The problem of spherical packing and the distribution points on a sphere are well-known unsolved mathematical problems. In particular, is included in list problems Steve Smale. Accordingly, significant interest for study both direct search solutions to research areas related known dense coating directly regular, irregular layered lattices, noise-resistant coding, synthesis analysis broadband si...

For the symmetrical mixture model and test area, lattice point set is used to partition, then corresponding statistics can be constructed. In this paper, we first propose partition methods under sets obtain several sub-simplexes without common interior points. Furthermore, present a method for constructing uniform design on simplex using center points of these sub-simplexes. The designs satisfy...

We give a criterion which characterizes real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of fully positive coefficients. Here is said coefficients if its monomial terms indexed by lattice points are positive. Our result generalizes an earlier Colin Tan and author, corresponds special case when translate st...

In this licentiate thesis we study relations among invariants of lattice polytopes, with particular focus on bounds for the volume. In the first paper we give an upper bound on the volume vol(P∗) of a polytope P∗ dual to a d-dimensional lattice polytope P with exactly one interior lattice point, in each dimension d . This bound, expressed in terms of the Sylvester sequence, is sharp, and is ach...

The objective of the present investigation was to prepare and evaluate an ispaghula husk based directly compressible (DC) adjuvant that can be used as matrixing agent using an agglomeration technique. Addition of hydroxypropyl methylcellulose was found necessary to improve cohesion. Lactose (X1), calcium hydrogen phosphate dihydrate (X2) and Avicel PH101 (X3), used along with ispaghula in prepa...

Penelitian ini bertujuan untuk mengetahui pengaruh kombinasi konsentrasi serta jumlah formula yang optimum dari Cetylstearyl alkohol dan glyceryl monostearat sebagai emulgator agar diperoleh sediaan dengan karakteristik fisik stabilitas baik. Untuk menentukan proporsi relative bahan-bahan digunakan dalam suatu formula, maka pada penelitian optimasi metode Simplex Lattice Design (SLD). Formula d...

Borozan and Cornuéjols introduced a semi-infinite relaxation for mixed-integer linear programs, derived from the simplex tableau relative to a fractional vertex f of the linear relaxation. They showed that any minimal valid inequality for such relaxation is determined by a maximal lattice-free convex set containing f . In this note we show that, for the purpose of generating cuts for the origin...

Nakamura [N] introduced the G-Hilbert scheme for a finite subgroup G ⊂ SL(3, C), and conjectured that it is a crepant resolution of the quotient C3/G. He proved this for a diagonal Abelian group A by introducing an explicit algorithm that calculates A-HilbC3. This note calculates A-HilbC3 much more simply, in terms of fun with continued fractions plus regular tesselations by equilateral triangl...