Angular Density Function Research Articles

Regression‐type models for extremal dependence

AbstractWe propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log‐likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate‐adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season.

A molecular dynamics approach concerning the structures of 2‐hydroxy‐ and 2‐methoxy‐benzyl methyl ethers based on thenJ(CH2,H) long‐range spin–spin couplings

AbstractA procedure for combining experimental NMR information and, for example, molecular mechanics is described. An iterative computer program and a strategy based on the approach are applied for the determination of the torsional behaviour of the CH2group in 2‐hydroxy‐ and 2‐methoxy‐benzyl methyl ethers. The analysis gives fairly well defined potentials of the torsion and angular density functions. The least‐squares model obtained for the5J(CH2,H) coupling is in accordance with previous observations. STO‐3G levelab initiocalculations for 2‐hydroxybenzyl methyl ether are reported and are in reasonable agreement with the dynamic model.

Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks

For a rock containing a distribution of uniaxial grains of anisotropic susceptibility k(θ, φ), for which the preferred orientation can be specified by an angular density function, f(θ, φ), the resultant susceptibility is: K = ∝ f( θ, φ) k( θ, φ) dω In deformed rocks the final preferred orientation and grain susceptibilities are determined by their respective initial values and by their modification during the deformation. This paper explores simple situations in which the relationship between these factors can be discussed quantitatively. Calculations for an assumed initial fabric, for three different strain response models which can be expressed mathematically, demonstrate the characteristic features of the progressive development of the magnetic fabric and emphasize the importance of a knowledge of the strain response model, if measurements of magnetic anisotropy are to be used to measure finite strain.