The reverse order rule (AB)† = B†A† for the Moore-Penrose inverse is established in several equivalent forms. Results related to other generalized inverses are also proved.

In this paper completely simple semigroups or generalized groups are considered. We characterize generalized groups which are normal generalized groups. Homomorphisms of generalized groups are considered. Equivalent conditions for the kernel of a homomorphism are deduced. We prove that the group components of a generalized group have the same cardinality. We also prove that if G is a finite nor...

In this paper we investigate Uludağ’s method for constructing new curves whose fundamental groups are central extensions of the fundamental group of the original curve by finite cyclic groups. In the first part, we give some generalizations to his method in order to get new families of curves with controlled fundamental groups. In the second part, we discuss some properties of groups which are ...

By investigating the construction of the split Cayley generalized hexagon, H(2), we get that there do not exist five distinct hexagon lines each a distance two apart from each other. From this we prove that the smallest Paige loop has a covering number of seven and that its automorphism group permutes these coverings transitively.

The purpose of this study is to investigate the effect of one year of regular “LEGO” training on pupils’ performances in schools. The underlying pedagogical perspective is the constructivist theory, where the main idea is that knowledge is constructed in the mind of the pupil by active learning. The investigation has been made in two steps. The first step was before the training and the second ...

We consider the case 1 interval censorship model in which the survival time has an arbitrary distribution function F 0 and the inspection time has a discrete distribution function G. In such a model one is only able to observe the inspection time and whether the value of the survival time lies before or after the inspection time. We prove the strong consistency of the generalized maximum likeli...

Abstract: In this paper we extend Fisher’s fiducial argument and obtain a generalized fiducial recipe that greatly expands the applicability of fiducial ideas. We do this assuming as little structure as possible. We demonstrate this recipe on many examples of varying complexity. We investigate, by simulation and by theoretical considerations, some properties of the statistical procedures derive...

Since different distributions and link functions have to be used for the different outcomes, we use a special device available in the SAS procedure PROC GLIMMIX, i.e., the ‘byobs=(.)’ specification that can be used to specify both the distribution in the ‘dist=’ option and the link function in the ‘link=’ option. Thus, before we start with the main analysis, two variables need to be created to ...

In this paper we investigate properties of rank correlation coefficients that can be derived from right-invariant generalized metrics on the symmetric group. We prove some new inequalities between a number of generalized metrics, and we characterize the sample sizes for which several (right-invariant) rank correlation coefficients can equal zero. Using the Hausdorff generalized metric, we show ...

We introduce a new R package called glmperm for inference in generalized linear models especially for small and moderate-sized data sets. The inference is based on the permutation of regressor residuals test introduced by Potter (2005). The implementation of glmperm outperforms currently available permutation test software as glmperm can be applied in situations where more than one covariate is...