Search results for "Modula"
showing 10 items of 1481 documents
A note on the admissibility of modular function spaces
2017
Abstract In this paper we prove the admissibility of modular function spaces E ρ considered and defined by Kozlowski in [17] . As an application we get that any compact and continuous mapping T : E ρ → E ρ has a fixed point. Moreover, we prove that the same holds true for any retract of E ρ .
Efficient computation of the branching structure of an algebraic curve
2012
An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant points of the curve are constructed via a minimal spanning tree of the discriminant points. This leads to paths of minimal length between the points, which is important for a later stage where these paths are used as integration contours to compute periods of the surface. The branching structure of the surface is obtained by analytically continuing the roots of the equation defining the algebraic curve along the constructed generators of the fundamental gro…
Intersection subgroups of complex hyperplane arrangements
2000
Abstract Let A be a central arrangement of hyperplanes in C n , let M( A ) be the complement of A , and let L ( A ) be the intersection lattice of A . For X in L ( A ) we set A X ={H∈ A : H⫆X} , and A /X={H/X: H∈ A X } , and A X ={H∩X: H∈ A \ A X } . We exhibit natural embeddings of M( A X ) in M( A ) that give rise to monomorphisms from π 1 (M( A X )) to π 1 (M( A )) . We call the images of these monomorphisms intersection subgroups of type X and prove that they form a conjugacy class of subgroups of π 1 (M( A )) . Recall that X in L ( A ) is modular if X+Y is an element of L ( A ) for all Y in L ( A ) . We call X in L ( A ) supersolvable if there exists a chain 0⫅X 1 ⫅⋯⫅X d =X in L ( A ) …
Remarks on mapping properties for the Bargmann transform on modulation spaces
2011
We investigate the mapping properties for the Bargmann transform and prove that this transform is isometricand bijective from modulation spaces to convenient Banach spaces of analytic functions.
Brauer characters and coprime action
2016
Abstract It is an open problem to show that under a coprime action, the number of invariant Brauer characters of a finite group is the number of the Brauer characters of the fixed point subgroup. We prove that this is true if the non-abelian simple groups satisfy a stronger condition.
Compactness of time-frequency localization operators on L2(Rd)
2006
Abstract In this paper, we consider localization operators on L 2 ( R d ) defined by symbols in a subclass of the modulation space M ∞ ( R 2 d ) . We show that these operators are compact and that this subclass is “optimal” for compactness.
A note on projective coordinate systems of modular lattices
1993
This note clarifies the combinatorial nature of projective coordinate systems of modular upper continuous lattices. It generalizes the classical relationship between 3-dimensional Desarguesian configurations and coordinate systems of projective 3-spaces.
Quantum computing thanks to Bianchi groups
2018
It has been shown that the concept of a magic state (in universal quantum computing: uqc) and that of a minimal informationally complete positive operator valued measure: MIC-POVMs (in quantum measurements) are in good agreement when such a magic state is selected in the set of non-stabilizer eigenstates of permutation gates with the Pauli group acting on it [1]. Further work observed that most found low-dimensional MICs may be built from subgroups of the modular group PS L(2, Z) [2] and that this can be understood from the picture of the trefoil knot and related 3-manifolds [3]. Here one concentrates on Bianchi groups PS L(2, O10) (with O10 the integer ring over the imaginary quadratic fie…
WQ*-algebras of measurable operators
2012
Every C*-algebra \(\mathfrak{A}\) has a faithful *-representation π in a Hilbert space \(\mathcal{H}\). Consequently it is natural to pose the following question: under which conditions, the completion of a C*-algebra in a weaker than the given one topology, can be realized as a quasi *-algebra of operators? The present paper presents the possibility of extending the well known Gelfand — Naimark representation of C*-algebras to certain Banach C*-modules.
Energy localization in a nonlinear discrete system
1996
International audience; We show that, in the weak amplitude and slow time limits, the discrete equations describing the dynamics of a one-dimensional lattice can be reduced to a modified Ablowitz-Ladik equation. The stability of a continuous wave solution is then investigated without and with periodic boundary conditions; Energy localization via modulational instability is predicted. Our numerical simulations, performed on a cyclic system of six oscillators, agree with our theoretical predictions.