The objective of the research was to perform computer simulation of diffusion in a mixture of ideal gases considering the dependence of the diffusion coefficient on the entropy of mixing according to the proposed mathematical model. Computer simulation was carried out in one-dimensional and two-dimensional settings using finite element method and Python programming language with the use of NumPy and SciPy libraries. The obtained results show that the proposed mathematical model of diffusion in a mixture of ideal gases could be used to solve computer simulation tasks of gas diffusion satisfying the principle of mass conservation, because the entropy is considered via the chemical potential. More >

Binary functions have a wide range of applications in the fields of machine learning, statistical learning, and so on. In this paper, we investigate the exponential inequalities for the independent $V$-statistics of binary affine functions and obtain a universal inequality for $V$-statistics. Due to the typical characteristics of this kind of binary function, including symmetry and affinity, this work has great practical significance. Finally, we derive the corresponding inequalities in the context of specific similarity learning. More >