Results 21 to 30 of about 2,164,697 (95)

Building Blocks of Topological Quantum Chemistry: Elementary Band Representations

, 2018
The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of "elementary" band ...
Aroyo, M. I., Bernevig, B. Andrei, Bradlyn, Barry, Cano, Jennifer, Elcoro, L., Felser, C., Vergniory, M. G., Wang, Zhijun   +7 more
core   +2 more sources

Twisted hyperk\"ahler symmetries and hyperholomorphic line bundles

, 2019
In this paper we propose and investigate in full generality new notions of (continuous, non-isometric) symmetry on hyperk\"ahler spaces. These can be grouped into two categories, corresponding to the two basic types of continuous hyperk\"ahler isometries
Ionas, Radu A.
core   +1 more source

Regularity of roots of polynomials

, 2016
We show that smooth curves of monic complex polynomials $P_a (Z)=Z^n+\sum_{j=1}^n a_j Z^{n-j}$, $a_j : I \to \mathbb C$ with $I \subset \mathbb R$ a compact interval, have absolutely continuous roots in a uniform way.
Parusinski, Adam, Rainer, Armin
core   +1 more source

Complex variables for separation of Hamilton-Jacobi equation on real pseudo-Riemannian manifolds

, 2006
In this paper the geometric theory of separation of variables for time-independent Hamilton-Jacobi equation is extended to include the case of complex eigenvalues of a Killing tensor on pseudo-Riemannian manifolds.
Degiovanni, Luca, Rastelli, Giovanni
core   +1 more source

Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces [PDF]

, 2011
Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors.
Lavicka, Roman
core  

Deep Complex Networks

, 2018
At present, the vast majority of building blocks, techniques, and architectures for deep learning are based on real-valued operations and representations.
Bengio, Yoshua, Bilaniuk, Olexa, Mehri, Soroush, Pal, Christopher J, Rostamzadeh, Negar, Santos, João Felipe, Serdyuk, Dmitriy, Subramanian, Sandeep, Trabelsi, Chiheb, Zhang, Ying   +9 more
core  

Generalized Robust Optimization using the Notion of Set-Valued Probability. [PDF]

J Optim Theory Appl
Torre D, Mendivil F, Rocca M.
europepmc   +1 more source

Evaluating generative AI tools for visual communication design using the CoCoSo method under interval valued spherical fuzzy environment. [PDF]

Sci Rep
Sun H, Liu S.
europepmc   +1 more source

A Unifying Framework for Complex-Valued Eigenfunctions via The Cartan Embedding. [PDF]

J Geom Anal
Gudmundsson S, Lindström A.
europepmc   +1 more source

A fiber channel modeling method based on complex neural networks. [PDF]

Sci Rep
Yang H, Wang Y, Li C, Han L, Zhang Q, Xin X.   +5 more
europepmc   +1 more source