We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩lZ (provided it is non-empty) contains a point whose coefficient ofasymmetry with respect to P is at most 8d · (8l+7)2d+1. If, moreover,P is a simplex, then this bound can be improved to 8 · (8l+ 7)d+1.As an application, we deduce new upper bounds on the volume ofa lattice polytope, given its ...

The Flatness theorem states that the maximum lattice width $$\mathrm {Flt}(d)$$ of a d-dimensional lattice-free convex set is finite. It key ingredient for Lenstra’s algorithm integer programming in fixed dimension, and much work has been done to obtain bounds on . While most results have concerned with upper bounds, only few techniques are known lower bounds. In fact, previously best bound {Fl...

This study develops mathematical models for obtaining optimum flexural strengths of normal laterised(NLC) and high strength laterised concretes (HSLC). The can be expressly used to evaluate the indirect tensile both types without going through traditional methods mix design. Optimum mixing ratios predicted are also supplied by models. three point load method was adopted testing strengths. Later...

Transdermal patch is drug delivery system that pasted through the skin. These preparations can provide a constant release, easy to use, reduce frequency of administration, eliminate first-pass metabolism, and side effects such as gastric irritation improve patient compliance. Blue pea (Clitoria ternatea L.) contains flavonoid compounds have anti-inflammatory activity. This study aims obtain opt...

Simplex lattice design was used to 15 sponge cakes formulations combining pea (PP), hemp (HP) and insect (IP) flours representing 15% of dough composition. Moisture, protein content, baking loss, specific volume, texture cost the samples plus control (0% added protein) were analysed. Results showed that effect PP, HP IP on cake properties could be modelled with linear regressions (96.80% < R 2 ...

Isolated from Annona squamosa L, Annonaceous acetogenins (ACGs) exhibit a broad range of biological properties yet absorbed badly due to the low solubility. Solid dispersion in polyethylene glycol 4000 (PEG 4000) has been developed to increase the solubility and oral absorption of ACGs. The formulation of ACGS-solid dispersion was optimized by a simplex lattice experiment design and carried out...