On rank and null space computation of the generalized Sylvester matrix

In this paper, we present new approaches computing the rank and the null space of the (m n + p)×(n + p) generalized Sylvester matrix of (m + 1) polynomials of maximal degrees n,p. We introduce an algorithm which handles directly a modification of the generalized Sylvester matrix, computing efficiently its rank and null space and replacing n by log ₂ n in the required complexity of the classical methods. We propose also a modification of the Gauss-Jordan factorization method applied to the appropriately modified Sylvester matrix of two polynomials for computing simultaneously its rank and null space. The methods can work numerically and symbolically as well and are compared in respect of their error analysis, complexity and efficiency. Applications where the computation of the null space of the generalized Sylvester matrix is required, are also given.     

Developing automated valuation models for estimating property values: a comparison of global and locally weighted approaches

Annals of Operations Research - Automated valuation models are widely used in real estate to provide estimates for property prices. Such models are typically developed through regression...     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

Kβ X-Ray Emission Spectroscopic Study of a Second-Row Transition Metal (Mo) and Its Application to Nitrogenase-Related Model Complexes

In recent years, X-ray emission spectroscopy (XES) in the Kβ (3p-1s) and valence-to-core (valence-1s) regions has been increasingly used to study metal active sites in (bio)inorganic chemistry and catalysis, providing information about the metal spin state, oxidation state and the identity of coordinated ligands. However, to date this technique has been limited almost exclusively to first-row transition metals. In this work, we present an extension of Kβ XES (in both the 4p-1s and valence-to-1s [or VtC] regions) to the second transition row by performing a detailed experimental and theoretical analysis of the molybdenum emission lines. It is demonstrated in this work that Kβ₂ lines are dominated by spin state effects, while VtC XES of a 4d transition metal provides access to metal oxidation state and ligand identity. An extension of Mo Kβ XES to nitrogenase-relevant model complexes shows that the method is sufficiently sensitive to act as a spectator probe for redox events that are localized at the Fe atoms. Mo VtC XES thus has promise for future applications to nitrogenase, as well as a range of other Mo-containing biological cofactors. Further, the clear assignment of the origins of Mo VtC XES features opens up the possibility of applying this method to a wide range of second-row transition metals, thus providing chemists with a site-specific tool for the elucidation of 4d transition metal electronic structure.     

Monitoring fuel quality: a case study for quinizarin marker content of unleaded petrol marketed in Greece

Fuel adulteration and cross-contamination lead to low-quality fuel products, which may cause increased environmental pollution, loss of taxes and engine problems. An establishment of a quality monitoring mechanism based on laboratory measurements may reveal problematic areas of the fuel supply chain. For the purposes of this work, 97 unleaded petrol samples were measured in order to quantify mass concentration of quinizarin, a substance used in Greece to easily mark the presence of 95 Research Octane Number unleaded petrol in other types of automotive fuels. The samples were obtained from petroleum retail stations selling different brands of fuels and located in different geographic regions of Greece. Statistical analysis of the results revealed quinizarin mass concentrations below the 3 mg L^?1 legislation specification limit and significant differences between brands and geographic regions, which may attributed to the structure of the fuel supply chain in Greece in combination with quinizarin properties and way of handling. Moreover, certain approaches were used for the calculation of decision limits for assessing compliance or non-compliance. These approaches take measurement reproducibility or estimated in-house uncertainty into account, in order to minimize the probability of false rejection.     

Thermally Activated Delayed Fluorescence in a Y3N@C80 Endohedral Fullerene: Time‐Resolved Luminescence and EPR Studies

The endohedral fullerene Y₃N@C₈₀ exhibits luminescence with reasonable quantum yield and extraordinary long lifetime. By variable‐temperature steady‐state and time‐resolved luminescence spectroscopy, it is demonstrated that above 60 K the Y₃N@C₈₀ exhibits thermally activated delayed fluorescence with maximum emission at 120 K and a negligible prompt fluorescence. Below 60 K, a phosphorescence with a lifetime of 192±1 ms is observed. Spin distribution and dynamics in the triplet excited state is investigated with X‐ and W‐band EPR and ENDOR spectroscopies and DFT computations. Finally, electroluminescence of the Y₃N@C₈₀/PFO film is demonstrated opening the possibility for red‐emitting fullerene‐based organic light‐emitting diodes (OLEDs).     

Estimation of the hyperbolic metric by using the punctured plane

Let denote the density of the hyperbolic metric for a domain Ω in the extended complex plane . We prove the inequality

1,2-Diphosphinobenzene as a synthon for the 1,2,3-triphospha- and 2-arsa-1,3-diphosphaindenyl anions and a stable organo derivative of the P8 unit of Hittorf's phosphorus

The electronic structure of the 1,2,3-triphosphaindenyl ligand suggests that it should exhibit enhanced pi-acceptor properties when compared to the eta(5)-indenyl system; this insight encouraged us to develop a simple synthetic pathway from 1,2-diphosphinobenzene to the 1,2,3-C(6)H(4)P(3) and 2-As-1,3-C(6)H(4)P(2) anions, both of which have been structurally characterised by X-ray crystallography; as a bonus from these studies we also obtained the first structurally characterised organo derivative of the P(8) unit present in Hittorf's phosphorus.     

Promotion of phosphaalkyne cyclooligomerisation by a Sb(v) to Sb(iii) redox process

A high yield of the tetraphosphaladderene, anti-tetraphosphatricyclo[4.2.0.0(2,5)]octa-3,7-diene, is obtained from reaction of the zirconocene 1,3-diphosphabicyclo[1.1.0]butane with Ph(2)SbCl(3) in THF or CH(2)Cl(2). Exploration of the reaction pathway using density functional theory suggests that an envelope-type adduct of Ph(2)SbCl and 1,3-diphosphabicyclo[1.1.0]butane plays a pivotal role in the reaction. The zwitterionic character of this intermediate species allows it to act simultaneously as both an ene and an eneophile, and a symmetry-allowed bimolecular reaction leads to the tetraphosphaladderene species via a spirocyclic intermediate.