In this work, growth and assembly of the micro polyhedral zinc oxide was performed using airbubble assisted Triton X100, as a templating agent. In absence of air bubbling in the reactionsystem the nano plate zinc oxide was synthesized. The prepared samples were characterized by Xraydiffraction (XRD), field emission scanning electron microscopy (FE-SEM) and UV-Visspectrop...

We show that the presentation of affine T-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra associated to a polyhedral divisor changes when we extend the scalars. As another application, we provide a combinatorial description of affine G-varieties of complexi...

Topology has an increasingly important role in the physics of condensed matter, quantum systems, material science, photonics and biology, with spectacular realizations of topological concepts in liquid crystals. Here we report on long-lived hidden topological states in thermally quenched, chiral nematic droplets, formed from string-like, triangular and polyhedral constellations of monovalent an...

In 1960, Nicolaas Kuiper showed that every surface can be tightly immersed in three-space except for the real projective plane and the Klein bottle, for which no such immersion exists, and the real projective plane with one handle, for which he could find neither a tight example nor a proof that one does not exist. It was not until more than 30 years later, in 1992, that François Haab proved th...

In this article we introduce the notion of Polyhedral Kähler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and classify the singularities of the metric. The singularities form a divisor and the residues of the flat connection on the complement of the divisor give us a syste...

We show that the number of topologically different orthographic views of a polyhedral terrain with n edges is O(n 5 +~), and that the number of topologically different perspective views of such a terrain is O(nS+0, for any e > 0. Both bounds are almost tight in the worst case. The proofs are simple consequences of the recent almost-tight bounds of [11] on the complexity of lower envelopes in hi...

We describe a simple technique to prepare superhydrophobic and superoleophobic micro-textured surfaces by spray coating a blend of poly(methyl methacrylate) (PMMA) and the low surface energy molecule 1H,1H,2H,2H-heptadecafluorodecyl polyhedral oligomeric silsesquioxane (fluorodecyl POSS, γsv ≈ 10 mN/m) using an air brush with a pressurized nitrogen stream. Scanning electron micrographs show the...

We study the problem of placing guard towers on a terrain such that the terrain can be seen from at least one tower. This problem is important in many applications, and has an extensive history in the literature (known as, e.g., multiple observer siting). In this paper, we consider the problem on polyhedral terrains, and we allow the guards to see only a fixed fraction of the terrain, rather th...

in this paper a certain class of polyhedral semigroups which has a presentation $$ is examined‎. ‎the completeness of the presentation and solvability of word problem of this class of semigroups is determined‎. ‎moreover the combinatorial distance between two words is determined‎.