Search results for "Polyhedron"

InternallyK-like spaces and internal inverse limits

2014

Abstract We establish equivalences between compacta that admit mappings that limit to the identity, and compacta that are inverse limits of the images under these maps. Our results have relationships to Mardesic and Segalʼs equivalence between polyhedra-like compacta and inverse limits of polyhedra, to the Anderson–Choquet Embedding Theorem, to approximative absolute neighborhood retracts, and to continua that are approximated from within as defined by C.A. Eberhart and J.B. Fugate.

Frames and representing systems in Fréchet spaces and their duals

2014

[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.

Bézier surfaces of minimal area

2002

There are minimal surfaces admitting a Bezier form. We study the properties that the associated net of control points must satisfy. We show that in the bicubical case all minimal surfaces are, up to an affine transformation, pieces of the Enneper's surface.

Almost square Banach spaces

2014

We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost one. These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square. We show that every separable space containing a copy of $c_0$ can be renormed to be almost square. A local and a weak version of almost square spa…

The influence of aromatic cations on the geometries of the Bi(III) halide polyhedra. Synthesis and crystal structures of quinolinium, isoquinolinium …

2001

Abstract The compounds [quinolinium]4[Bi2Cl10] (1), [isoquinolinium]4[Bi2Cl10].2H2O (2) and [8-hydroxyquinolinium]4[BiCl6]·Cl·2H2O (3) have been obtained by reacting bismuthate oxide and the appropriate base in HCl acid medium. The crystal structures of 1 and 2 consist of quinolinium and isoquinolinium cations, respectively, interacting through hydrogen bonding with [Bi2Cl10]4− dimers. The different degree of interactions in the two derivatives causes significant differences in the bond distances of the anions. The crystal structure of 3 is made of [BiCl6]3− and Cl− anions and 8-hydroxyquinolinium cations. Hydrogen bond interactions including the N-bonded and O-bonded H atoms together with …

Self-Assembly of M24L48 Polyhedra Based on Empirical Prediction

2012

Predictive control of convex polyhedron LPV systems with Markov jumping parameters

2012

The problem of receding horizon predictive control of stochastic linear parameter varying systems is discussed. First, constant coefficient matrices are obtained at each vertex in the interior of linear parameter varying system, and then, by considering semi-definite programming constraints, weight coefficients between each vertex are calculated, and the equal coefficients matrices for the time variable system are obtained. Second, in the given receding horizon, for each mode sequence of the stochastic convex polyhedron linear parameter varying systems, the optimal control input sequences are designed in order to make the states into a terminal invariant set. Outside of the receding horizon…

Net currents obtained from zero-average potentials in single amphoteric nanopores

2013

We have studied experimentally and theoretically the rectifying properties of a single asymmetric nanopore functionalized with amphoteric lysine groups and characterized the net current obtained with zero-average time dependent potentials. The pH-controlled rectification phenomena may be relevant to bio-electrochemistry, pH sensing and regulation, and energy conversion. (C) 2013 Elsevier B.V. All rights reserved.