Results 41 to 50 of about 381 (256)

LAPLACE EQUATIONS, CONFORMAL SUPERINTEGRABILITY AND BÔCHER CONTRACTIONS

Acta Polytechnica, 2016
Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often ``hidden''.The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define ...
Ernest G. Kalnins, Willard Miller, Jr, Eyal Subag   +2 more
doaj   +1 more source

Solvable Lie algebras are not that hypo [PDF]

Transformation Groups, 2011
We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain associated cohomology groups, determine a ...
CONTI, DIEGO, Fernàndez, M, Santisteban, J.   +2 more
openaire   +2 more sources

An exciting Approach to Theoretical Spectroscopy

Advanced Science, EarlyView.
ABSTRACT Theoretical spectroscopy, and more generally, electronic‐structure theory, are powerful concepts for describing the complex many‐body interactions in materials. They cover methods from ground‐state properties to lattice excitations and light‐matter interaction, including time‐resolved variants.
Martí Raya‐Moreno, Alexander Buccheri, Noah Alexy Dasch, Nasrin Farahani, Ignacio Gonzalez Oliva, Andris Gulans, Seokhyun Hong, Manoar Hossain, Hannah Kleine, Martin Kuban, Sven Lubeck, Benedikt Maurer, Pasquale Pavone, Fabian Peschel, Daria Popova‐Gorelova, Lu Qiao, Elias Richter, Santiago Rigamonti, Ronaldo Rodrigues Pela, Maximilian Schebek, Kshitij Sinha, Daniel T. Speckhard, Jan Stutz, Sebastian Tillack, Dmitry Tumakov, Jānis Užulis, Mara Voiculescu, Cecilia Vona, Mao Yang, Claudia Draxl   +29 more
wiley   +1 more source

Solvability and Nilpotency of Lie Algebras in Cryptography and Steganography

Mathematics
This paper investigates the role of solvable and nilpotent Lie algebras in the domains of cryptography and steganography, emphasizing their potential in enhancing security protocols and covert communication methods.
Amor Hasić, Melisa Azizović, Emruš Azizović, Muzafer Saračević   +3 more
doaj   +1 more source

On Lie solvable restricted enveloping algebras

Journal of Algebra, 2007
Let \(u(L)\) be the restricted enveloping algebra of a restricted Lie algebra \(L\) over a field of positive characteristic \(p\). As any associative algebra, \(u(L)\) can be viewed as a Lie algebra with the Lie product defined by \([x,y]:=xy-yx\). In [J. Algebra 162, No.1, 46-61 (1993; Zbl 0798.17011)], \textit{D. M. Riley} and \textit{A.
openaire   +3 more sources

Exact Discrete Stochastic Simulation With Deep‐Learning‐Scale Gradient Optimization

Advanced Science, EarlyView.
A 203,796‐parameter gene regulatory network classifies handwritten digits with 98.4% accuracy using exact stochastic dynamics. The framework decouples forward simulation from backward differentiation, making continuous‐time Markov chain models compatible with deep‐learning optimization.
Jose M. G. Vilar, Leonor Saiz
wiley   +1 more source

Simple left-symmetric algebras with solvable Lie algebra [PDF]

Manuscripta Mathematica, 1998
Let \(K\) be a field of characteristic 0 and \(A\) a \(K\)-vector space. A left symmetric algebra structure on \(A\) is a bilinear product \((x,y) \mapsto x\cdot y\) satisfying \[ x\cdot (y\cdot z)- (x\cdot y) \cdot z=y \cdot(x \cdot z)- (y\cdot x) \cdot z. \tag{*} \] The condition (*) implies that the commutator \([x,y]:=x\cdot y-y\cdot x\) turns \(A\)
openaire   +3 more sources

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

Locally conformally Kähler structures on four-dimensional solvable Lie algebras

Complex Manifolds, 2019
We classify and investigate locally conformally Kähler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma ...
Angella Daniele, Origlia Marcos
doaj   +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