Results 21 to 30 of about 1,476 (137)

Characterizing Lie Algebra Structure via the Commutativity Degree

Journal of Mathematics
The aim of this paper is to determine the possible values of the commutativity degree of Lie algebras. We define the asymptotic commutativity degree of Lie algebras and obtain the asymptotic commutativity degree for some of them.
Afsaneh Shamsaki, Ahmad Erfanian, Mohsen Parvizi   +2 more
doaj   +1 more source

A Perspective on Interactive Theorem Provers in Physics

Advanced Science, EarlyView.
Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
wiley   +1 more source

Commutative subalgebras from Serre relations

Physics Letters B, 2023
We demonstrate that commutativity of numerous one-dimensional subalgebras in W1+∞ algebra, i.e. the existence of many non-trivial integrable systems described in recent arXiv:2303.05273 follows from the subset of relations in algebra known as Serre ...
A. Mironov, V. Mishnyakov, A. Morozov, A. Popolitov   +3 more
doaj   +1 more source

FIRE‐GNN: Force‐Informed, Relaxed Equivariance Graph Neural Network for Rapid and Accurate Prediction of Surface Properties

Advanced Intelligent Discovery, EarlyView.
This study introduces FIRE‐GNN, a force‐informed, relaxed equivariant graph neural network for predicting surface work functions and cleavage energies from slab structures. By incorporating surface‐normal symmetry breaking and machine learning interatomic potential‐derived force information, the approach achieves state‐of‐the‐art accuracy and enables ...
Circe Hsu, Claire Schlesinger, Karan Mudaliar, Jordan Leung, Robin Walters, Peter Schindler   +5 more
wiley   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Generalized periodic rings

International Journal of Mathematics and Mathematical Sciences, 1996
Let R be a ring, and let N and C denote the set of nilpotents and the center of R, respectively. R is called generalized periodic if for every x∈R\(N⋃C), there exist distinct positive integers m, n of opposite parity such that xn−xm∈N⋂C.
Howard E. Bell, Adil Yaqub
doaj   +1 more source

Advances in Position‐Momentum Entanglement: A Versatile Tool for Quantum Technologies

Laser &Photonics Reviews, EarlyView.
Position–momentum entanglement constitutes a high‐dimensional continuous‐variable resource in quantum optics. Recent advances in its generation, characterization, and control are reviewed, with emphasis on spontaneous parametric down‐conversion and modern measurement techniques.
Satyajeet Patil, Rajshree Swarnkar, Jonas L. Moos, Sebastian Töpfer, Sergio Tovar‐Pérez, Jorge Fuenzalida, Markus Gräfe   +6 more
wiley   +1 more source

Joint Distributions and Quantum Nonlocal Models

Axioms, 2014
A standard result in quantum mechanics is this: if two observables are commuting then they have a classical joint distribution in every state. A converse is demonstrated here: If a classical joint distribution for the pair agrees with standard quantum ...
James D. Malley, Anthony Fletcher
doaj   +1 more source

Interaction of Dirac δ$$ \delta $$‐Waves in the Inviscid Levine and Sleeman Chemotaxis Model

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This article investigates interactions of δ$$ \delta $$‐shock waves in the inviscid Levine and Sleeman chemotaxis model ut−λ(uv)x=0$$ {u}_t-\lambda {(uv)}_x=0 $$, vt−ux=0$$ {v}_t-{u}_x=0 $$. The analysis employs a distributional product and a solution concept that extends the classical solution concept.
Adelino Paiva
wiley   +1 more source

Space‐Efficient Logical Qubit Architecture with a Bus for Magic State Consumption

Advanced Quantum Technologies, EarlyView.
This paper proposes a logical qubit architecture, considering the consumption of magic states. By constructing the patch to the magic state using the repetition code and data qubits using the surface code, the proposed architecture minimizes the number of qubits, referred to as the space cost.
Yujin Kang, Youshin Chung, Jun Heo
wiley   +1 more source