Graphics Evolutionary Computations in Higher Order Parametric Bezier Curves

This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves. Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above. Bezier curves find real life applications in diverse areas of Engineering and Computer Science, such as computer graphics, robotics, animations, virtual reality, among others. Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations, proof of related theorems, first and second order calculus related computations, among others. A Practical case is demonstrated using a graphical design, physical hand sketching, and programmatic implementation of two opposite-faced handless cups, all evolved using quadratic Bezier curves. The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript. This work will no doubt find relevance in computational researches in the areas of graphics, web programming, automated theorem proofs, robotic motions, among others.     

Photocatalytic activity of a new composite material of Fe (III) oxide nanoparticles wrapped by a matrix of polymeric carbon nitride and amorphous carbon

Polymeric carbon nitride was synthesized from urea and doped with Cu and Fe to act as co-catalysts. The material doped with Fe was a new composite material composed of Fe(III) oxides (acting as a co-catalyst) wrapped by the polymer layers and amorphous carbon. Furthermore, the copper doped material was described in a previous report. The photocatalytic degradation of the azo dye direct blue 1 (DB) was studied using as photocatalysts: pure carbon nitride (CN), carbon nitride doped with Cu (CN-Cu) and carbon nitride doped with Fe (CN-Fe). The catalysts were characterized by Fourier transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), by X-ray photoelectron spectroscopy (XPS) and Brunauer–Emmett–Teller method (BET), etc. The adsorption phenomenon was studied using the Langmuir and Freundlich models. For the kinetic study, a solution of 500 mg L^?1 of DB1 was treated with each catalyst, visible light and H₂O₂. The dye concentration was measured by spectrophotometry at the wavelength of 565 nm, and the removal of the total organic content (TOC) was quantified. BET analysis yielded surface areas of 60.029, 20.116 and 70.662 m²g^?1 for CN, CN-Cu and CN-Fe, respectively. The kinetics of degradation were pseudo-first order, whose constants were 0.093, 0.039 and 0.110 min^?1 for CN, CN-Cu and CN-Fe, respectively. The total organic carbon (TOC) removal reached the highest value of 14.46% with CN-Fe.     

Vademecum‐based GFEM (V‐GFEM): optimal enrichment for transient problems

This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off‐line and stored in memory in the form of a computational vademecum so that they can be used on‐line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum‐generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes. Copyright © 2016 John Wiley & Sons, Ltd.     

NURBS-Enhanced Finite Element Method (NEFEM)

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.     

All normalized anti-monotonic overlap graph measures are bounded

In graph mining, a frequency measure for graphs is anti-monotonic if the frequency of a pattern never exceeds the frequency of a subpattern. The efficiency and correctness of most graph pattern miners relies critically on this property. We study the case where frequent subgraphs have to be found in one graph. Vanetik et al. (Data Min Knowl Disc 13(2):243?C260, 2006) already gave sufficient and necessary conditions for anti-monotonicity of graph measures depending only on the edge-overlaps between the instances of the pattern in a labeled graph. We extend these results to homomorphisms, isomorphisms and homeomorphisms on both labeled and unlabeled, directed and undirected graphs, for vertex- and edge-overlap. We show a set of reductions between the different morphisms that preserve overlap. As a secondary contribution, we prove that the popular maximum independent set measure assigns the minimal possible normalized frequency and we introduce a new measure based on the minimum clique partition that assigns the maximum possible normalized frequency. In that way, we obtain that all normalized anti-monotonic overlap graph measures are bounded from above and below. We also introduce a new measure sandwiched between the former two based on the polynomial time computable Lovász ??-function.     

A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation

In this contribution, we present an a posteriori error estimator for the incompressible Stokes problem valid for a conventional mixed FE formulation. Due to the saddle-point property of the problem, conventional error estimators developed for pure minimization problems cannot be utilized straight-forwardly. The new estimator is built up by two key ingredients. At first, a computed error approximation, exactly fulfilling the continuity equation for the error, is obtained via local Dirichlet problems. Secondly, we adopt the approach of solving local equilibrated flux-free problems in order to bound the remaining, incompressible, error. In this manner, guaranteed upper and lower bounds, of the velocity “energy norm” of the error as well as goal-oriented (linear) output functionals, with respect to a reference (overkill) mesh are obtained. In particular, it should be noted that this approach requires no computation of hybrid fluxes. Furthermore, the estimator is applicable to mixed FE formulations using continuous pressure approximations, such as the Mini and Taylor–Hood class of elements. In conclusion, a few simple numerical examples are presented, illustrating the accuracy of the error bounds.     

A polynomial time computable metric between point sets

Measuring the similarity or distance between sets of points in a metric space is an important problem in machine learning and has also applications in other disciplines e.g. in computational geometry, philosophy of science, methods for updating or changing theories, . Recently Eiter and Mannila have proposed a new measure which is computable in polynomial time. However, it is not a distance function in the mathematical sense because it does not satisfy the trian gle inequality. We introduce a new measure which is a metric while being computable in polynomial time. We also present a variant which computes a normalised metric and a variant which can associate different weights with the points in the set. Received: 18 October 1999 / 8 January 2001