We construct a continuous family of new homogeneous Einstein spaces with negative Ricci curvature, obtained by deforming from the quaternionic hyperbolic space of real dimension 12. We give an explicit description of this family, which is made up of Einstein solvmanifolds which share the same algebraic structure (eigenvalue type) as the rank one symmetric space HH. This deformation includes a c...

With an object to study neurosis through stressful life events, personality dimension, family interactional patterns and other sociological variables, certain hypotheses are tested in two populations, namely 60 neurotics and 60 normals, matched at individual level for age, sex, and education. This paper is divided into two parts. In this part the main observations are that neurotic patients exp...

The probably approximately correct (PAC) model of learning and its extension to real-valued function classes sets a rigorous framework based upon which the complexity of learning a target from a function class using a finite sample can be computed. There is one main restriction, however, that the function class have a finite VC-dimension or scale-sensitive pseudo-dimension. In this paper we pre...

We analyze the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application, we prove the existence of nonaffine and nonproduct threefolds Y with t...

We compute the Minkowski dimension for a family of self-affine sets on R. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.

For all m ≥ 1 we build a two-dimensional family of smooth manifolds of real dimension 3m + 2 and use it to interpolate between the anticanonical family in CP and its mirror dual. The main tool is the notion of self-dual manifold.

The aim of this study was to examine the differences in manifestations three schizotypal dimensions (cognitive-perceptive, interpersonal, disorganized), depending on attachment style and exposure different adverse experiences during childhood. conducted 181 participants, with a mean age 20.09 years (SD = 2.19). Schizotypy measured using Schizotypal Personality Questionnaire - Brief Revised (SPQ...

Let k be a field. We are interested in the families of r-dimensional subspaces of k with the following transversality property: any linear subspace of kn of dimension n − r is transversal to at least one element of the family. While it is known how to build such families in polynomial time over infinite fields k, no such technique is known for finite fields. However, transversal families in dim...

In this paper we disprove a conjecture stated in [4] on the equality of two notions of dimension for closed cones. Moreover, we answer in the negative to the following question, raised in the same paper. Given a compact family C of closed cones and a set S such that every blow-up of S at every point x ∈ S is contained in some element of C, is it true that the dimension of S is smaller then or e...

We prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures ^ of Markov type. For each value of a parameter a between a minimum amin and maximum amax, we define 'multifractal components' K^ a) of K, and show that they are fractals in the sense of Taylor. The dimension /(or) of K^ is computed from the data of the pro...