistic operations.