The Kostant partition functions for twisted Kac-Moody algebras

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2007

In this paper, codes which reduce the peak-to-average power ratio (PAPR) in multi-code code division multiple access (MC-CDMA) communication systems are studied. It is known that using bent functions to define binary codewords gives constant amplitude signals. Based on the concept of quarter bent functions, a new inequality relating the minimum order of terms of a bent function and the maximum Walsh spectral magnitude is proved, and it facilitates the generalization of some known results.

2008

We discuss the reduction and reconstruction problem for ordinary differential equations that admit a linear symmetry group. The goal is to prove that modulo reduction there remain only linear differential equations, and to construct these explicitly. Extending previous work on one-parameter groups, we show this for certain unipotent and solvable groups, and for all semisimple groups. Some applications to relative equilibria are given.

Computational Statistics & Data Analysis, 2010

We propose a new method in two variations for the identification of most relevant covariates in linear models with homoscedastic errors. In contrast to AIC, BIC and other information criteria, our method is based on an interpretable scaled quantity. This quantity measures a maximal relative error one makes by selecting covariates from a given set of all available covariates. The proposed model selection procedures rely on asymptotic normality of test statistics, and therefore normality of the errors in the regression model is not required. In a simulation study the performance of the suggested methods along with the performance of the standard model selection criteria AIC and BIC is examined.

The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.

2009

Geometriae Dedicata, 2010

We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N, g) satisfy the matrix equation

Arxiv preprint math/0605660, 2006

2010

Let (X, µ) be a measure space, and let L 1 , . . . , L n be (possibly unbounded) selfadjoint operators on L 2 (X, µ), which commute strongly pairwise, i.e., which admit a joint spectral resolution E on R n . A joint functional calculus is then defined via spectral integration: for every Borel function m : R n → C,