Results 71 to 80 of about 31,249 (173)

Random Diophantine equations in the primes

Mathematika, Volume 72, Issue 3, July 2026.
Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley   +1 more source

On the Foundational Arguments of Sufficient Dimension Reduction

WIREs Computational Statistics, Volume 18, Issue 2, June 2026.
Contemporary Sufficient Dimension Reduction, a versatile method for extracting material information from data, can serve as a preprocessor for classical modeling and inference, or as a standalone theory that leads directly to statistical inference. ABSTRACT Sufficient dimension reduction (SDR) refers to supervised methods of dimension reduction that ...
R. Dennis Cook
wiley   +1 more source

A Tapestry of Ideas with Ramanujan’s Formula Woven In

Axioms
Zeta-functions play a fundamental role in many fields where there is a norm or a means to measure distance. They are usually given in the forms of Dirichlet series (additive), and they sometimes possess the Euler product (multiplicative) when the domain ...
Nianliang Wang, Takako Kuzumaki, Shigeru Kanemitsu   +2 more
doaj   +1 more source

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1151-1298, May 2026.
Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley   +1 more source

A survey of the alternating sum-of-divisors function

Acta Universitatis Sapientiae, Mathematica, 2013
Abstract We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function β defined by β(pa) = pa − pa−1 + pa−2 − · · · + (−1)a for every prime power pa (a ≥ 1), and extended by multiplicativity. Certain open problems are also stated.
openaire   +5 more sources

Time‐resolved XPCS analysis across broad time‐scales using multi‐tau two‐time correlations

Journal of Synchrotron Radiation, Volume 33, Issue 3, Page 698-707, May 2026.
A scalable multi‐tau two‐time correlation framework enables efficient, time‐resolved XPCS analysis of long duration high‐frame‐rate modern synchrotron data while preserving sensitivity to non‐stationary dynamics.We present a multi‐tau two‐time correlation (MT‐2TC) analysis for X‐ray photon correlation spectroscopy that enables efficient analysis of ...
Fabio Brugnara, Marco Cammarata, Yuriy Chushkin, Irene Festi, Massimo Granata, David Hofman, Matteo Leonardi, Daniele Marzi, Denis Nabari, Angela Trapananti, Simone Ziglio, Federico Zontone, Marco Zanatta, Giacomo Baldi   +13 more
wiley   +1 more source

A note on twin practical numbers

Le Matematiche, 2002
A positive integer m is a practical number if every positive integer n < m is a sum of distinct divisors of m. Let P_2 (x) be the counting function of the pairs (m, m + 2) of twin practical numbers. Margenstern gave a conjecture on P_2 (x).
Giuseppe Melfi
doaj  

Glass bead games: enumeration of possible polytypes based on two stacking vectors and applications to the iron‐ore sinter phases SFCA and SFCA‐I

Acta Crystallographica Section A, Volume 82, Issue 3, Page 145-162, May 2026.
General formulas are presented that allow for the enumeration of polytypes based on translationally equivalent layers and two equivalent arrangements of adjacent layers involving distinct possible stacking vectors, t1 and t2. The results have been applied to the polytypism among two different polysomes of the family of so‐called silico‐ferrites of ...
Michael Francesco Salzmann, Volker Kahlenberg, Hannes Krüger, Tim Netzer   +3 more
wiley   +1 more source

Wild conductor exponents of curves

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We give an explicit formula for wild conductor exponents of plane curves over Qp$\mathbb {Q}_p$ in terms of standard invariants of explicit extensions of Qp$\mathbb {Q}_p$, generalising a formula for hyperelliptic curves. To do so, we prove a general result relating the wild conductor exponent of a simply branched cover of the projective line ...
Harry Spencer
wiley   +1 more source

Gauged permutation invariant matrix quantum mechanics: partition functions

Journal of High Energy Physics
The Hilbert spaces of matrix quantum mechanical systems with N × N matrix degrees of freedom X have been analysed recently in terms of S N symmetric group elements U acting as X → UXU T .
Denjoe O’Connor, Sanjaye Ramgoolam
doaj   +1 more source