In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

Chang, Y.-W., M.S. Jacobson, CL. Monma and D.B. West, Subtree and substar intersection numbers. Discrete Applied Mathematics 44 (1993) 205-220. We introduce the star number [free number] of a graph, being the minimum t such that G is the intersection graph of unions of t substars [subtrees] of a host tree. We study bounds on these parameters, compare them with interval number, and characterize ...

We show that the sectional capacity of an adelic subset of a projective variety over a number field is a quasi-canonical limit of arithmetic top self-intersection numbers, and we establish the functorial properties of extremal plurisubharmonic Green’s functions. We also present a conjecture that the sectional capacity should be a top selfintersection number in an appropriate adelic arithmetic i...

An outerstring graph is an intersection graph of curves lying in a halfplane with one endpoint on the boundary of the halfplane. It is proved that the outerstring graphs are χ-bounded, that is, their chromatic number is bounded by a function of their clique number. This generalizes a series of previous results on χ-boundedness of outerstring graphs with various restrictions of the shape of the ...

We conclude, in this third part, the presentation of an algorithm for computing an exact and proper parameterization of the intersection of two quadrics. The coordinate functions of the parameterizations in projective space are polynomial, whenever it is possible. They are also near-optimal in the sense that the number of distinct square roots appearing in the coefficients of these functions is...

INTRODUCTION For the assessment on medical response capacity for disaster in local area (such as rescue capacity, transport capacity and treatment capacity), it is necessary to assess it in peace time, and understand how many sufferers from disaster the hospital can respond to. Here the estimated formula of Hospital Treatment Capacity (hereinafter shortened to HTC), the maximum receivable numbe...

We study the properties of geodesic currents on free groups, particularly the " intersection form " that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces .

We study the properties of geodesic currents on free groups, particularly the " intersection form " that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces .