Publications related to Grassmann number

Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a ...

2011

Divisibility in Grassmann algebra

Bernard Dacorogna, Olivier Kneuss

Given a k-form f and an l-form g with 0

2011

Subspaces Indexing Model on Grassmann Manifold for Image Search

Xinchao Wang

Conventional linear subspace learning methods like principal component analysis (PCA), linear discriminant analysis (LDA) derive subspaces from the whole data set. These approaches have limitations in the sense that they are linear while the data distribut ...

Institute of Electrical and Electronics Engineers2011

Crystal Structure and Optical and Magnetic Properties of Pr2(MoO4)3

Gervais Chapuis, Alla Arakcheeva, Philip Pattison, Dmitry Logvinovich

Praseodymium molybdate Pr2(MoO4)3 was synthesized using the standard ceramic route. The crystal structure of the material has been successfully solved in superspace group I2/b(Rβ0)00 with lattice constants a = 5.30284(4), b = 5.32699(3), c = 11.7935(1)A° , ...

2010

Validating the model of a (3+1)-dimensional incommensurately modulated structure as generator of a family of compounds for the Eu2(MoO4)3 scheelite structure

Gervais Chapuis, Alla Arakcheeva, Philip Pattison, Jorge Martinez Garcia

The previously proposed model postulating that the incommensurately modulated KNd(MoO

_4

)

_2

structure can act as a generator of the scheelite family members is validated here by refining the crystal structure of europium molybdate, Eu

_2

(MoO

_4

)

_3

. ...

2009

A sufficient condition for computing n-finger force-closure grasps of 3D objects

Sahar El Khoury

We address the problem of computing n-finger force-closure grasps of 3D objects. As 3D force-closure grasps involve 6D wrench space, we use Pl¨ucker coordinates and Grassmann algebra, to demonstrate that wrenches associated to any three non-aligned contact ...

2008

From space to superspace and back: Superspace Group Finder

Gervais Chapuis, Ivan Orlov

The symmetry of a commensurately modulated crystal structure can be described in two different ways: in terms of a conventional three-dimensional space group or using the superspace concept in (3 + d) dimensions. The three-dimensional space group is obtain ...

2008

Application of the superspace approach to members of the ferrite family

Ivan Orlov

The superspace concept is a new crystallographic approach for the generalisation of symmetry, structural models and structure dependent properties. Although the original motivation for the superspace was intended to describe symmetry of aperiodic crystals, ...

EPFL2007

The study of incommensurate structures as a probe to reveal atomic interactions in crystals

Gervais Chapuis, Alla Arakcheeva

The structure of aperiodic crystals which includes incommensurate, quasi- and composite crystals is usually described in spaces of higher dimension, the so called superspace. The main advantage of the superspace formalism is that an aperiodic structure in ...

2004

The Structure of Diaqua (15-Crown-5) Copper (II) Dinitrate Described in (3 + 1)-Dimensional Superspace

Gervais Chapuis

Diaqua (15-crown-5) copper (II) dinitrate is an organic salt presenting an one-dimensional commensurate modulation. The diffraction pattern is characterized by strong Bragg reflections and weaker superstructure reflections (satellites). The structure is de ...

2004

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Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

Divisibility in Grassmann algebra

Subspaces Indexing Model on Grassmann Manifold for Image Search

Crystal Structure and Optical and Magnetic Properties of Pr2(MoO4)3

Validating the model of a (3+1)-dimensional incommensurately modulated structure as generator of a family of compounds for the Eu2(MoO4)3 scheelite structure

A sufficient condition for computing n-finger force-closure grasps of 3D objects

From space to superspace and back: Superspace Group Finder

Application of the superspace approach to members of the ferrite family

The study of incommensurate structures as a probe to reveal atomic interactions in crystals

The Structure of Diaqua (15-Crown-5) Copper (II) Dinitrate Described in (3 + 1)-Dimensional Superspace

Divisibility in Grassmann algebra

Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

Application of the superspace approach to members of the ferrite family

A sufficient condition for computing n-finger force-closure grasps of 3D objects

The study of incommensurate structures as a probe to reveal atomic interactions in crystals

Crystal Structure and Optical and Magnetic Properties of Pr2(MoO4)3

From space to superspace and back: Superspace Group Finder

The Structure of Diaqua (15-Crown-5) Copper (II) Dinitrate Described in (3 + 1)-Dimensional Superspace

Subspaces Indexing Model on Grassmann Manifold for Image Search

Validating the model of a (3+1)-dimensional incommensurately modulated structure as generator of a family of compounds for the Eu2(MoO4)3 scheelite structure