Results 41 to 50 of about 12,326 (180)
Journal of Synchrotron Radiation, EarlyView.The Micro‐Computed Tomography (MCT) beamline at the Australian Synchrotron has undergone significant advancements in data acquisition and processing infrastructure to support the growing diversity of user needs and experimental techniques. Recent developments in data acquisition and processing infrastructure at the beamline are presented.The Micro ...
Darren Thompson +2 more
wiley +1 more source
Differences of Harmonic Numbers and the $abc$-Conjecture [PDF]
, 2017 Our main source of inspiration was a talk by Hendrik Lenstra on harmonic numbers, which are numbers whose only prime factors are two or three. Gersonides proved 675 years ago that one can be written as a difference of harmonic numbers in only four ways ...
da Silva, Natalia +2 more
core +2 more sources
Pseudo-factorials, elliptic functions, and continued fractions
, 2009 This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials.
Bacher, Roland, Flajolet, Philippe
core +3 more sources
The hard X‐ray ptychography endstation at the Taiwan Photon Source
Journal of Synchrotron Radiation, EarlyView.The newly commissioned hard X‐ray ptychography endstation at the Taiwan Photon Source, TPS 25A2, is introduced, detailing the instrumental specifications and demonstrating a benchmark spatial resolution of 6.9 nm in 2D, showcased through the imaging of a standard test pattern, inorganic nanoparticles and a complex biological structure.Following our ...
Yi-Wei Tsai +9 more
wiley +1 more source
Integer Factorization – Cryptology Meets Number Theory
Scientific Journal of Gdynia Maritime University, 2019 Integer factorization is one of the oldest mathematical problems. Initially, the interest in factorization was motivated by curiosity about behaviour of prime numbers, which are the basic building blocks of all other integers.
Josef Pieprzyk
doaj +1 more source
Linear complexity problems of level sequences of Euler quotients and their related binary sequences
, 2014 The Euler quotient modulo an odd-prime power $p^r~(r>1)$ can be uniquely decomposed as a $p$-adic number of the form $$ \frac{u^{(p-1)p^{r-1}} -1}{p^r}\equiv a_0(u)+a_1(u)p+\ldots+a_{r-1}(u)p^{r-1} \pmod {p^r},~ \gcd(u,p)=1, $$ where $0\le a_j(u)1$.
Chen, Zhixiong, Du, Xiaoni, Niu, Zhihua
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The Role of Dice in the Emergence of the Probability Calculus
International Statistical Review, EarlyView.Summary The early development of the probability calculus was clearly influenced by the roll of dice. However, while dice have been cast since time immemorial, documented calculations on the frequency of various dice throws date back only to the mid‐13th century.
David R. Bellhouse, Christian Genest
wiley +1 more source
, 2009 We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any ...
A. Kriegl +16 more
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Rational points on even‐dimensional Fermat cubics
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract We show that even‐dimensional Fermat cubic hypersurfaces are rational over any field of characteristic not equal to three, by constructing explicit rational parameterizations with polynomials of low degree. As a byproduct of our rationality constructions, we obtain estimates for the number of their rational points over a number field and ...
Alex Massarenti
wiley +1 more source
On the emergence of the Quanta Prime sequence
Arab Journal of Basic and Applied SciencesThis paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications.
Moustafa Ibrahim
doaj +1 more source