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...

A k-dimensional lattice simplex σ ⊆ Rd is the convex hull of k + 1 affinely independent integer points. General lattice polytopes are obtained by taking convex hulls of arbitrary finite subsets of Zd . A lattice simplex or polytope is called empty if it intersects the lattice Zd only at its vertices. (Such polytopes are studied also under the names elementary and latticefree.) In dimensions d >...

For a minimal inequality derived from a maximal lattice-free simplicial polytope in R, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers R. We then use this characterization to show that a minimal inequality derived from a maximal lattice-free simplex in R with exactly one lattice point in the relative interior of each facet has a...

the purpose of this research was to prepare a floating matrix tablet containing domperidone as a model drug. polyethylene oxide (peo) and hydroxypropyl methylcellulose (hpmc) were evaluated for matrix-forming properties. a simplex lattice design was applied to systemically optimize the drug release profile. the amounts of peo wsr 303, hpmc k15m and sodium bicarbonate were selected as independen...

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 ...

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...

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...