Results 21 to 30 of about 337 (147)

The Role of Dice in the Emergence of the Probability Calculus

International Statistical Review, Volume 94, Issue 2, Page 464-483, August 2026.
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

Numerical stability of the branched continued fraction expansion of Horn's hypergeometric function $H_4$

Математичні Студії
In this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions.
R. Dmytryshyn, C. Cesarano, I.-A. Lutsiv, M. Dmytryshyn   +3 more
doaj   +1 more source

Fast and Accurate GPU‐Accelerated Computation of Two‐Electron Four‐Center Coulomb Repulsion Integrals

Journal of Computational Chemistry, Volume 47, Issue 20, July 30, 2026.
Our GPU software rapidly and accurately computes two‐electron, four‐center Coulomb repulsion integrals using Slater‐type orbitals. It involves applying a simple transformation to eliminate the Coulomb singularity and using the trapezoidal quadrature rule. The quadrature rule converges rapidly, as demonstrated in this graph.
Avleen Kaur, William Chen, Gautam Kirshan Luhana, Lior Silberman, Mark Ewert, Alexandra Bünger, Ury Segal, Chen Greif   +7 more
wiley   +1 more source

FloeNet: A Mass‐Conserving Global Sea Ice Emulator That Generalizes Across Climates

Geophysical Research Letters, Volume 53, Issue 14, 28 July 2026.
Abstract We introduce FloeNet, a graph neural network trained to emulate the Geophysical Fluid Dynamics Laboratory global sea ice model, SIS2. FloeNet is a mass‐conserving model, emulating 6‐hr mass and area budget tendencies related to sea ice and snow‐on‐sea‐ice growth, melt, and advection.
William Gregory, Mitchell Bushuk, James Duncan, Elynn Wu, Adam Subel, Spencer K. Clark, Bill Hurlin, Oliver Watt‐Meyer, Alistair Adcroft, Chris Bretherton, Laure Zanna   +10 more
wiley   +1 more source

On the numerical stability of the branched continued fraction expansion of the ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$

Математичні Студії
Continued fractions and their generalization, branched continued fractions, are the effective tools used to study special functions. In this aspect, an important problem of continued fractions and branched continued fractions is the study of their ...
M. V. Dmytryshyn, C. Cesarano, O. Kondur, I.-A. Lutsiv   +3 more
doaj   +1 more source

Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver

International Journal for Numerical Methods in Fluids, Volume 98, Issue 7, Page 804-839, July 2026.
A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley   +1 more source

Gram Decay and Intrinsic Dimensions of Krylov Subspaces

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT Krylov subspace methods solve large sparse linear systems Ax=b$$ Ax=b $$ by building a sequence of polynomial approximations to A−1b$$ {A}^{-1}b $$ from successive matrix‐vector products. In finite precision, the number of numerically independent directions that can be extracted from this sequence is bounded by the intrinsic information ...
Stephen J. Thomas
wiley   +1 more source

Toward an Efficient Shifted Cholesky QR for Applications in Model Order Reduction Using pyMOR

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT Many model order reduction (MOR) methods rely on the computation of an orthonormal basis of a subspace onto which the large full order model is projected. Numerically, this entails the orthogonalization of a set of vectors. The nature of the MOR process imposes several requirements for the orthogonalization process.
Maximilian Bindhak, Art J. R. Pelling, Jens Saak   +2 more
wiley   +1 more source

Local continuum consistent peridynamics with bond‐associated modeling and dynamic fracture

GAMM-Mitteilungen, Volume 49, Issue 1-2, March/June 2026.
Abstract This paper explores the theoretical foundations and practical challenges of peridynamics as a nonlocal continuum mechanics method. We establish connections between classical continuum mechanics principles and peridynamics formulations, with a particular focus on understanding how the pairwise force function in peridynamics relates to stress ...
Kai Partmann, Robert I. Weinbrenner, Christian Wieners, Kerstin Weinberg   +3 more
wiley   +1 more source

The Climate Modeling Alliance Atmosphere Dynamical Core: Concepts, Numerics, and Scaling

Journal of Advances in Modeling Earth Systems, Volume 18, Issue 3, March 2026.
Abstract This paper presents the dynamical core of the Climate Modeling Alliance (CliMA) atmosphere model, designed for efficient simulation of a wide range of atmospheric flows across scales. The core uses the nonhydrostatic equations of motion for a deep atmosphere, discretized with a hybrid approach that combines a spectral element method (SEM) in ...
Dennis Yatunin, Simon Byrne, Charles Kawczynski, Sriharsha Kandala, Gabriele Bozzola, Akshay Sridhar, Zhaoyi Shen, Anna Jaruga, Julia Sloan, Jia He, Daniel Zhengyu Huang, Valeria Barra, Ray Chew, Anudhyan Boral, Yi‐fan Chen, Oswald Knoth, Paul Ullrich, Cheikh Mbengue, Tapio Schneider   +18 more
wiley   +1 more source