Results 1  10
of
18
The Equivariant Noncommutative AtiyahPatodiSinger Index Theorem ∗
, 2006
"... In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection.
Ploop Oscillator on Clifford manifolds and Black Hole Entropy
"... A new relativity theory, or more concretely an extended relativity theory, actively developed by one of the authors incorporated 3 basic concepts. They are the old Chu’s idea about bootstarpping, Nottale’s scale relativity, and enlargement of the conventional timespace by inclusion of noncommutativ ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
of noncommutative Clifford manifolds where all pbranes are treated on equal footing. The latter allowed one to write a master action functional. The resulting functional equation is simplified and applied to the ploop oscillator. Its respective solution is a generalization of the conventional point oscillator
ChernConnes Character for the Invariant Dirac Operator in Odd Dimensions ∗
, 2006
"... In this paper we give a proof of the Lefschetz fixed point formula of Freed [1] for an orientationreversing involution on an odd dimensional spin manifold by using the direct geometric method introduced in [2] and then we generalize this formula under the noncommutative geometry framework. Keywords ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. Keywords: Clifford asymptotics; Even spectral triple; ChernConnes character 2000 MR Subject Classification 58j20
Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroscedastic Disturbances
, 2006
"... One important goal of this study is to develop a methodology of inference for a widely used CliffOrd type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first gener ..."
Abstract

Cited by 104 (6 self)
 Add to MetaCart
One important goal of this study is to develop a methodology of inference for a widely used CliffOrd type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first
Heat content asymptotics for operators of Laplace type with Neumann boundary conditions
 Math. Z
, 1994
"... Abstract. Let P be an operator of Dirac type and let D = P 2 be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for D. 1. introduction Let P be an operator of Dirac type on a vector bundle V over a compact Riemannian man ..."
Abstract

Cited by 20 (12 self)
 Add to MetaCart
manifold M of dimension m with smooth boundary ∂M. Let D: = P 2 be the associated operator of Laplace type. The leading symbol γ of P defines a Clifford module structure on V. Choose an auxiliary connection ∇ on V so that ∇γ = 0. Adopt the Einstein convention and sum over repeated indices; indices i, j
Asymptotic Compressibility of Entanglement and Classical Communication in Distributed Quantum Computation
, 2014
"... We consider implementations of a bipartite unitary on many pairs of unknown input states by local operation and classical communication assisted by shared entanglement. We investigate to what extent the entanglement cost and the classical communication cost can be compressed by allowing nonzero but ..."
Abstract
 Add to MetaCart
but vanishing error in the asymptotic limit of infinite pairs. We show that a lower bound on the minimal entanglement cost, the forward classical communication cost, and the backward classical communication cost per pair is given by the Schmidt strength of the unitary. We also prove that an upper bound
Aperiodic Univariate and Multivariate Merit Factors
 SETA’04, Sequences and their Applications, Seoul, Accepted for Proceedings of SETA04, Lecture Notes in Computer Science
, 2004
"... Abstract. Merit factor of a binary sequence is reviewed, and constructions are described that appear to satisfy an asymptotic merit factor of 6.3421... Multivariate merit factor is characterised and recursive Boolean constructions are presented which satisfy a nonvanishing asymptote in multivariate ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
in multivariate merit factor. Clifford merit factor is characterised as a generalisation of multivariate merit factor and as a type of quantum merit factor. Recursive Boolean constructions are presented which, however, only satisfy an asymptotic Clifford merit factor of zero. It is demonstrated that Boolean
Fillmore–Springer–Cnops constructions implemented in GiNaC
 Adv. Appl. Clifford Algebr
, 2007
"... Abstract. This is an implementation of the Fillmore–Springer–Cnops construction (FSCc) based on the Clifford algebra capacities [11] of the GiNaC computer algebra system. FSCc linearises the linearfraction action of the Möbius group. This turns to be very useful in several theoretical and applied f ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Abstract. This is an implementation of the Fillmore–Springer–Cnops construction (FSCc) based on the Clifford algebra capacities [11] of the GiNaC computer algebra system. FSCc linearises the linearfraction action of the Möbius group. This turns to be very useful in several theoretical and applied
A FRAMEWORK FOR APPROXIMATING QUBIT UNITARIES
"... Abstract. We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves εapproximations using circuits of length O(log(1/ε)), which is asymptotically optimal. The algorithm achieves the same quality of approxi ..."
Abstract
 Add to MetaCart
Abstract. We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves εapproximations using circuits of length O(log(1/ε)), which is asymptotically optimal. The algorithm achieves the same quality
Results 1  10
of
18