Results 71 to 80 of about 6,317 (306)

Tropical Grassmannians, cluster algebras and scattering amplitudes

Journal of High Energy Physics, 2020
We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians Gr(k, n). A finite cluster algebra provides a natural triangulation for the tropical Grassmannian whose
James Drummond, Jack Foster, Ömer Gürdoğan, Chrysostomos Kalousios   +3 more
doaj   +1 more source

Bertini theorems for differential algebraic geometry [PDF]

Proceedings of the American Mathematical Society, 2023
We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the differential analogue of Bertini’s theorem, namely that for an arbitrary geometrically irreducible differential algebraic ...
openaire   +2 more sources

Extrinsic Geometry and Linear Differential Equations

, 2021
We give a unified method for the general equivalence problem of extrinsic geometry, based on our formulation of a general extrinsic geometry as that of an osculating map : (, f) → /⁰ ⊂ Flag(, ) from a filtered manifold (, f) to a homogeneous space /⁰ in ...
Morimoto, Tohru, Machida, Yoshinori, Doubrov, Boris   +2 more
core   +1 more source

Intrinsic Dual‐Phase Regulated GeSe2 Nanoparticles Triggered by Ball‐Milling Treatment for Photonic Multi‐Valued Logic Circuits

Advanced Science, EarlyView.
We report the solid‐state ball milling, a traditional, reliable, mass‐productive material processing, to prepare the air‐stable and dual‐phase GeSe2‐x nanoparticles with extended photodetection feasibility toward optical‐wavelength regions. We further display photonic multi‐valued logic (MVL) circuit through the employment of a hybrid PMMA/GeSe2‐x ...
An‐Ting Tsai, Chun‐Jen Wang, Pin‐Chao Liao, Chin Shan Lue, Chia‐Nung Kuo, Le Vo Phuong Thuan, Po‐Hsuan Hsiao, Chang‐Hyun Kim, Chia‐Yun Chen   +8 more
wiley   +1 more source

Yano F structures and extended supersymmetry

Journal of High Energy Physics, 2022
It is shown how extended supersymmetry realised directly on the (2, 2) semichiral superfields of a symplectic sigma model gives rise to a geometry on the doubled tangent bundle consisting of two Yano F structures on an almost para-hermitian manifold ...
Ulf Lindström
doaj   +1 more source

Diagonals of Rational Functions: From Differential Algebra to Effective Algebraic Geometry

Symmetry, 2022
We show that the results we had previously obtained on diagonals of 9- and 10-parameter families of rational functions in three variables x, y, and z, using creative telescoping, yielding modular forms expressed as pullbacked 2F1 hypergeometric functions, can be obtained much more efficiently by calculating the j-invariant of an elliptic curve ...
Youssef Abdelaziz, Salah Boukraa, Christoph Koutschan, Jean-Marie Maillard   +3 more
openaire   +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

The Geometry of T-Varieties

, 2012
The Wroński determinant (Wrońskian), usually introduced in standard courses in Ordinary Differential Equations (ODE), is a very useful tool in algebraic geometry to detect ramification loci of linear systems.
Nathan Ilten, Ilten, Nathan Owen, Süß, Hendrik, Vollmert, R., Scherbak I., Hendrik Süß, Altmannk, K., Vollmert, Robert, Suess, Hendrik, GATTO, Letterio, Petersen, L., Süß, H., Petersen, Lars, Robert Vollmert, Lars Petersen, I. Scherbak, Klaus Altmann, Altmann, Klaus, L. Gatto, Ilten, N.   +19 more
core   +1 more source

Capacitive versus Faradaic Microelectrodes for Extracellular Stimulation: A Fully Coupled FEM–Hodgkin–Huxley Study of Thresholds and Current Redistribution

Advanced Electronic Materials, EarlyView.
A fully coupled FEM–HH model shows that ideally capacitive microelectrodes can achieve lower charge‐density thresholds than Faradaic contacts under current‐controlled stimulation. The advantage stems from the dynamics of surface current density on capacitive interfaces, which redirects current beneath adherent neurons.
Aleksandar Opančar, Eric Daniel Głowacki, Vedran Đerek   +2 more
wiley   +1 more source

Meromorphic modular forms and the three-loop equal-mass banana integral

Journal of High Energy Physics, 2022
We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms.
Johannes Broedel, Claude Duhr, Nils Matthes   +2 more
doaj   +1 more source