This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on density and time space variables $t$ $x$. The assumptions contain only locally Lipschitz assumption respect to variable some hypothesis extra variables. It may be seen as first step consider heat-conducting physical laws such truncated virial assum...

for the existence of an approximate system of numerical representation. Such a system, commonly referred to as the “analog magnitude system,” seems to have no upper limit but is subject to a ratio limit in accordance with Weber’s Law, which states that the capacity to discriminate between two quantities becomes more accurate as the ratio between the smaller and the larger quantity increases (Be...

In this paper, a simple, robust, fast and effective method based on the conserved quantities is developed to approximate analyse shape, structure interaction characters of solitary waves described by Benjamin–Bona–Mahony (BBM) equation. Due invariant character quantities, there no need solve related complex nonlinear partial differential BBM equation simulate interactions between at most mergin...

in this paper, an approximate axisymmetric method is developed which can reliably calculate fully viscous hypersonic flow over blunt-nosed bodies. in this method, a maslen’s second-order pressure expression is used instead of the normal momentum equation. the combination of maslen’s second-order pressure expression and viscous shock layer equations is developed to accurately and efficiently com...

Following recent result of L. M. Tóth [Tót21, Annales Henri Lebesgue, Volume 4 (2021)] we show that every 2Δ-regular Borel graph

Distinct elements (F0). In this note we will consider the distinct elements problem, also known as the F0 problem, defined as follows. We are given a stream of integers i1, . . . , im ∈ [n] where [n] denotes the set {1, 2, . . . , n}. We would like to output the number of distinct elements seen in the stream. As with Morris’ approximate counting algorithm, our goal will be to minimize our space...

We present a new approach to multi-dimensional parsing using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the two-dimensional structure of written mathematics. Our approach makes no hard decisions; recognized math expressions are reported to the user in ranked order. A flexible correction mechanism enables users to quickly choose the corre...

This study investigated changes in the complexity (magnitude and structure of variability) of the collective behaviours of association football teams during competitive performance. Raw positional data from an entire competitive match between two professional teams were obtained with the ProZone tracking system. Five compound positional variables were used to investigate the collective patterns...