Using implicit equations of parametric curves and surfaces without computing them: Polynomial algebra by values

The availability of the implicit equation of a plane curve or of a 3D surface can be very useful in order to solve many geometric problems involving the considered curve or surface: for example, when dealing with the point position problem or answering intersection questions. On the other hand, it is well known that in most cases, even for moderate degrees, the implicit equation is either difficult to compute or, if computed, the high degree and the big size of the coefficients makes extremely difficult its use in practice.We will show that, for several problems involving plane curves, 3D surfaces and some of their constructions (for example, offsets), it is possible to use the implicit equation (or, more precisely, its properties) without needing to explicitly determine it. We replace the computation of the implicit equation with the evaluation of the considered parameterizations in a set of points. We then translate the geometric problem in hand, into one or several generalized eigenvalue problems on matrix pencils (depending again on several evaluations of the considered parameterizations).This is the so-called “polynomial algebra by values” approach where the huge polynomial equations coming from Elimination Theory (e.g., using resultants) are replaced by big structured and sparse numerical matrices. For these matrices there are well-known numerical techniques allowing to provide the results we need to answer the geometric questions on the considered curves and surfaces.     

Cost-effective energy carriers for transport – The role of the energy supply system in a carbon-constrained world

The aim of this study is to examine how the options for producing electricity, fuels, and heat in a carbon-constrained world affect the cost-effectiveness of a range of fuels and propulsion technologies in the transportation sector. GET 7.0, a global energy system model with five end-use sectors, is used for the analysis. We find that an energy system dominated either by solar or by nuclear tends to make biofuels in plug-in hybrids cost-effective. If coal with carbon capture and storage (CCS) dominates the energy system, hydrogen cars, rather than plug-in hybrids tend to become cost-effective. Performing a Monte Carlo simulation, we then show that the general features of our results hold for a wide range of assumptions for the costs of vehicle propulsion technologies (e.g., batteries and fuel cells). However, sufficiently large changes in say the battery costs may overturn the impact of changes in the energy supply system, so that plug-in hybrid vehicles become cost-effective even if coal with CCS dominate the energy supply. We conclude that analyses of future energy carriers and propulsion technologies need to consider developments in the energy supply system.     

Tell Me Who I Am: An Interactive Recommendation System

We consider a model of recommendation systems, where each member from a given set of players has a binary preference to each element in a given set of objects: intuitively, each player either likes or dislikes each object. However, the players do not know their preferences. To find his preference of an object, a player may probe it, but each probe incurs unit cost. The goal of the players is to learn their complete preference vector (approximately) while incurring minimal cost. This is possible if many players have similar preference vectors: such a set of players with similar “taste” may split the cost of probing all objects among them, and share the results of their probes by posting them on a public billboard. The problem is that players do not know a priori whose taste is close to theirs. In this paper we present a distributed randomized peer-to-peer algorithm in which each player outputs a vector which is close to the best possible approximation of the player’s real preference vector after a polylogarithmic number of rounds. The algorithm works under adversarial preferences. Previous algorithms either made severely limiting assumptions on the structure of the preference vectors, or had polynomial overhead. Research of N. Alon supported in part by the Israel Science Foundation and by the Von Neumann Fund. B. Awerbuch supported by NSF grants ANIR-0240551, CCF-0515080 and CCR-0311795. Research of Y. Azar supported in part by the German-Israeli Foundation and by the Israel Science Foundation. Research of B. Patt-Shamir supported in part by Israel Ministry of Science and Technology and by the Israel Science Foundation (grant 664/05).     

On some questions regarding k -regular and k -context-free sequences

We answer two questions of Allouche and Shallit regarding k-regular sequences and k-context-free sequences. One of these has been solved independently in another way by Bell. We also provide a partial solution to another question of Allouche and Shallit regarding the subword complexity of k-context-free sequences.     

Performance-based seismic design of steel frames using ant colony optimization

In this paper, a performance-based optimal seismic design of frame structures is presented using the ant colony optimization (ACO) method. This discrete metaheuristic algorithm leads to a significant improvement in consistency and computational efficiency compared to other evolutionary methods. A nonlinear analysis is utilized to arrive at the structural response at various seismic performance levels, employing a simple computer-based method for push-over analysis which accounts for first-order elastic and second-order geometric stiffness properties. Two examples are presented to illustrate the capabilities of ACO in designing lightweight frames, satisfying multiple performance levels of seismic design constraints for steel moment frame buildings, and a comparison is made with a standard genetic algorithm (GA) implementation to show the superiority of ACO for the discussed optimization problem.     

Properties of waste‐poly(ethylene terephthalate)/acrylonitrile butadiene styrene blends compatibilized with maleated acrylonitrile butadiene styrene

Waste poly(ethylene terephthalate) (W‐PET)/acrylonitrile‐butadiene‐styrene (ABS) blends were prepared with a variety of compositions at several rotor speeds in an internal mixer, replacing ABS with different maleated ABS (ABS‐g‐MA) samples in compatibilized blends. A Box–Behnken model for three variables, with three levels, was chosen for the experimental design. ABS‐g‐MA‐based samples exhibited finer particles with a more uniform particle size distribution than ABS‐based ones, as a consequence of the compatibilizing process. Rheological results implied a greater elastic nature for compatibilized blends which increased in the presence of more ABS content; the same trend was observed for complex viscosity. With increasing ABS‐g‐MA or MA concentration, more shear thinning behavior was observed similar to that of ABS; whereas the uncompatibilized blends showed Newtonian behavior like that of W‐PET. The observed shifting in T_gW‐PET and T_gABS obtained from dynamic mechanical thermal analysis confirmed the good compatibility in W‐PET/ABS‐g‐MA blends in contrast with that in ordinary W‐PET/ABS blends. The mechanical properties were measured and modeled versus the various factors considered in a response surface methodology. The experimental data found a good fit with the obtained equation models. The mechanical properties of the compatibilized blends showed a large positive deviation from the mixing rule, while the uncompatibilized samples had lower properties, even compared to those predicted by the mixing rule. J. VINYL ADDIT. TECHNOL., 2010. © 2010 Society of Plastics Engineers     

Hydrothermal degradation of adsorbed sulfur mustard on activated carbon

Thermal and hydrothermal degradations of adsorbed sulfur mustard (HD) on activated carbon particles from a chemical protective over-garment were studied. Carbon loaded with 5 wt.% HD was heated in a closed reactor at temperatures up to 160 °C for 0.5–6 h and analyzed by solid-state ¹³C MAS NMR. On dry carbon at room temperature, HD was stable for months. On a thoroughly pre-wetted carbon, adsorbed HD partially degraded to thiodiglycol (TDG) and TDG-sulfoxide (TDG-SO) within 2–3 months. Heating dry HD-loaded carbon to 160 °C caused partial degradation within 4 h to 1,4-thioxane, along with 1,4-dithiane and vinyl sulfides. Complete degradation within 2.5 h to the same products occurred upon hydrothermal treatment of the HD-loaded carbon, using a water/carbon ratio of 0.3:1. With higher water/carbon ratios of 0.6:1–5:1 at temperatures of 120 °C and above, adsorbed HD hydrolyzed rapidly within 0.5 h. The latter reaction led to the formation of TDG concurrent with either thioxane (at 160 °C) or TDG-SO and TDG-dimer (at 120 °C). The mechanisms of the observed degradation processes are discussed.     

Effect of Particle Additions on Drying Stresses and the Green Density of Sol-Gel-Processed Three-Dimensional Ceramic-Matrix Composites

This paper investigates sol-gel processing of three-dimensional (3-D) ceramic-matrix composites, focusing on the effect of addition of particles on drying stresses and composite green density. A 3-D woven carbon fiber/silica composite was used as the model material system for the investigation. Composites were fabricated with silica particle additions to the silica sol using a pressure infiltration technique, and the drying rate and matrix cracking were characterized. The particle size was varied in order to study the role of particle additions in the processing. Ammonium hydroxide (NH₄OH) and a particle coating agent, 3-(trimethoxysilyl)propyl methacrylate (TPM), were added in the mixture of particles and sol to improve particle packing in the preform. Sol-gel processing with the addition of particles proves to be an effective route to fabricate 3-D ceramic-matrix composites with higher green density and less matrix cracking.