We show that for any C∗-algebra A, a sufficiently large Hilbert space H and a unit vector ξ ∈ H, the natural application rep(A:H) θξ −−→ Q(A), π 7→ 〈π(−)ξ, ξ〉 is a topological quotient, where rep(A:H) is the space of representations on H and Q(A) the set of quasi-states, i.e. positive linear functionals with norm at most 1. This quotient might be a useful tool in the representation theory of C∗...

We generalize the well-known numerical criterion for projective spaces by Cho, Miyaoka and Shepherd-Barron to varieties with at worst quotient singularities. Let X be a normal projective variety of dimension n ≥ 3 with at most quotient singularities. Our result asserts that if C · (−KX) ≥ n + 1 for every curve C ⊂ X, then X ∼= P .

Epilepsy is one of the most prevalent chronic disorders of childhood which can threaten child development and mental health. Among cognitive disorders, dyscalculia is one of the most important. In this study, 39 children and adolescents with idiopathic epilepsy underwent clinical and neuropsychological assessment to determine the intellectual level, math skills, reading and writing performance ...

Throughout our evolutionary history, humankind has always lived in contact with large numbers of pathogens. Some cultural traits, such as sedentarization and animal domestication, have considerably increased new parasitic contacts and epidemic transitions. Here, we review the various phenotypic traits that have been proposed to be affected by the highly parasitic human environment, including fe...

Normocephalic children found to have ventriculomegaly during evaluation of long-standing (4.5-8.5 years) neurological disorder were tested for academic achievement, intellectual quotient and neuropsychological functioning. Radioactive iodinated serum cisternography, pre and post-shunt electrophysiological studies (visual evoked responses, brainstem auditory evoked potentials, sleep electroencep...

Because persons with mental retardation cannot be executed for murder, the diagnosis becomes a life and death matter. The American Association on Mental Retardation (now the American Association on Intellectual and Developmental Disabilities) and other associations agree that IQ alone is an insufficient criterion and adaptive functioning also needs to be considered. However, there is no satisfa...

In this paper, we grasp an inverse eigenvalue problem which constructs a tridiagonal matrix with specified multiple eigenvalues, from the viewpoint of the quotient difference (qd) recursion formula. We also prove that the characteristic and the minimal polynomials of a constructed tridiagonal matrix are equal to each other. As an application of the qd formula, we present a procedure for getting...

An extension of a group A by a group G is thought of here simply as a group H containing A as a normal subgroup with quotient H/A isomorphic to G. It is called a central Frattini extension if A is contained in the intersection of the centre and the Frattini subgroup of H . The result of the paper is that, given a finite abelian A and finite G, there exists a central Frattini extension of A by G...

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W , we show that the Chevalley morphism π : t/W → g/G is an isomorphism except for the group Sp2n over a base with 2-torsion...

For Gorenstein quotient spaces C d =G, a direct generalization of the classical McKay correspondence in dimensions d 4 would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstei...