structure of alpha lattice designs makes removing the effects of incomplete blocks from residual effect of plots, and maximizes precision of comparison between genotypes at the same incomplete block. this investigation was conducted to study the international chickpea germplasm, for finding desirable lines regarding seed yield and other traits. two trials including cien-la-2010 and cien-s-2010 ...

Propranolol hidroklorida merupakan penghambat reseptor beta-1 yang digunakan untukterapi angina, aritmia jantung, dan hipertensi. Penggunaannya secara oral memiliki beberapamasalah seperti mengalami first pass effect, indeks terapi sempit, rasa pahit.Kekurangan tersebut bisa diatasi dengan memformulasikannya sebagai sediaan transdermalberupa patch. Komponen dalam patch transdermal adalah kombin...

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.

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.

Linear programming (LP) is an important tool for many inter-disciplinary optimization problems. The Simplex method is the most widely used algorithm to solve LP problems and has immense impact on several developments in various fields. With development of public domain and commercial software solvers, it has been automated and made available for use. A serious bottleneck in implementation of Si...

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, ...

We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩ lZ (provided it is non-empty) contains a point whose coefficient of asymmetry 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 9 · (8l+ 7) d+1 . This implies that the maximum volume of a lattice polytope P ⊂ R d containing exactly k ≥ 1 points of lZ in its interior, is...

Nakamura [N] introduced the G-Hilbert scheme G-Hilb C3 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-Hilb C3 much more simply, in terms of fun with continued fractions plus regular tesselations by equilate...