We consider the problem of generating a lattice-free convex set to find a valid inequality that minimizes the sum of its coefficients for 2-row simplex cuts. Multi-row simplex cuts has been receiving considerable attention recently and we show that a pseudo-polytime generation of a lattice-free convex set is possible. We conclude with a short numerical study.

We generalize Ehrhart’s idea ([Eh]) of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n+ 1 rational vertices, we use its description as the intersection of n+1 halfspaces, which determine the facets of the simplex. Instead of just a single dilation factor, we allow different dilation factors for each of these facets. We g...

We generalize Ehrhart’s idea ([Eh]) of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n+ 1 rational vertices, we use its description as the intersection of n+ 1 halfspaces, which determine the facets of the simplex. Instead of just a single dilation factor, we allow different dilation factors for each of these facets. We ...

Chewable ferrous fumarate tablet is the best iron dosage form for children due to better compliance and lower teeth staining compared to the oral drop. Because of the different desirable properties of chewable tablets and the opposing effects of fillers on them, the mathematical experimental design was used as the formulation approach. Different series of formulations based on single filler (La...

Sphere close packed (SCP) lattice arrangements of points are well-suited for formulating symmetric quadrature rules on simplexes, as they are symmetric under affine transformations of the simplex unto itself in 2D and 3D. As a result, SCP lattice arrangements have been utilized to formulate symmetric quadrature rules with Np = 1, 4, 10, 20, 35, and 56 points on the 3-simplex (Shunn andHam, 2012...

A modified Scheffe's simplex lattice design method is proposed to study the properties of multicomponent materials. This allowed determining optimal compositions cordierite and corundum based ceramic materials that are used as catalyst carrier for gas purification equipment. The obtained material (0.63-1.25 mm weight fraction 0.35 mass% fraction; < 0.63 0.06 0.2 1.25-2.5 fraction) was succes...

There is a simple formula for the Ehrhart polynomial of a cyclic polytope. The purpose of this paper is to show that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any d-dimensional simplex in general position into d! signed sets, each of which corresponds to a permutation in the symmetric group Sd, and reduce the problem of...