In the theory of hyperplane arrangements, most important and difficult problem is combinatorial dependency several properties. this article, we prove that Terao's celebrated addition theorem for free arrangements combinatorial. Combining other developments in these days, can show all addition-deletion framework As a corollary, define new class called additively arrangement hyperplanes, which be...

A tuition-free teacher candidate is an undergraduate who receives tuition-free teacher education and must work as a teacher in a middle school after their graduation. Tuition-free candidates are of the focus of many researchers; however, no study reports how tuition-free teacher candidates think about teachers. The present study explored stereotypes about middle school and university teachers h...

Three experiments investigate how stereotypes form as justifications for prejudice. The authors created novel content-free prejudices toward unfamiliar social groups using either subliminal (Experiment 1, N = 79) or supraliminal (Experiment 2, N = 105; Experiment 3, N = 130) affective conditioning and measured the consequent endorsement of stereotypes about the groups. Following the stereotype ...

The addition-deletion theorems for hyperplane arrangements, which were originally shown in [T1], provide useful ways to construct examples of free arrangements. In this article, we prove addition-deletion theorems for multiarrangements. A key to the generalization is the definition of a new multiplicity, called the Euler multiplicity, of a restricted multiarrangement. We compute the Euler multi...