A new class of hybrid schemes and composite inner-outer iterative schemes in conjunction with Picard and Newton methods based on explicit approximate inverse arrowtype matrix techniques is introduced. Isomorphic methods in conjunction with explicit preconditioned schemes based on approximate inverse matrix techniques are presented for the efficient solution of arrow-type linear systems. Applica...

In this paper, we present a numerical method for solving nonlinear Hammerstein fractional integral equations. The approximates the solution by Picard iteration together with integration designed weakly singular integrals. Error analysis of proposed is also investigated. Numerical examples approve its efficiency in terms accuracy and computational cost.

We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbit varieties with Picard number 1 that satisfy this latter property. Mathematics Subject Classifi...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate th...

Morphological characteristics of Stomoxys spp. were studied and recorded for the first time in Thailand. Specimens were collected in central Thailand at Nakhon Pathom, Kanchanaburi and Saraburi Province, using Vavoua traps and sweep net. It was found that Stomoxys calcitrans (L.) was the most commonly abundant species, followed by Stomoxys sitiens Rondani, Stomoxys indica Picard and Stomoxys be...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate the...

We compute the Picard group of the moduli space U ′ of semistable vector bundles of rank n and degree d on an irreducible nodal curve Y and show that U ′ is locally factorial. We determine the canonical line bundles of U ′ and U ′ L, the subvariety consisting of vector bundles with a fixed determinant. For rank 2, we compute the Picard group of other strata in the compactification of U ′.

We study Cox rings of K3-surfaces. A first result is that a K3surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3-surfaces of Picard number two, and explicitly compute the Cox rings of generic K3-surfaces with a non-symplectic involution that have Picard number 2 to 5...

A K3-surface is a (smooth) surface which is simply connected and has trivial canonical bundle. In these notes we investigate three particular pencils of K3-surfaces with maximal Picard number. More precisely the general member in each pencil has Picard number 19 and each pencil contains four surfaces with Picard number 20. These surfaces are obtained as the minimal resolution of quotients X/G, ...

We deene Picard-Einstein metrics on complex algebraic surfaces as KK ahler-Einstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along cycles. We demonstrate how the tool of orbital heights, especially the Proportionality Theorem presented in H98], works for detecting such orbital cycles on the projective plan...