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...

PROMS, a computer-music service under development at the University of Bonn, Germany, aims at designing and implementing PROcedures for Music Search. This paper discusses an eÆcient algorithm for searching a music pattern, e.g., a melody or a sequence of chords, in a large database of polyphonic music, given in a score-like format. Our algorithm is a variant of the now classic inverted le index...

We present a new indexing method for the approximate string matching problem. The method is based on a suux tree combined with a partitioning of the pattern. We analyze the resulting algorithm and show that the retrieval time is O(n), for 0 < < 1, whenever < 1 ? e= p , where is the error level tolerated and is the alphabet size. We experimentally show that this index outperforms by far all othe...

We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energyefficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This paper presents dynamic-analysis tools to debug and monitor the quality of approximate computations. We propose ...

We present a method to speed up approximate string matching by mapping the factual alphabet to a smaller alphabet. We apply the alphabet reduction scheme to a tuned version of the approximate Boyer– Moore algorithm utilizing the Four-Russians technique. Our experiments show that the alphabet reduction makes the algorithm faster. Especially in the k-mismatch case, the new variation is faster tha...