In particular,δ(Tp)>0.63for all primesp. For a video summary of this paper, please visithttps://youtu.be/3ujCuVwH8k8.doi:10.1016/j.jnt.2016.11.027Wu, Bing-LingChen, Yong-GaoESJournal of Number TheoryB.-L. Wu, Y.-G. Chen, On certain properties of harmonic numbers, J. Num- ber...
The main idea of ranking-based selection is that the performance of the base classifiers is ranked according to a certain algorithm, and the preferred selection is based on the ranking result30. The essence of clustering-based selection is to first use a clustering algorithm to classify the ...
Polyspace for Ada ©️ — Provide code verification that proves the absence of overflow, divide-by-zero, out-of-bounds array access, and certain other run-time errors in source code. SPARK ©️ — Static analysis and formal verification toolset for Ada.Assembly...
While they are non-commutative, they do keep many other properties of the complex numbers: Being non-commutative, the quaternions do not form a field. However, they are still a skew field (or division ring): multiplication is associative, and every non-zero quaternion has a unique ...
substructure-level attributions; the former can help understand the “counterfactual” predictions to discover potential biases from datasets, and the latter can provide more granular references (such as the confidence of a certain chemical bond being broken) to inspire researchers to design customized ...
So far is certain and demonstrable. I think it also possible that there is a centre of gravity to each set of three, and that the line joining each such centre with the outside apex will intersect in a common point the centre of gravity of the whole body of aesthetic; but what that ...
As regards the co-ordination of all ordinary properties of matter, Rutherford’s model of the atom puts before us a task reminiscent of the old dream of philosophers: to reduce the interpretation of the laws of nature to the consideration of pure numbers. ...
The well-known abc conjecture and twin prime conjecture, are two typical examples. The largest prime factor of shifted integer P+(n+a) with n imposed certain restrictions on its multiplicative properties, is also of this type, where P+(n) denotes the largest prime factor of n with the ...
Other kinds of inharmonicity can be produced by certain percussion instruments, for example the metallophones of Indonesian gamelans and the xylophone-likerenatsused in Thai classical music15. Each instrument will have an idiosyncratic spectrum that reflects its particular physical construction, with po...
of virtual edges. In detail, pairs of atoms with interatomic distances below a certain threshold are bonded via covalent localized edges because chemical bonds can dominate interatomic forces when two atoms are close enough to each other while global edges are linked to the remaining pairs of ...