Minimal K-type formula

1983 ◽  
pp. 107-118 ◽  
Author(s):  
A. W. Knapp
Keyword(s):  
Type Formula

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

scholarly journals Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

2021 ◽  
Author(s):  
Andreas Bernig ◽  
Dmitry Faifman ◽  
Gil Solanes
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Riemannian Space ◽  
Space Forms ◽  
Type Formula ◽  
Isometric Embeddings ◽  
Curvature Measures ◽  
Riemannian Space Forms

AbstractThe recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

SPACE-CHARGE LAYER, INTRINSIC "BULK" AND SURFACE COMPLEX DEFECTS IN ZnO NANOPARTICLES — A HIGH-FIELD ELECTRON PARAMAGNETIC RESONANCE ANALYSIS

2013 ◽  
Vol 06 (04) ◽  
pp. 1330004 ◽  
Author(s):  
RÜDIGER-A. EICHEL ◽  
EMRE ERDEM ◽  
PETER JAKES ◽  
ANDREW OZAROWSKI ◽  
JOHAN VAN TOL ◽  
...  
Keyword(s):  
Electron Paramagnetic Resonance ◽  
Space Charge ◽  
Zno Nanoparticles ◽  
High Field ◽  
Space Charge Layer ◽  
Paramagnetic Resonance ◽  
Charge Layer ◽  
Type Formula ◽  
Field Electron ◽  
Electron Paramagnetic

The defect structure of ZnO nanoparticles is characterized by means of high-field electron paramagnetic resonance (EPR) spectroscopy. Different point and complex defects could be identified, located at the "bulk" or the surface region of the nanoparticles. In particular, by exploiting the enhanced g-value resolution at a Larmor frequency of 406.4 GHz, it could be shown that the resonance commonly observed at g = 1.96 is comprised of several overlapping resonances from different defects. Based on the high-field EPR analysis, the development of a space-charge layer could be monitored that consists of (shallow) donor-type [Formula: see text] defects at the "bulk" and acceptor-type [Formula: see text] and complex [Formula: see text] defects at the surface. Application of a core-shell model allows to determine the thickness of the depletion layer to 1.0 nm for the here studied compounds [J.J. Schneider et al., Chem. Mater.22, 2203 (2010)].

Quantum Homomorphisms of Associative Algebras

1997 ◽  
Vol 12 (38) ◽  
pp. 2963-2974
Author(s):  
A. E. F. Djemai
Keyword(s):  
Quantum Group ◽  
Associative Algebra ◽  
Associative Algebras ◽  
Type Formula ◽  
Algebra Of Functions ◽  
Inhomogeneous Quantum

Given an associative algebra A generated by {ek, k=1, 2,…} and with an internal law of type: [Formula: see text], we first show that it is possible to construct a quantum bi-algebra [Formula: see text] with unit and generated by (non-necessarily commutative) elements [Formula: see text] satisfying the relations: [Formula: see text]. This leads one to define a quantum homomorphism[Formula: see text]. We then treat the example of the algebra of functions on a set of N elements and we show, for the case N=2, that the resulting bihyphen;algebra is an inhomogeneous quantum group. We think that this method can be used to construct quantum inhomogeneous groups.

Stability conditions and braid group actions on affine An quivers

2021 ◽  
pp. 2250174
Author(s):  
Chien-Hsun Wang
Keyword(s):  
Moduli Space ◽  
Braid Group ◽  
Group Actions ◽  
Stability Conditions ◽  
Quadratic Differentials ◽  
Spherical Subgroup ◽  
Type Formula ◽  
Affine Type

We study stability conditions on the Calabi–Yau-[Formula: see text] categories associated to an affine type [Formula: see text] quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order [Formula: see text]. We follow Ikeda’s work to show that this moduli space of quadratic differentials is isomorphic to the space of stability conditions quotient by the spherical subgroup of the autoequivalence group. We show that the spherical subgroup is isomorphic to the braid group of affine type [Formula: see text] based on the Khovanov–Seidel–Thomas method.

scholarly journals Minimal Universal Model for Chaos in Laser with Feedback

2021 ◽  
Vol 31 (04) ◽  
pp. 2130013
Author(s):  
Riccardo Meucci ◽  
Stefano Euzzor ◽  
F. Tito Arecchi ◽  
Jean-Marc Ginoux
Keyword(s):  
Laser Physics ◽  
Nonlinear Oscillator ◽  
Three Dimensional ◽  
Universal Model ◽  
Type Formula ◽  
The Third ◽  
Proposed Model ◽  
Homoclinic Bifurcations ◽  
Electronic Implementation ◽  
Different Time Scales

We revisit the model of the laser with feedback and the minimal nonlinearity leading to chaos. Although the model has its origin in laser physics, with peculiarities related to the [Formula: see text] laser, it belongs to the class of the three-dimensional paradigmatic nonlinear oscillator models giving chaos. The proposed model contains three key nonlinearities, two of which are of the type [Formula: see text], where [Formula: see text] and [Formula: see text] are the fast and slow variables. The third one is of the type [Formula: see text], where [Formula: see text] is an intermediate feedback variable. We analytically demonstrate that it is essential for producing chaos via local or global homoclinic bifurcations. Its electronic implementation in the range of kilo Hertz region confirms its potential in describing phenomena evolving on different time scales.

Sign in / Sign up

Export Citation Format

Share Document