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 a continuous-time symmetric branching random walk on multidimensional lattice with finite set of particle generation centers, i.e., sources. The existence positive eigenvalue the evolutionary operator means exponential growth first moment total number particles both at an arbitrary point and entire lattice. Branching walks or negative intensities sources that have simplex configurat...

A discrete Fourier analysis on the fundamental domain Ωd of the d-dimensional lattice of type Ad is studied, where Ω2 is the regular hexagon and Ω3 is the rhombic dodecahedron, and analogous results on d-dimensional simplex are derived by considering invariant and anti-invariant elements. Our main results include Fourier analysis in trigonometric functions, interpolation and cubature formulas o...

In this paper, we prove that given a lattice simplex $$\Delta $$ with its $$h^*$$ -polynomial $$\sum _{i \ge 0}h_i^*t^i$$ , if $$h_{k+1}^*=\cdots =h_{2k}^*=0$$ holds, then there exists face of whose coincides _{i=0}^k h_i^*t^i$$ . Moreover, present examples showing the condition $$h_{k+1}^*=h_{k+2}^*=\cdots =h_{2k-1}^*=0$$ is necessary.

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...

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...

In this paper we explore the geometry of the integer points in a cone rooted at a rational point. This basic geometric object allows us to establish some links between lattice point free bodies and the derivation of inequalities for mixed integer linear programs by considering two rows of a simplex tableau simultaneously.

This describes the map χ in the exact sequence. The map L in the sequence gives us a matrix such that ImL = kerχ. This matrix will generate a integer lattice Λ ⊆ Zm−n. Such an exact sequence gives rise to many different interpretations. The most familiar interpretation is that of a polytope in R which introduces geometry to the system. We can also view the exact sequence as defining a system of...

We consider a finite set of lattice points and their convex hull. The author previously gave a geometric proof that the sumsets of these lattice points take over the central regions of dilated convex hulls, thus revealing an interesting connection between additive number theory and geometry. In this paper, we will see an algebraic proof of this fact when the convex hull of points is a simplex, ...