We investigate a special class of polytopes, the zonotopes, and show that their flag f -vectors satisfy only the affine relations fulfilled by flag f -vectors of all polytopes. In addition, we determine the lattice spanned by flag f -vectors of zonotopes. By duality, these results apply as well to the flag f -vectors of central arrangements of hyperplanes.

introduction: complete knowledge of root canal curvature is a critical factor in successful dental treatment .the aim of this study was to investigate the direction, radius and degree of curvature of maxillary anterior teeth and the relation between radius and degree of curvature in babol city. methods &materials;: this study was performed on 242 anterior teeth radiographs were taken by periapi...

The FLAG peptide, AspTyrLysAspAspAspAspLys, has been used as an epitope tag in a variety of cell types. The modification of the cytomegalovirus (CMV) promoter containing vector, pCMV5, to create two transient expression vectors designed for secretion and intracellular expression of FLAG-fusion proteins in mammalian cells is described. As a functional test, the bacterial alkaline phosphatase gen...

The flag Whitney numbers (also referred to as the flag f -numbers) of a geometric lattice count the number of chains of the lattice with elements having specified ranks. We give a collection of inequalities which imply all the linear inequalities satisfied by the flag Whitney numbers of rank 3 geometric lattices. We further describe the smallest closed convex set containing the flag Whitney num...

The broadcast flag is supposed to protect digital broadcast content from unauthorized distribution. This paper critically examines the broadcast flag as a security mechanism in the context of digital content control. A threat model analysis from the computer security field is presented as a framework for evaluating the flag. The model identifies stated and potential goals of the flag’s proponen...

The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres. A conjecture of Heinz Hopf asserts that the sign of the Euler characteristic of a smooth Riemannian 2d-dimensional manifold of non-positive sectional curvature is the same for all such manifolds, tha...

The flag f-vectors of three-colored complexes are characterized. This also characterizes the flag h-vectors of balanced Cohen-Macaulay complexes of dimension two, as well as the flag h-vectors of balanced shellable complexes of dimension two.

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manif...