1,721,401 research outputs found
Pentagram-Shaped Ag@Pt Core–Shell Nanostructures as High-Performance Catalysts for Formaldehyde Detection
No full textHigh-performance
HCHO sensors are of great importance in various application fields
such as indoor air quality assessments. Herein, bimetallic Ag–Pt
nanoparticles are synthesized as high-performance catalysts for ZnO-based
gas sensors. Spherical aberration (Cs)-corrected transmission electron
microscopy images with atomic resolution clearly indicate that the
prepared nanoparticles exhibit a novel Ag@Pt core–shell nanostructure
with a pentagram shape. For high-performance HCHO sensor construction,
integrated micro-electrodes are first fabricated with the microelectromechanical
system (MEMS) technology. Then, the hydrothermal route is used to
self-assemble well-aligned ZnO nanowire arrays onto the sensing microregion.
After that, the pentagram-shaped Ag@Pt nanoparticles are loaded onto
the surface of ZnO nanowires with the inkjet printing technique to
form MEMS sensors with Ag@Pt@ZnO as the sensing material. The thoroughly
sensing experiments indicate that the Ag@Pt nanoparticles exhibit
satisfied catalytic activation to HCHO molecules. The experimental
observed detection limit of our sensor to HCHO reaches the parts per
billion level. To elucidate the HCHO-sensing mechanism, the online
mass spectrum (online MS) is utilized to analyze the components of
exhaust gas stream of HCHO flowing through the Ag@Pt@ZnO material.
The online MS indicates that with the Ag@Pt catalyst, HCHO molecules
are partially oxidized to HCOOH molecules at low temperatures and
are completely oxidized to CO2 molecules at high temperatures
Pentagram Geometry
Get PDFThe Natural Constant Phi is included in the geometrical figure of a Pentagram as many artists have found out. Michelangelo may be the most famous one, whose sketch was transported in the payload of the first sucessful mission to the moon. By deriving this natural constant from the geometrics of the Pentagram a new analytical expression is found for Phi
The Pentagram, No. 2
Get PDFWith the second issue, the editors with to thank all of those who have contributed to the Pentagram. Students and faculty interest has made this issue possible. Your interest and contributions will make future issues possible.https://scholarworks.sfasu.edu/pentagram/1001/thumbnail.jp
Pentagram maps over rings, Grassmannians, and skewers
No full textThe pentagram map is a discrete dynamical system on planar polygons. By definition, the image of a polygon under the pentagram map is the polygon whose vertices are the intersection points of consecutive shortest diagonals of . The pentagram map was introduced by R. Schwartz in 1992, and is now one of the most renowned discrete integrable systems. Several authors proposed generalizations of the pentagram map to other geometries, in particular to Grassmannians, where the role of points and lines is played by higher-dimensional subspaces, as well to skewer geometry, where both points and lines are affine lines in the three-dimensional Euclidean space. In the present paper, we develop a common framework for these kinds of generalizations. Specifically, we show that those maps can be viewed as pentagram maps in the projective plane over an appropriate ring. In general, those rings need not be division rings or commutative. We show that the Grassmannian pentagram map corresponds to the ring of matrices, while the skewer map is the pentagram map over the ring of dual numbers. Furthermore, we prove that the pentagram map remains integrable for any stably finite ground ring
Pentagram maps over rings, Grassmannians, and skewers
Get PDFThe pentagram map is a discrete dynamical system on planar polygons. By definition, the image of a polygon P under the pentagram map is the polygon P’ whose vertices are the intersection points of consecutive shortest diagonals of P. The pentagram map was introduced by R. Schwartz in 1992, and is now one of the most renowned discrete integrable systems. Several authors proposed generalizations of the pentagram map to other geometries, in particular to Grassmannians, where the role of points and lines is played by higher-dimensional subspaces, as well to skewer geometry, where both points and lines are affine lines in the three-dimensional Euclidean space. In the present paper, we develop a common framework for these kinds of generalizations. Specifically, we show that those maps can be viewed as pentagram maps in the projective plane over an appropriate ring. In general, those rings need not be division rings or commutative. We show that the Grassmannian pentagram map corresponds to the ring of matrices, while the skewer map is the pentagram map over the ring of dual numbers. Furthermore, we prove that the pentagram map remains integrable for any stably finite ground ring R
Pentagram maps over rings, Grassmannians, and skewers
Get PDFThe pentagram map is a discrete dynamical system on planar polygons. By
definition, the image of a polygon under the pentagram map is the polygon
whose vertices are the intersection points of consecutive shortest
diagonals of . The pentagram map was introduced by R. Schwartz in 1992, and
is now one of the most renowned discrete integrable systems. Several authors
proposed generalizations of the pentagram map to other geometries, in
particular to Grassmannians, where the role of points and lines is played by
higher-dimensional subspaces, as well to skewer geometry, where both points and
lines are affine lines in the three-dimensional Euclidean space. In the present
paper, we develop a common framework for these kinds of generalizations.
Specifically, we show that those maps can be viewed as pentagram maps in the
projective plane over an appropriate ring. In general, those rings need not be
division rings or commutative. We show that the Grassmannian pentagram map
corresponds to the ring of matrices, while the skewer map is the pentagram map
over the ring of dual numbers. Furthermore, we prove that the pentagram map
remains integrable for any stably finite ground ring .Comment: 27 pages, 1 figur
The pentagram map: A discrete integrable system
No full textInternational audienceThe pentagram map is a projectively natural transformation defined on (twisted) polygons. A twisted polygon is a map from ℤ into ℝℙ2 that is periodic modulo a projective transformation called the monodromy. We find a Poisson structure on the space of twisted polygons and show that the pentagram map relative to this Poisson structure is completely integrable. For certain families of twisted polygons, such as those we call universally convex, we translate the integrability into a statement about the quasi-periodic motion for the dynamics of the pentagram map. We also explain how the pentagram map, in the continuous limit, corresponds to the classical Boussinesq equation. The Poisson structure we attach to the pentagram map is a discrete version of the first Poisson structure associated with the Boussinesq equation
Quasiperiodic Motion for the Pentagram Map
No full textThis note is a short announcement of arXiv:0810.5605The pentagram map is a projectively natural iteration defined on polygons, and also on a generalized notion of a polygon which we call {\it twisted polygons\/}. In this note we describe our recent work on the pentagram map, in which we find a Poisson structure on the space of twisted polygons and show that the pentagram map relative to this Poisson structure is completely integrable in the sense of Arnold-Liouville. For certain families of twisted polygons, such as those we call {\it universally convex\/}, we translate the integrability into a statement about the quasi-periodic notion of the pentagram-map orbits. We also explain how the continuous limit of the Pentagram map is the classical Boissinesq equation, a completely integrable PDE
Quasiperiodic Motion for the Pentagram Map
No full textThis note is a short announcement of arXiv:0810.5605The pentagram map is a projectively natural iteration defined on polygons, and also on a generalized notion of a polygon which we call {\it twisted polygons\/}. In this note we describe our recent work on the pentagram map, in which we find a Poisson structure on the space of twisted polygons and show that the pentagram map relative to this Poisson structure is completely integrable in the sense of Arnold-Liouville. For certain families of twisted polygons, such as those we call {\it universally convex\/}, we translate the integrability into a statement about the quasi-periodic notion of the pentagram-map orbits. We also explain how the continuous limit of the Pentagram map is the classical Boissinesq equation, a completely integrable PDE
The pentagram map: A discrete integrable system
No full textInternational audienceThe pentagram map is a projectively natural transformation defined on (twisted) polygons. A twisted polygon is a map from ℤ into ℝℙ2 that is periodic modulo a projective transformation called the monodromy. We find a Poisson structure on the space of twisted polygons and show that the pentagram map relative to this Poisson structure is completely integrable. For certain families of twisted polygons, such as those we call universally convex, we translate the integrability into a statement about the quasi-periodic motion for the dynamics of the pentagram map. We also explain how the pentagram map, in the continuous limit, corresponds to the classical Boussinesq equation. The Poisson structure we attach to the pentagram map is a discrete version of the first Poisson structure associated with the Boussinesq equation
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