Search results for "Geometric"

Characterizing Cavities in Model Inclusion Fullerenes: A Comparative Study

2001

Abstract: The fullerene-82 cavity is selected as a model system in order to test several methods for characterizing inclusion molecules. The methods are based on different technical foundations such as a square and triangular tessellation of the molecular surface, spherical tessellation of the molecular surface, numerical integration of the atomic volumes and surfaces, triangular tessellation of the molecular surface, and cubic lattice approach to the molecular volume. Accurate measures of the molecular volume and surface area have been performed with the pseudorandom Monte Carlo (MCVS) and uniform Monte Carlo (UMCVS) methods. These calculations serve as a reference for the rest of the meth…

Two‐dimensional metric spheres from gluing hemispheres

2022

We study metric spheres (Z,dZ) obtained by gluing two hemispheres of S2 along an orientation-preserving homeomorphism g:S1→S1, where dZ is the canonical distance that is locally isometric to S2 off the seam. We show that if (Z,dZ) is quasiconformally equivalent to S2, in the geometric sense, then g is a welding homeomorphism with conformally removable welding curves. We also show that g is bi-Lipschitz if and only if (Z,dZ) has a 1-quasiconformal parametrization whose Jacobian is comparable to the Jacobian of a quasiconformal mapping h:S2→S2. Furthermore, we show that if g−1 is absolutely continuous and g admits a homeomorphic extension with exponentially integrable distortion, then (Z,dZ) …

Sobolev homeomorphic extensions onto John domains

2020

Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous $W^{1,2}$-extension but not even a homeomorphic $W^{1,1}$-extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents $p<2$. John disks, being one sided quasidisks, are of fundamental importance in Geometric Function Theory.

A comprehensive approach to the 3D geological modelling of sedimentary basins: example of Latvia, the central part of the Baltic Basin

2015

This paper presents a semi-automatic approach adapted to the modelling of the geological structure of sedimentary basins. The modelling approach is based on developing the algorithm of the main geological processes so that the geometrical relationship is automatically defined between model elements. The algorithm is based on the assumption that sedimentary basins are formed as a result of the repeated sequence of sedimentation, faulting and erosion. This approach allows of successful modelling of the geological structure of the sedimentary basins with limited data coverage: stratigraphic intervals from well logs describing the thicknesses of sedimentary strata and a limited amount of struct…

Geometric Brownian Motion (GBM) of Stock Indexes and Financial Market Uncertainty in the Context of Non-Crisis and Financial Crisis Scenarios

2022

The present article proposes a methodology for modeling the evolution of stock market indexes for 2020 using geometric Brownian motion (GBM), but in which drift and diffusion are determined considering two states of economic conjunctures (states of the economy), i.e., non-crisis and financial crisis. Based on this approach, we have found that the GBM proved to be a suitable model for making forecasts of stock market index values, as it describes quite well their future evolution. However, the model proposed by us, modified geometric Brownian motion (mGBM), brings some contributions that better describe the future evolution of stock indexes. Evidence in this regard was provided by analyzing …

Some considerations on Hydra groups and a new bound for the length of words

2013

From Dupin cyclides to scaled cyclides

2003

Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. They have a low algebraic degree and have been proposed as a solution to a variety of geometric modeling problems. The circular curvature line’s property facilitates the construction of the cyclide (or the portion of a cyclide) that blends two circular quadric primitives. In this context of blending, the only drawback of cyclides is that they are not suitable for the blending of elliptic quadric primitives. This problem requires the use of non circular curvature blending surfaces. In this paper, we present another formulation of cyclides: Scaled cyclides. A scaled cy…

Analysis and reconstruction in stages of the design and construction process of the old and new basilica of S. Peter in Vatican, and its surroundings

2020

Resumen 1. Objetivos El objetivo general de esta Tesis Doctoral es reconstruir el proceso de diseño y construcción de la antigua y nueva basílica de San Pedro en el Vaticano, y de su entorno cercano. De forma complementaria, se reconstruye la evolución de la trama urbana del área del Vaticano, desde su origen hasta la actualidad. La reconstrucción del proceso de diseño y construcción se realizará de forma descriptiva y, especialmente, de forma gráfica. Los planos se realizarán con gran detalle, a escala y con gran precisión, utilizando las más avanzadas herramientas de dibujo digital. La reconstrucción de las diferentes etapas del proceso de diseño y construcción de la antigua basílica se r…

Kompleksy metali przejściowych z zasadami Lewisa jako prekursory katalizatorów polimeryzacji olefin. Cz. I. Postęp w komputerowym modelowaniu procesu…

2001

A review with 35 references covering molecular modeling in coordination polymerization over homogeneous and heterogeneous Ziegler-Natta catalysts. The study includes supports, cocatalysts, Lewis bases and solvents. Recent progress in elucidating the mechanisrn of elementary polymerization steps is presented against the background of rapidly deveIoping computational methods and available computational power. Theoretical studies on polymerization mcchanisms and structure of active centers are described (egns. 1-4). Authors own calculations are used to compare [MtC14(THF)2] complex-based (Mt = Ti, Hf or Zr) heterogeneous catalysts. The geometrical characteristics of precursors is presented (Ta…

On Augmented Reality for the Learning of 3D-Geometric Contents: A Preliminary Exploratory Study with 6-Grade Primary Students

2019

Nowadays, Augmented Reality (AR) is one of the emerging technologies with a greater impact in the Education field. Research has proved that AR-based activities improve the teaching and learning processes. Also, the use of this type of technology in classroom facilitates the understanding of contents from different areas as Arts, Mathematics or Science. In this work we propose an AR-based instruction in order to explore the benefits in a 6th-grade Primary course related to 3D-geometry shapes. This first experiment, designed from an exploratory approach, will shed light on new study variables to perform new implementations whose conclusions become more consistent. The results obtained allow u…