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...

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...

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.

Moody, P. J. and A. W. Roscoe, Acyclic monotone normality, Topology and its Applications 47 (1992) 53-67. A space X is acyclic monotonically normal if it has a monotonically normal operator M(., .) such that for distinct points x,,, ,x._, in X and x, =x,], n::i M(x,, X\{x,+,}) = (d. It is a property which arises from the study of monotone normality and the condition “chain (F)“. In this paper i...

The normality equations for the Newtonian dynamical systems on an arbitrary Riemannian manifold of the dimension n ≥ 3 are considered. Locally the solution of such equations reduces to three possible cases: in two of them the solution is written out explicitly, and in the third case the equations of normality are reduced to an ordinary differential equation of the second order. Some new example...

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...

Several criteria, such as CV, C p, AIC, CAIC, and MAIC, are used for selecting variables in linear regression models. It might be noted that C p has been proposed as an estimator of the expected standardized prediction error, although the target risk function of CV might be regarded as the expected prediction error RPE. On the other hand, the target risk function of AIC, CAIC, and MAIC is the e...