The aliasing‐phenomenon in visual terms

In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more.     

Certificates of infeasibility via nonsmooth optimization

An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by solving a linearly constrained nonsmooth optimization problem. Furthermore, the constructed certificate can be used to enlarge an exclusion box by solving a nonlinearly constrained nonsmooth optimization problem.     

Short Syntheses of some ‘Decalin‐1,8‐diones’ and their Derivatives: Breaking the Pretended Symmetry

A cheap synthesis of the so‐called ‘decalin‐1,8‐diones’ started with the conjugate (1,4‐) addition of cyclohex‐2‐en‐1‐one derivatives to the γ‐position of the dilithium derivative (buta‐1,3‐diene‐1,1‐bis(olate)) of crotonic acid. Hydrogenation of these ‘1,4‐γ’ adducts and final cyclization afforded the enol tautomers of decalin‐1,8‐diones. Nucleophilic substitutions at these 3‐oxoenols by NH₃ or primary amines created only monoamino products (namely, 3‐oxoenamines) whose reactions with OPCl₃ yielded dihydro(1,3,2)oxazaphosphinin‐2‐one derivatives. The two regioisomers of a trimethyl‐3‐oxoenamine served as models for the constitutional assignments of the two rapidly interconverting (hence, individually NMR‐invisible), tautomeric trimethyl‐3‐oxoenols. Such methyl substitutions served to break the ‘pretended’ symmetry of ‘decalin‐1,8‐dione’. Hydrazine and 3‐oxoenols furnished oxygen‐free indazole derivatives whose N?H bonds exchanged with t_1/2=ca. 0.00035 s at ca. ?58(9) °C.     

Stable Quinome Methides: Regioselective Para-Oxidation of a 2,4-Bisalkylthiomethenol and Addition Reaction Reaction to Quinonemethides

Abstract

The 2.4-bisfunctionalized phenol 1, a commercial antioxidant, is dehydrogenated regioselectively with potassium ferricyanide. affording the corresponding p-quinone methide 2. 1,6-Addition of nucleophiles e.g. thiols to 2 gives rise to the corresponding addition products e.g. the dithioacetals 4 of the corresponding substituted benzaldehyde. On the other hand, treatment of 2 with αα′-azoisobutyronitrile at 90°C leads to compounds 5a-b and 6, addition products of the cyanopropyl radical to the quinone methide 2. The structures of all products are confirmed mainly by ¹H-NMR-and ¹³C-NMR-spectroscopy and the mode of their formation is discussed.     

Phosphorus and Energy Recovery from Manure and Digestion Residues

Abstract

Human and animal excrements, in particular manure, stand for a significant and undisputable source of plant nutrients and renewable energy. In Europe, only 36% of P-inputs to soils originate from primary resources (rock phosphate) whereas 63% come from animal and human excretions applied to cropland as manure, digestion residues and sewage sludge. Simultaneously these waste flows represent a potential hazard to human health and aquatic bodies because of pathogens and eutrophication. Management of these waste flows is far from being sustainable, in part due to the lack of efficient processing technologies. A cooperative InnoEnergy—EIT financed KIC Knowledge and Innovation Community—research project pursues development and demonstration of highly efficient technologies to overcome the constraints and to yield renewable phosphate fertilizers and energy from waste flows that may have a combined technical energy potential of 3,600 PJ/year and an annual phosphate recovery potential of 4.5–5.5 million tonnes (as P₂O₅) in Europe.