In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate som...

We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in ...

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing, and the stat...

background : progression of systemic lupus erythematosus (sle) could be due to oxidative stress especially through reactive oxygen species (ros). detoxification of ros is largely performed by glutathione s-transferases (gsts), therefore polymorphisms of gstm1, gstt1 and gstp1 genes which decrease enzymes activity could affect sle susceptibility. the aim of this study was to determine the effect...

Contents 1. Introduction 1 2. Conventions 2 3. Unramified morphisms 2 4. Three other characterizations of unramified morphisms 4 5. The functorial characterization of unramified morphisms 5 6. Topological properties of unramified morphisms 6 7. Universally injective, unramified morphisms 7 8. Examples of unramified morphisms 9 9. Flat morphisms 10 10. Topological properties of flat morphisms 11...

We show that all harmonic morphisms from 3-dimensional Minkowski space with values in a surface have a Weierstrass representation involving the complex numbers or the hyperbolic numbers depending on the signature of the codomain. We deduce that there is a nontrivial globally defined submersive harmonic morphism from Minkowski 3-space to a surface, in contrast to the Riemannian case. We show tha...

Abstract Pirashvili’s Dold–Kan type theorem for finite pointed sets follows from the identification in terms of surjections morphisms between tensor powers a functor playing role augmentation ideal; these functors are projective. We give an unpointed analogue this result: namely, we compute corresponding context. also calculate Ext groups such objects, particular showing that not projective; is...

The many criticisms of null hypothesis testing suggest when it is not useful and what is should not be used for. This article explores when and why its use is appropriate. Null hypothesis testing is insufficient when size of effect is important, but it is ideal for testing ordinal claims relating the order of conditions, which are common in psychology. Null hypothesis testing also is insufficie...

Contents 1. Introduction 1 2. Conventions 2 3. Unramified morphisms 2 4. Three other characterizations of unramified morphisms 4 5. The functorial characterization of unramified morphisms 5 6. Topological properties of unramified morphisms 6 7. Universally injective, unramified morphisms 7 8. Examples of unramified morphisms 9 9. Flat morphisms 10 10. Topological properties of flat morphisms 11...