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 .

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...

Adversity quotient is the capacity to adjust with the adversities in life. A person with good Adversity quotient can achieve the goal by fighting against all odds. It is also related to many other factors like self esteem, motivation, fighting spirit, creativity, sincerity, positive attitude, optimism, emotional stability etc. Adversity quotient is also related to the Academic problems of stude...

conclusions chronic and moderate malnutrition did not influence the cognitive function, the intelligence quotient, and the impulsivity index. background undernutrition is the most common cause of growth retardation in developing countries. we aimed to assess the effect of undernutrition on cognition, intelligence quotient, and impulsivity index of 7-11 year-old children in shiraz, southern iran...