Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of (λ+ 1)2.

We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [14] concerning functions on nonspecial nilpotent orbits for E6.

Let KG be the group ring of a group G over a commutative ring K with unity. The rings KG are described for which xxσ = xσx for all x = ∑ g∈G αgg ∈ KG, where x → xσ = ∑ g∈G αgf(g)σ(g) is an involution of KG; here f : G → U(K) is a homomorphism and σ is an antiautomorphism of order two of G. Let R be a ring with unity. We denote by U(R) the group of units of R. A (bijective) map : R → R is called...

We consider conditioned Galton–Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. The offspring distribution defining the random tree is ass...

The most important building blocks of symmetric cryptographic primitives such as the DES or the AES, are vectorial Boolean functions, also called S-boxes. In this paper, we extend the definition of normality for Boolean functions into several new affine invariant properties for vectorial Boolean functions. We compute the probability of occurrence of these properties and present practical algori...

hypothesis being tested with the WMW test is not easily described; conventional interpretation (including examples provided by statistical packages) would have it that the null hypothesis is one of equal group medians, but such is not the case; rather it is a test for equality of group mean ranks. Because the WMW test is a test of both location and shape, its interpretation as a test of medians...

Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via a single jump relation that can be regarded as interchange stability condition. Although this relation appears in the setting of equilibrium el...

“Normality” of Stock Prices Bo Shi Abstract. The Black-Scholes Model, often simply called Black-Scholes, models the varying price of financial instruments over time: stocks in particular. This model assumes that returns on the underlying stock are lognormally distributed, which can be reasonable for many assets that offer options. However, from a selection of 100 stock histories, I found that a...

BACKGROUND Others have described a relationship between hemoglobin A levels and gestational age, gender and ethnicity. However, studies are needed to determine normal cut-off points considering these factors. To address this issue we designed a study to determine the percentiles of normality of neonatal hemoglobin A levels taking these factors into account. METHODS This cross-sectional study ...