Search results for "Polyhedron"
showing 10 items of 38 documents
Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra
2003
We give an upper estimate for the Łojasiewicz exponent $\ell(J,I)$ of an ideal $J\subseteq A(K^{n})$ with respect to another ideal I in the ring $A(K^{n})$ of germs analytic functions $f$ : $(K^{n},\mathrm{O})\rightarrow K$ , where $K=C$ or $R$ , using Newton polyhedrons. In particular, we give a method to estimate the Łojasiewicz exponent $\alpha_{0}(f)$ of a germ $f\in A(K^{n})$ that can be applied when $f$ is Newton degenerate with respect to its Newton polyhedron.
A branch-and-cut algorithm for the Profitable Windy Rural Postman Problem
2016
[EN] In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its associated polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm…
Enantiomerically pure [M(6)L(12)] or [M(12)L(24)] polyhedra from flexible bis(pyridine) ligands.
2013
Coordination-driven self-assembly is one of the most powerful strategies to prepare nanometer-sized discrete (supra)molecular assemblies. Herein, we report on the use of two constitutionally isomeric BINOL-based bis(pyridine) ligands for this purpose. Upon coordination to Pd(II) ions these self-assemble into enantiomerically pure endo- and exo-functionalized hexa- and dodecanuclear metallosupramolecular spheres with a chiral skeleton depending on the substitution pattern of the BINOL core. These aggregates were characterized by NMR, MS, DLS, TEM, and EELS as well as ECD. Furthermore, experimental ECD data could be compared to those obtained from theoretical simulations using a simplified Ta…
The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations
1994
A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC∞-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
Finite element analysis of varitional crimes for a quasilinear elliptic problem in 3D
2000
We examine a finite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into account. We apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains in the $W^1_2$ -norm to the true solution without any additional regularity assumptions.
Modeling and design of Net ZEBs as integrated energy systems
2015
Net-zero energy buildings (Net ZEBs) are emerging as a quantifiable design concept and a promising solution to minimizing the environmental impact of buildings. This is the main concept that is focused on this chapter with emphasis on dynamic modeling and examples of technological approaches to achieve net-zero energy. Appropriate modeling of building-integrated solar energy systems is essential for the design of Net ZEBs and the study of optimal control strategies. The net-zero energy balance may be achieved through a combination of passive and active solar technologies, heat pumps, combined heat and power, and energy efficiency measures to reduce energy consumption for lighting and applia…
The project scheduling polyhedron: Dimension, facets and lifting theorems
1993
Abstract The Project scheduling with resource constraints can be formulated as follows: given a graph G with node set N, a set H of directed arcs corresponding to precedence relations, and a set H′ of disjunctive arcs reflecting the resource incompatibilities, find among the subsets of H′ satisfying the resource constraints the set S that minimizes the longest path in graph (N, H ∪ S). We define the project scheduling polyhedron Qs as the convex hull of the feasible solutions. We investigate several classes of inequalities with respect to their facet-defining properties for the associated polyhedron. The dimension of Qs is calculated and several inequalities are shown to define facets. For …
Structural phase transition to disorder low-temperature phase in [Fe(ptz)6](BF4)2 spin-crossover compounds.
2012
In the spin-crossover compound [Fe(ptz)6](BF4)2 (where ptz=1-n-propyltetrazole) six different phases are observed. When a single crystal is slowly cooled from high temperatures to those below 125 K, the reflections broaden into diffuse maxima and split into two maxima along the c* direction [Kusz, Gütlich & Spiering (2004). Top. Curr. Chem. 234, 129–153]. As both maxima are broad along the c* direction, the short-range order exists only along the c direction and in the ab plane the structure remains long-range ordered. In this disordered phase additional satellite reflections appear. Upon heating above 135 K, the diffuse maxima return to their previous shape and this process is complete…
Structure of the new mineral sarrabusite, Pb5CuCl4(SeO3)4, solved by manual electron-diffraction tomography.
2012
The new mineral sarrabusite Pb5CuCl4(SeO3)4 has been discovered in the Sardinian mine of Baccu Locci, near Villaputzu. It occurs as small lemon–yellow spherical aggregates of tabular crystals (< 10 µm) of less than 100 µm in diameter. The crystal structure has been solved from and refined against electron diffraction of a microcrystal. Data sets have been measured by both a manual and an automated version of the new electron-diffraction tomography technique combined with the precession of the electron beam. The sarrabusite structure is monoclinic and consists of (010) layers of straight chains formed by alternating edge-sharing CuO4Cl2 and PbO8 polyhedra parallel to the c axis, which sha…