A Clark-Ocone Type Formula via Itô Calculus and its Application to Finance

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).

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A Class of Integral Operators that Fix Exponential Functions

Mediterranean Journal of Mathematics ◽

10.1007/s00009-021-01819-0 ◽

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.

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Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

Journal of Geometric Analysis ◽

10.1007/s12220-021-00702-4 ◽

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.

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

Functional Materials Letters ◽

10.1142/s1793604713300041 ◽

2013 ◽

Vol 06 (04) ◽

pp. 1330004 ◽

Cited By ~ 11

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)].

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Quantum Homomorphisms of Associative Algebras

Modern Physics Letters A ◽

10.1142/s0217732397003083 ◽

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.

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Continuity of the scattering function and Levinson-type formula of Klein-Gordon equation

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.2707 ◽

2012 ◽

Vol 36 (12) ◽

pp. 1583-1590

Author(s):

Özkan Karaman ◽

Nida P. Kosar

Keyword(s):

Gordon Equation ◽

Scattering Function ◽

Type Formula ◽

Klein Gordon ◽

Klein Gordon Equation

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Stability conditions and braid group actions on affine An quivers

Journal of Algebra and Its Applications ◽

10.1142/s0219498822501742 ◽

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.

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