Classification of polynomial translation hypersurfaces of finite type

In this paper we prove that any hypersurface in Eⁿ⁺¹ of the form where P ₁ is a polynomial of degree ≥2 and P ₂, ... , P _n are functions such that P _i ^′ P _i ^″ = 0 somewhere for all i = 2, ... , n, is of infinite type. As a consequence, we deduce that a polynomial translation hypersurface in Eⁿ⁺¹, i. e. a hypersurface of the above form where P ₁, ... , P _n are polynomials, is of finite type if and only if it is a hyperplane. This provides some partial solutions to a problem of B. Y. Chen [C3].     

Gas chromatography-mass spectrometry as a tool for estimating odour concentrations of biofilter effluents at aerobic composting and rendering plants

The relationship between chemical concentrations (gas chromatography–mass spectrometry analysis) and odour concentrations (olfactometry) was studied for biofilter emissions from four aerobic vegetable, fruit and garden waste (VFG) composting plants and one animal rendering plant. For the VFG composting plants, the study revealed a good linear relationship of the odour concentration with the total volatile organic compounds (VOC) concentration (R²=0.97, n=16) as well as with the concentration of esters and ketones (R²=0.9, n=19). For biofilter emissions of the animal rendering plant, the total VOC concentration was a poor estimator for odour concentration. However, for this type of odour, concentrations of organic sulphur containing compounds correlated well with odour concentrations (R²=0.94, n=8). The results of the study also showed that the relationship between chemical and odour concentrations is specific for each type of odour and cannot be generalized.     

Beyond Mechanical Recycling: Giving New Life to Plastic Waste

Increasing the stream of recycled plastic necessitates an approach beyond the traditional recycling via melting and re‐extrusion. Various chemical recycling processes have great potential to enhance recycling rates. In this Review, a summary of the various chemical recycling routes and assessment via life‐cycle analysis is complemented by an extensive list of processes developed by companies active in chemical recycling. We show that each of the currently available processes is applicable for specific plastic waste streams. Thus, only a combination of different technologies can address the plastic waste problem. Research should focus on more realistic, more contaminated and mixed waste streams, while collection and sorting infrastructure will need to be improved, that is, by stricter regulation. This Review aims to inspire both science and innovation for the production of higher value and quality products from plastic recycling suitable for reuse or valorization to create the necessary economic and environmental push for a circular economy.     

QuickFF: A program for a quick and easy derivation of force fields for metal‐organic frameworks from ab initio input

QuickFF is a software package to derive accurate force fields for isolated and complex molecular systems in a quick and easy manner. Apart from its general applicability, the program has been designed to generate force fields for metal‐organic frameworks in an automated fashion. The force field parameters for the covalent interaction are derived from ab initio data. The mathematical expression of the covalent energy is kept simple to ensure robustness and to avoid fitting deficiencies as much as possible. The user needs to produce an equilibrium structure and a Hessian matrix for one or more building units. Afterward, a force field is generated for the system using a three‐step method implemented in QuickFF. The first two steps of the methodology are designed to minimize correlations among the force field parameters. In the last step, the parameters are refined by imposing the force field parameters to reproduce the ab initio Hessian matrix in Cartesian coordinate space as accurate as possible. The method is applied on a set of 1000 organic molecules to show the easiness of the software protocol. To illustrate its application to metal‐organic frameworks (MOFs), QuickFF is used to determine force fields for MIL‐53(Al) and MOF‐5. For both materials, accurate force fields were already generated in literature but they requested a lot of manual interventions. QuickFF is a tool that can easily be used by anyone with a basic knowledge of performing ab initio calculations. As a result, accurate force fields are generated with minimal effort. © 2015 Wiley Periodicals, Inc.     

The Chen-Type of the Spiral Surfaces

We show that a spiral surface M in E³ is of finite type if and only if M is minimal Also, the plane is the only spiral surface in E³ whose the Gauss map G is of finite type, or satisfies the condition ΔG = ΛG, where Λ ∈ R^3×3.     

On 2-Quasi-Umbilical Hypersurfaces in Conformally Flat Spaces

The main result of this paper states that any 2-quasi-umbilical hypersurface of a semi-Riemannian conformally flat space is a manifold with pseudosymmetric Weyl tensor.     

A Reactive Molecular Dynamics Study of Chlorinated Organic Compounds. Part II: A ChemTraYzer Study of Chlorinated Dibenzofuran Formation and Decomposition Processes

In our two-paper series, we first present the development of ReaxFF CHOCl parameters using the recently published ParAMS parametrization tool. In this second part, we update the reactive Molecular Dynamics – Quantum Mechanics coupling scheme ChemTraYzer and combine it with our new ReaxFF parameters from Part I to study formation and decomposition processes of chlorinated dibenzofurans. We introduce a self-learning method for recovering failed transition-state searches that improves the overall ChemTraYzer transition-state search success rate by 10 percentage points to a total of 48 %. With ChemTraYzer, we automatically find and quantify more than 500 reactions using transition state theory and DFT. Among the discovered chlorinated dibenzofuran reactions are numerous reactions that are new to the literature. In three case studies, we discuss the set of reactions that are most relevant to the dibenzofuran literature: (i) bimolecular reactions of the chlorinated-dibenzofuran precursors phenoxy radical and 1,3,5-trichlorobenzene, (ii) dibenzofuran chlorination and pyrolysis, and (iii) oxidation of chlorinated dibenzofurans.     

Properties of a scalar curvature invariant depending on two planes

Based on Schouten’s interpretation of the Riemann–Christoffel curvature tensor R, a geometrical meaning for the tensor R·R is presented. It follows that the condition of semi-symmetry, i.e. R·R = 0, can be interpreted as the invariance of the sectional curvature of every plane after parallel transport around an infinitesimal parallelogram. Using the tensor R· R, and in analogy with the definition of the sectional curvature K(p,π) of a plane π, a scalar curvature invariant L(p,π, \({\overline{\pi}}\)) is constructed which in general depends on two planes π and \({\overline{\pi}}\) at the same point p. This invariant can be geometrically interpreted in terms of the parallelogramoïds of Levi–Civita and it is shown that it completely determines the tensor R· R. Further it is demonstrated that the isotropy of this new scalar curvature invariant L(p,π, \({\overline{\pi}}\)) with respect to both the planes π and \({\overline{\pi}}\) amounts to the Riemannian manifold to be pseudo-symmetric in the sense of Deszcz.