Magnetic moments and the high field susceptibilities of MnFe2O4

An extended version of the noncollinear spin model bySawatzky et al. is developed to derive a dependence of the differential high field susceptibility on the degree of inversion of the ferrite MnFe₂O₄. Using the available data on the main molecular field coefficients it is shown that the present model imposes restrictions on values of. Determination of from the measurements of the field dependence of the saturated moments at low temperatures on samples with varying degrees of inversion reveals good quantitative agreement with the present model.     

A Nonparametric Graphical Tests of Significance in Functional GLM

Methodology and Computing in Applied Probability - A new nonparametric graphical test of significance of a covariate in functional GLM is proposed. Our approach is especially interesting due to its...     

On the influence of the magnetic diffusion after-effect on the complex susceptibility. — The logarithmic distribution of time constants

The general formula for complex initial susceptibility has been derived from the Néel theory of the magnetic diffusion after-effect in the case of the continuous distribution of time constants. The influence of the logarithmic distribution on the frequency dependence of the complex susceptibility and the temperature dependence of the loss-factor is examined in detail. The theoretical and experimental curves, tanδ vs.T, of three ferrite samples are compared.     

Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

We deal with a posteriori error control of discontinuous Galerkin approximations for linear boundary value problems. The computational error is estimated in the framework of the Dual Weighted Residual method (DWR) for goal-oriented error estimation which requires to solve an additional (adjoint) problem. We focus on the control of the algebraic errors arising from iterative solutions of algebraic systems corresponding to both the primal and adjoint problems. Moreover, we present two different reconstruction techniques allowing an efficient evaluation of the error estimators. Finally, we propose a complex algorithm which controls discretization and algebraic errors and drives the adaptation of the mesh in the close to optimal manner with respect to the given quantity of interest.     

Construction of function with gradient violating Lusin (N) condition

We construct , such that maps onto . This shows that a mapping which maps a set of zero measure onto the set of positive measure can be a gradient mapping.     

Example of a Smooth Homeomorphism Violating the Luzin N−1 Property

This paper discusses some results concerning the validity of the Luzin N and N^?1 properties for homeomorphisms. Also, we present a counterexample in the form of a C^∞-homeomorphism that violates the N^?1 property.