Results 41 to 50 of about 2,562,424 (201)

Symmetry‐Imposed Selection Rules for Excitations of Nontrivial Plasmonic Topologies

Advanced Science, EarlyView.
A unified group‐theory selection rule governs the excitation of vectorial nearfield topologies across three plasmonic spin states. Derived from first principles, it predicts spin–orbit vortex splitting and multidimensional nested vortices, confirmed by phase‐resolved in situ measurements.
Jie Yang, Pengyi Feng, Fei Han, Weijin Chen, Zhongwei Jin, Jincheng Ni, Yuanjie Yang, Anxue Zhang, Guy A. E. Vandenbosch, Niels Verellen, Ewald Janssens, Jiafu Wang, Benfeng Bai, Cheng‐Wei Qiu, Xuezhi Zheng   +14 more
wiley   +1 more source

Updatable Closed‐Form Evaluation of Arbitrarily Complex Multiport Network Connections

Advanced Electronic Materials, EarlyView.
The inverse design of electrically large wave devices often uses reduced‐order multiport models with discrete optimization, requiring many evaluations of complex interconnections between subsystems that differ only in a few blocks. This paper introduces a closed‐form framework enabling efficient Woodbury low‐rank updates of related, previous ...
Hugo Prod'homme, Philipp del Hougne
wiley   +1 more source

Relative commutativity degree of some dihedral groups

, 2013
The commutativity degree of a finite group G was introduced by Erdos and Turan for symmetric groups, finite groups and finite rings in 1968. The commutativity degree, P(G), is defined as the probability that a random pair of elements in a group commute ...
Mohd. Ali, N. M., Nor Haniza Sarmin, Abd. Manaf, F. N., Nor Muhainiah Mohd Ali, Muhanizah Abdul Hamid, Sarmin, N. H., Fadila Normahia Abd Manaf, Abdul Hamid, M.   +7 more
core   +1 more source

On division rings with algebraic commutators of bounded degree

manuscripta mathematica, 2004
Using results on generalized polynomial and rational identities, the authors prove results about algebras with algebraic commutators. One result is that if \(R\) is a prime ring with extended centroid \(C\), and if for a positive integer \(n\) and all \(x,y\in R\), \(xy-yx\) is algebraic over \(C\) of degree at most \(n\), then \([RC:C]\leq n^2\).
Chebotar, M. A., Lee, P. H., Fong, Y.
openaire   +2 more sources

The Quartic Commutativity Degree of Dihedral Groups

Malaysian Journal of Fundamental and Applied Sciences, 2023
The combination of group theory and probability theory was used in studying the connection between the two. In recent years, probability theory has been widely used in solving several difficult problems in group theory. The commutativity degree of a group,  is defined as the probability that two random elements in a group commute.
Muhanizah Abdul Hamid, Adnin Afifi Nawi
openaire   +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

Commutativity Degree of Finite Groups

, 2010
The commutativity degree of a group is the probability that two randomly selected (with replacement) elements of the group commute. We find bounds on the commutativity degree of a finite group, equate restricted values of commutativity degree to ...
Castelaz, Anna
core   +1 more source

On the Exterior Degree of a Finite-Dimensional Lie Algebra

Journal of Mathematics
In this paper, we define the exterior degree for a finite-dimensional Lie algebra over the field Fq and give upper and lower bounds. Also, we give some relations between this concept and commutativity degree, capability, and Schur multiplier.
Afsaneh Shamsaki, Mohsen Parvizi, Ahmad Erfanian   +2 more
doaj   +1 more source

Some bounds on commutativity degree

, 2011
The relative commutativity degree of a subgroup $H$ of a finite group $G$, denoted by $\Pr(H, G)$, is the probability that an element of $G$ commutes with an element of $H$. In this article we obtain some lower and upper bounds for $\Pr(H, G)$ and their consequences.
Nath, R. K., Yadav, M. K.
openaire   +2 more sources

A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws

Advanced Intelligent Discovery, EarlyView.
The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows, G. Zhang, S. Anand, Z. Chen, J. Lin, A. Desai, S. Martiniani, F. Caravelli   +7 more
wiley   +1 more source