Keplerian trigonometry

Taking the hint from usual parametrization of circle and hyperbola, and inspired by the pathwork initiated by Cayley and Dixon for the parametrization of the “Fermat” elliptic curve $$x^3+y^3=1$$ x 3 + y 3 = 1 , we develop an axiomatic study of what we call “Keplerian maps”, that is, functions $${{\,\mathrm{{\mathbf {m}}}\,}}(\kappa )$$ m ( κ ) mapping a real interval to a planar curve, whose variable $$\kappa $$ κ measures twice the signed area swept out by the O-ray when moving from 0 to $$\kappa $$ κ . Then, given a characterization of k-curves, the images of such maps, we show how to recover the k-map of a given parametric or algebraic k-curve, by means of suitable differential problems.

Quantum holonomies and the Heisenberg group

Quantum holonomies of closed paths on the torus [Formula: see text] are interpreted as elements of the Heisenberg group [Formula: see text]. Group composition in [Formula: see text] corresponds to path concatenation and the group commutator is a deformation of the relator of the fundamental group [Formula: see text] of [Formula: see text], making explicit the signed area phases between quantum holonomies of homotopic paths. Inner automorphisms of [Formula: see text] adjust these signed areas, and the discrete symplectic transformations of [Formula: see text] generate the modular group of [Formula: see text].

Improved Simultaneous Mesh Untangling and Quality Improvement Methods of 2D Triangular Meshes

Few inverted or poor quality elements can ruin both the accuracy and efficiency of numerical solutions. This paper proposes improved mesh untangling and quality improvement methods using the modified mesh quality metric for 2D triangular meshes. The new mesh quality metric ensures highly inverted elements assign higher penalty when the signed area of the element is negative, and also produces more accurate signed areas for valid elements. Therefore, the proposed methods can quickly remove inverted elements and also improve worst element qualities compared with the existing methods. We also combine Delaunay-based edge flip with optimization-based mesh untangling and quality improvement methods to further improve worst element qualities. Numerical results show that the proposed methods yield better quality meshes for improvement of the worst quality and are faster than existing methods.

Formation Tracking of Heterogeneous Mobile Agents Using Distance and Area Constraints

This paper presents two formation tracking control strategies for a combined set of single and double integrator agents with an arbitrary undirected communication topology. The first approach is based on the design of distance-based potential functions with interagent collision avoidance using local information about the distance and orientation between agents and the desired trajectory. The second approach adds signed area constraints to the desired formation specification and a control strategy that uses distance as well as area terms is designed to achieve tracking convergence. Numerical simulations show the performance from both control laws.

RANCANGAN CITY BRANDING KOTA PADANG PENTINGNYA SEBUAH BRANDING DALAM PERKEMBANGAN KOTA

The final work is titled Draft City Branding Padang city. The introduction has not been packagedproperly. It creates an image that is less attractive for tourists, when in fact the City The potential thatought to be proud of by the people. This design uses the theory of city branding, communication theory,design theory and the theory of color. Therefore, in the design of this time are highlighted in The laterthrough verbal and visual messages, tagline and media applications that are effective and efficient.As for media design is the logo along with the explanation. Design a billboard mediaapplications, facebook account, t-shirts, mugs, keychains, signed area, posters, pins, post card, sticker,calendar and jlaxchange. All the media is part of the process of city branding Padang city.Keywords: Concept, City Branding, Padang.

A QUANTUM GOLDMAN BRACKET FOR LOOPS ON SURFACES

In the context of (2+1)–dimensional gravity, we use holonomies of constant connections which generate a q–deformed representation of the fundamental group to derive signed area phases which relate the quantum matrices assigned to homotopic loops. We use these features to determine a quantum Goldman bracket (commutator) for intersecting loops on surfaces, and discuss the resulting quantum geometry.