scholarly journals "Some Small Discrepancy": Jean-Christophe Bailly's Creaturely Ontology

2013 ◽  
Vol 3 (2) ◽  
pp. 163
Author(s):  
Pick
Keyword(s):  
2019 ◽  
Vol 14 (1) ◽  
pp. 53-86
Author(s):  
Florian Pausinger

AbstractThe intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri’s 80th birthday we aim to survey (some of) his contributions over the last four decades which considerably improved our understanding of one-dimensional van der Corput sequences and inspired a lot of related work. We recall and compare the different approaches in the search for generalised van der Corput sequences with low discrepancy, i.e., using a single generating permutation versus using a sequence of permutations. Throughout, we collect, sharpen and extend open questions which all stem from the extensive work of Henri and his coworkers and which will hopefully inspire more work in the future.


2013 ◽  
Vol 22 (3) ◽  
pp. 342-345 ◽  
Author(s):  
CHRISTOPH AISTLEITNER

In a paper published in this journal, Alon, Kohayakawa, Mauduit, Moreira and Rödl proved that the minimal possible value of the normality measure of an N-element binary sequence satisfies \begin{equation*} \biggl( \frac{1}{2} + o(1) \biggr) \log_2 N \leq \min_{E_N \in \{0,1\}^N} \mathcal{N}(E_N) \leq 3 N^{1/3} (\log N)^{2/3} \end{equation*} for sufficiently large N, and conjectured that the lower bound can be improved to some power of N. In this note it is observed that a construction of Levin of a normal number having small discrepancy gives a construction of a binary sequence EN with (EN) = O((log N)2), thus disproving the conjecture above.


1987 ◽  
Vol 104 (4) ◽  
pp. 273-337 ◽  
Author(s):  
Harald Niederreiter
Keyword(s):  

1980 ◽  
Vol 90 (4) ◽  
pp. 315-329 ◽  
Author(s):  
R. Tijdeman ◽  
G. Wagner
Keyword(s):  

2002 ◽  
Vol 57 (1-2) ◽  
pp. 45-48 ◽  
Author(s):  
Shao-Yi Wu ◽  
Wen-Chen Zheng

The anisotropic g-factors gx, gy , and gz for Co2+ in rutile crystal are studied from the secondorder perturbation formulas based on the cluster approach. In the studies, the contributions due to covalency effects, the configuration interaction and the rhombic crystal field are taken into account. The calculated values are close to the observed ones. The small discrepancy between calculation and experiment is discussed


In 1864 John Marshall, of University College Hospital, London, published in the ‘ Philosophical Transactions ’ an account of a brain of exceptional interest, that of a Bushwoman. The original documents and photographs relating to this brain were recently handed to Professor Elliot Smith by his daughter, Miss Marshall, On his advice these documents have been studied anew.* In making his drawings from these photographs the lithographer made some slight changes which convey an erroneous impression of the primitive features that confer exceptional importance on this Bushwoman’s brain. The progress of knowledge of this subject since 1864 enables us to interpret the photographs in another way and so make this interesting evidence available for the interpretation of such archaic forms of brain as are revealed in the endocranial casts of Pithecanthropus , Sinanthropus , and Eoanthropus . The original photographs represent the dorsal, ventral, lateral, anterior and posterior aspects of both hemispheres and the medial aspect of the left hemisphere. There is no photograph of the medial aspect of the right hemisphere. In addition to the photographs of the brain there are photographs of the head before the removal of the brain, and fortunately a photograph of the left hemisphere in situ within the cranium. Marshall’s photographs are exactly the same size as the lithographic figures ; and he states that the figures agree in size with the preserved brain. He also gives measurements of the cerebrum taken from intracranial casts. There is a small discrepancy between the length of the cerebrum as measured on the photograph showing the brain in the cranium and the figures in his table. The amount of shrinkage is shown in fig. 25, Plate 3. In estimating the form and size of the outline of the endocranial cast of the Bushwoman figured in this paper, Marshall’s maximum figures are taken; allowing for this possible error, his illustrations enable us to reproduce the form fairly accurately. In Marshall' s table of measurements, in which he contrasts the European brain with the Bushwoman’s, the European brain is smaller in certain dimensions. This indicates that he specially selected an abnormally small European brain for comparison.


2011 ◽  
Vol 291-294 ◽  
pp. 1582-1588
Author(s):  
Tie Neng Guo ◽  
Bin Song ◽  
Dong Liang Guo ◽  
Zhong Qing Chen

The joint has a significant effect on the dynamic characteristic of the mechanism, and the identification of the stiffness of the joints has become a key problem. In this paper, a method is presented for identifying the dynamic characteristic of joints. An experiment is designed to test the dynamic parameter of the bolted joints specimen; the identification method, based on experiment, has a high accuracy result. By taking a specimen to experiment and identify the dynamic characteristic of joints, the relationship between the preload on the bolts and the joints stiffness is acquired. In order to validate the accuracy of the result, the FEM software is used to simulate. There are only a small discrepancy between the results of identification and simulation.


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