These are introductory lecture notes on complex geometry, Calabi–Yau manifolds and toric geometry. We first define basic concepts of complex and Kähler geometry. We then proceed with an analysis of various definitions of Calabi–Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi–Yau manifolds in two different ways; as hypersurfaces in to...

Using a simplex-crossing counting technique we prove: if the number of non-improperly intersecting simplices with vertices in a set S of n labeled points in ~d is O(nra/2]) , then there are 2 °('~rd/21) different geometric simplicial complexes with vertices in S. © 1997 Elsevier Science B.V.

A very interesting abstract simplicial complex T (k) n has faces in bijection with the trees with at most n interior vertices, all of which have degrees at least k+2 and are congruent to 2 mod k, and whose leaves are labelled by the distinct integers in [0, 1, ..., m], where m+1 :=nk+2 is the number of leaves (n 0, k 1). Thus the facets of T n correspond to the leaf-labelled trees with n interi...

to investigation non-bonded interaction of the [cuf4]2- complex inside nanoring, we focus on the single wall boron-nitride b18n18 nanoring. thus, the geometry of b18n18 nanoring has been optimized by b3lyp method with epr-ii basis set and geometry of the [cuf4]2- complex has been optimized at b3lyp method with def2-tzvp basis set and stuttgart rsc 1997 effective core potential. also electronic ...

the complex-forming ability of 2-methyl-3-hydroxypyran-4-one ( 1a ), 2-ethyl-3-hydroxypyran-4-one ( 1b ), 1,2-dimethyl-3-hydroxypyridin-4-one ( 4a ) and 1-ethyl-2-methyl-3-hydroxypyridin-4-one ( 4b ) with nickel(ni(ii)) were characterized by infrared, ultraviolet, proton nuclear magnetic resonance spectroscopy and melting point. the mole-ratio of nickel:ligands was analyzed by atomic-absorption...

The structure and relative stability of Molybdata-Phosphonic Acid (MP) Complex in different solventshave been carried out using Density Functional Theory (DP[) methods. The methods me used forcalculations are B3LYP and 83PW91. that have been studied in two series of basis sets: D95"and 6-31+0(cl,p) for hydrogen and oxygen atoms; LANL2OZ for Mn and Phosphorus. Predicted geometw and relativestabi...

in this research, this possibility was investigated the relative stablilty geometry and bindingenergies of the hydrogen bonds of molybdate-phosphonic acid (mpa) complex in gas phase onthe basis of result of ab initio and dft calculations. three dft methods have been applied forcalculations are b3lyp, bp86 and b3pw91 that have been studied in two series of basis sets:d95** and 6-31+g(d,p) for hy...

using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-d domains with complex geometry. the petrov-galerkin finite element formulation is adopted to avoid numerical oscillations. turbulence is modeled using the two equation k-ω model. the discretized equations are written in the form o...