Results 31 to 40 of about 537 (169)

Two New Factors of Fermat Numbers [PDF]

Mathematics of Computation, 1975
A new prime factor is given for each of the Fermat numbers F 12 {F_{12}} and F 13 {F_{13}} (none was previously known for F 13 {F_{13}}
Hallyburton, John C. jun., Brillhart, John   +1 more
openaire   +2 more sources

Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices

Advances in Difference Equations, 2019
In this paper, we deal mainly with a class of periodic tridiagonal Toeplitz matrices with perturbed corners. By matrix decomposition with the Sherman–Morrison–Woodbury formula and constructing the corresponding displacement of matrices we derive the ...
Yunlan Wei, Xiaoyu Jiang, Zhaolin Jiang, Sugoog Shon   +3 more
doaj   +1 more source

Condorcet interpretation of probability’s theory: the use of a mathematical construct to the field of social action [PDF]

Кантовский сборник, 2015
Probability theory, which emerged as early as the 17th century thanks to the works of Pascal and Fermat, served for a long time as a tool of professional mathematicians. It was not considered a means of rational prediction of social actions.
Yastrebtseva A.
doaj   +1 more source

Six New Factors of Fermat Numbers [PDF]

Mathematics of Computation, 1982
A new prime factor is given for each of the Fermat numbers F 29 {F_{29}} , F 36 {F_{36}} , F 99 {F_{99}} , F
Gostin, Gary B., McLaughlin, Philip B. jun.   +1 more
openaire   +2 more sources

Photon‐Sphere Modes in Curved Optical Microcavities: A Black‐Hole Analogue Laser

Advanced Science, EarlyView.
An optical analogue of a Schwarzschild black hole is realized using curved microcavities that preserve light‐like geodesics. A new family of laser modes confined around the photon sphere is identified alongside conventional whispering‐gallery modes. Analytical theory, numerical simulations, and experiments reveal curvature‐induced confinement, enabling
Chenni Xu, Aswathy Sundaresan, Nazire‐Begüm Kazkal, Clement Lafargue, Lior Zarfaty, Li‐Gang Wang, Ofek Birnholtz, Dominique Decanini, Melanie Lebental, Patrick Sebbah   +9 more
wiley   +1 more source

Micro‐Computed Tomography beamline at the Australian Synchrotron: data acquisition and processing pipeline

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, Benedicta D. Arhatari, Andrew Stevenson   +2 more
wiley   +1 more source

SPECIAL COURSE FOR SCHOOLCHILDREN: PROOF OF FERMAT'S GREAT THEOREM BY EXAMPLE x^3+y^3+z^3=0 [PDF]

Vestnik Issyk-Kulʹskogo universiteta
It is difficult to find a person among mathematicians who is not familiar with and does not study the solution of the equation x^2+y^2+z^2=0, or x^3+y^3+z^3=0 in integers.
Srashidinov A.
doaj   +1 more source

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, Gung-Chian Yin, Bo-Yi Chen, Hsin-Wei Chen, Kang-Ching Chu, Chi-Yuan Cheng, Po-Wei Lee, Jhih-Min Lin, Chun-Yu Chen, Yu-Shan Huang   +9 more
wiley   +1 more source

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

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