Normality and Disease

Normality, Projective Normality and Egz Theorem

In this note, we prove that the projective normality of (P(V )/G,L), the celebrated theorem of Erdös-Ginzburg-Ziv and normality of an affine semigroup are all equivalent, where V is a finite dimensional representation of a finite cyclic group G over C and L is the descent of the line bundle O(1)⊗|G|.

Defining Normality and Abnormality

Much of the practice and research conducted by clinical psychologists focuses on abnormality, also known as mental disorders, psychiatric diagnoses, or, more broadly, psychopathology. Through their training and their professional activities, clinical psychologists become very familiar with the definitions of various forms of abnormal behavior and the ways it differs from normal behavior. But be...

Resolvability and Monotone Normality

A space X is said to be κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). X is maximally resolvable iff it is ∆(X)-resolvable, where ∆(X) = min{|G| : G 6= ∅ open}. We show that every crowded monotonically normal (in short: MN) space is ω-resolvable and almost μ-resolvable, where μ = mi...

Generalized Descents and Normality

We use Janson’s dependency criterion to prove that the distribution of d-descents of permutations of length n converge to a normal distribution as n goes to infinity. We show that this remains true even if d is allowed to grow with n.

ReductionCriterion and Multivariate Normality