Melting of cubic boron nitride at extreme pressures

Due to its large pressure range of stability and inert nature, cubic boron nitride has been proposed as a potential pressure standard for high pressure experiments. It is extremely refractive upon compression, although its melting temperature is not known beyond 10 GPa. We apply first-principles molecular dynamics to evaluate the thermodynamics of zincblende structured (cubic) and liquid boron nitride at extreme temperatures and pressures, and compute the melting curve up to 1 TPa by integration of the Clapeyron equation. The resulting equations of state reveal that liquid boron nitride becomes denser than the solid phase at pressures of around 0.5 TPa. This is expressed as a turnover in the melting curve, which reaches a maximum at 510 GPa and 6550 ± 700 K. The origin of this density crossover is explained in terms of the underlying liquid structure, which diverges from that of the zincblende structured solid as the phases are compressed.     

The identification problem for complex-valued Ornstein–Uhlenbeck operators in $$L^p(\mathbb {R}^d,\mathbb {C}^N)$$

In this paper we study perturbed Ornstein–Uhlenbeck operators

$$\begin{aligned} \left[ \mathcal {L}_{\infty } v\right] (x)=A\triangle v(x) + \left\langle Sx,\nabla v(x)\right\rangle -B v(x),\,x\in \mathbb {R}^d,\,d\geqslant 2, \end{aligned}$$

for simultaneously diagonalizable matrices \(A,B\in \mathbb {C}^{N,N}\). The unbounded drift term is defined by a skew-symmetric matrix \(S\in \mathbb {R}^{d,d}\). Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. We prove under certain conditions that the maximal domain \(\mathcal {D}(A_p)\) of the generator \(A_p\) belonging to the Ornstein–Uhlenbeck semigroup coincides with the domain of \(\mathcal {L}_{\infty }\) in \(L^p(\mathbb {R}^d,\mathbb {C}^N)\) given by

$$\begin{aligned} \mathcal {D}^p_{\mathrm {loc}}(\mathcal {L}_0)=\left\{ v\in W^{2,p}_{\mathrm {loc}}\cap L^p\mid A\triangle v + \left\langle S\cdot ,\nabla v\right\rangle \in L^p\right\} ,\,1<p<\infty . \end{aligned}$$

One key assumption is a new \(L^p\)-dissipativity condition

$$\begin{aligned} |z|^2\mathrm {Re}\,\left\langle w,Aw\right\rangle + (p-2)\mathrm {Re}\,\left\langle w,z\right\rangle \mathrm {Re}\,\left\langle z,Aw\right\rangle \geqslant \gamma _A |z|^2|w|^2\;\forall \,z,w\in \mathbb {C}^N \end{aligned}$$

for some \(\gamma _A>0\). The proof utilizes the following ingredients. First we show the closedness of \(\mathcal {L}_{\infty }\) in \(L^p\) and derive \(L^p\)-resolvent estimates for \(\mathcal {L}_{\infty }\). Then we prove that the Schwartz space is a core of \(A_p\) and apply an \(L^p\)-solvability result of the resolvent equation for \(A_p\). In addition, we derive \(W^{1,p}\)-resolvent estimates. Our results may be considered as extensions of earlier works by Metafune, Pallara and Vespri to the vector-valued complex case.

     

Mittag–Leffler Functions and the Truncated $${\mathcal {}}$$-fractional Derivative

In this paper, we introduce a new type of fractional derivative, which we called truncated \({\mathcal {V}}\)-fractional derivative, for \(\alpha \)-differentiable functions, by means of the six-parameter truncated Mittag–Leffler function. One remarkable characteristic of this new derivative is that it generalizes several different fractional derivatives, recently introduced: conformable fractional derivative, alternative fractional derivative, truncated alternative fractional derivative, M-fractional derivative and truncated M-fractional derivative. This new truncated \({\mathcal {V}}\)-fractional derivative satisfies several important properties of the classical derivatives of integer order calculus: linearity, product rule, quotient rule, function composition and the chain rule. Also, as in the case of the Caputo derivative, the derivative of a constant is zero. Since the six parameters Mittag–Leffler function is a generalization of Mittag–Leffler functions of one, two, three, four and five parameters, we were able to extend some of the classical results of the integer-order calculus, namely: Rolle’s theorem, the mean value theorem and its extension. In addition, we present a theorem on the law of exponents for derivatives and as an application we calculate the truncated \({\mathcal {V}}\)-fractional derivative of the two-parameter Mittag–Leffler function. Finally, we present the \({\mathcal {V}}\)-fractional integral from which, as a natural consequence, new results appear as applications. Specifically, we generalize the inverse property, the fundamental theorem of calculus, a theorem associated with classical integration by parts, and the mean value theorem for integrals. We also calculate the \({\mathcal {V}}\)-fractional integral of the two-parameter Mittag–Leffler function. Further, we were able to establish the relation between the truncated \({\mathcal {V}}\)-fractional derivative and the truncated \({\mathcal {V}}\)-fractional integral and the fractional derivative and fractional integral in the Riemann–Liouville sense when the order parameter \(\alpha \) lies between 0 and 1 (\(0<\alpha <1\)).     

A new lot sizing and scheduling heuristic for multi-site biopharmaceutical production

Biopharmaceutical manufacturing requires high investments and long-term production planning. For large biopharmaceutical companies, planning typically involves multiple products and several production facilities. Production is usually done in batches with a substantial set-up cost and time for switching between products. The goal is to satisfy demand while minimising manufacturing, set-up and inventory costs. The resulting production planning problem is thus a variant of the capacitated lot-sizing and scheduling problem, and a complex combinatorial optimisation problem. Inspired by genetic algorithm approaches to job shop scheduling, this paper proposes a tailored construction heuristic that schedules demands of multiple products sequentially across several facilities to build a multi-year production plan (solution). The sequence in which the construction heuristic schedules the different demands is optimised by a genetic algorithm. We demonstrate the effectiveness of the approach on a biopharmaceutical lot sizing problem and compare it with a mathematical programming model from the literature. We show that the genetic algorithm can outperform the mathematical programming model for certain scenarios because the discretisation of time in mathematical programming artificially restricts the solution space.     

High resolution end group determination of low molecular weight polymers by matrix-assisted laser desorption ionization on an external ion source fourier transform ion cyclotron resonance mass spectrometer

Matrix-assisted laser desorption ionization was performed on an external ion source Fourier transform ion cyclotron resonance mass spectrometer equipped with a 7-T superconducting magnet to analyze end groups of synthetic polymers in the mass range from 500 to 5000 u. Native, perdeutero methylated, propylated, and acetylated polyethylene glycol and polyvinyl pyrrolidone with unknown end-group elemental composition were investigated in the mass range up to 5000 u by using a 2,5-dihydroxybenzoic acid matrix. A small electrospray setup was used for the deposition of the samples. Two methods to process data were evaluated for the determination of end groups from the measured masses of the component molecules in the molecular weight ranges: a regression method and an averaging method. The averaging method is demonstrated to allow end-group mass determinations with an accuracy within 3 mu for the molecular weight range from 500 to 1400 and within 20 mu for the molecular weight range from 3400 to 5000. This is sufficient to identify the elemental composition of end groups in unknown polymer samples.     

Semi-permeable surface analytical reversed-phase column for the improved trace analysis of acidic pesticides in water with coupled-column reversed-phase liquid chromatography with UV detection. Determination of bromoxynil and bentazone in surface water.

The coupled-column (LC-LC) configuration consisting of a 3 microm C18 column (50 x 4.6 mm I.D.) as the first column and a 5 microm C18 semi-permeable-surface (SPS) column (150 x 4.6 mm I.D.) as the second column appeared to be successful for the screening of acidic pesticides in surface water samples. In comparison to LC-LC employing two C18 columns, the combination of C18/SPS-C18 significantly decreased the baseline deviation caused by the hump of the co-extracted humic substances when using UV detection (217 nm). The developed LC-LC procedure allowed the simultaneous determination of the target analytes bentazone and bromoxynil in uncleaned extracts of surface water samples to a level of 0.05 microg/l in less than 15 min. In combination with a simple solid-phase extraction step (200 ml of water on a 500 mg C18-bonded silica) the analytical procedure provides a high sample throughput. During a period of about five months more than 200 ditch-water samples originating from agricultural locations were analyzed with the developed procedure. Validation of the method was performed by randomly analyzing recoveries of water samples spiked at levels of 0.1 microg/l (n=10), 0.5 microg/l (n=7) and 2.5 microg/l (n=4). Weighted regression of the recovery data showed that the method provides overall recoveries of 95 and 100% for bentazone and bromoxynil, respectively, with corresponding intra-laboratory reproducibilities of 10 and 11%, respectively. Confirmation of the analytes in part of the samples extracts was carried out with GC-negative ion chemical ionization MS involving a derivatization step with bis(trifluoromethyl)benzyl bromide. No false negatives or positives were observed.     

Mechanically Interlocked Single‐Wall Carbon Nanotubes

Extensive research has been devoted to the chemical manipulation of carbon nanotubes. The attachment of molecular fragments through covalent‐bond formation produces kinetically stable products, but implies the saturation of some of the C? C double bonds of the nanotubes. Supramolecular modification maintains the structure of the SWNTs but yields labile species. Herein, we present a strategy for the synthesis of mechanically interlocked derivatives of SWNTs (MINTs). In the key rotaxane‐forming step, we employed macrocycle precursors equipped with two π‐extended tetrathiafulvalene SWNT recognition units and terminated with bisalkenes that were closed around the nanotubes through ring‐closing metathesis (RCM). The mechanically interlocked nature of the derivatives was probed by analytical, spectroscopic, and microscopic techniques, as well as by appropriate control experiments. Individual macrocycles were observed by HR STEM to circumscribe the nanotubes.     

Recent advances in capillary electrophoretic migration techniques for pharmaceutical analysis (2013–2015)

This review updates and follows‐up a previous review by highlighting recent advancements regarding capillary electromigration methodologies and applications in pharmaceutical analysis. General approaches such as quality by design as well as sample injection methods and detection sensitivity are discussed. The separation and analysis of drug‐related substances, chiral CE, and chiral CE‐MS in addition to the determination of physicochemical constants are addressed. The advantages of applying affinity capillary electrophoresis in studying receptor–ligand interactions are highlighted. Finally, current aspects related to the analysis of biopharmaceuticals are reviewed. The present review covers the literature between January 2013 and December 2015.     

Gas chromatographic analysis of trace impurities in chlorine trifluoride

The gas chromatographic determination of trace gaseous impurities in highly reactive fluorinated gaseous matrices presents unique requirements to both equipment and techniques. Especially problematic are the gases normally present in ambient air namely oxygen and nitrogen. Analysing these gases at the low microl/l (ppm) level requires special equipment and this publication describes a custom-designed system utilising backflush column switching to protect the columns and detectors. A thermal conductivity detector with nickel filaments was used to determine ppm levels of impurities in ClF3.     

Mössbauer Investigation of Characteristic Distribution of Iron Oxides in Sediments from the Antarctica

Sediments from the Admiralty Bay, King George Island, Antarctica, were investigated by ⁵⁷Fe Mössbauer spectroscopy, X-ray diffractometry, and radiometry. Quartz, feldspar, chlorite, calcite, dolomite, mica, kaolinite, hematite and magnetite were identified as constituent minerals in the sediment samples. The phase composition and the iron distribution among the crystallographic sites of iron-bearing minerals (silicates, magnetite and hematite) of samples from different location have been derived from the complex Mössbauer spectra. At different locations sediments had significant characteristic differences in the mineral composition, in the iron distribution among the crystallographic site of silicates, and in the specific radioactivity of Cs radionuclides. These results indicate differences in the rock formation and alteration by the sediments in this maritime part of Antarctica. There is a much higher amount of iron oxides in the sediments from south part of the geological fault across the Admiralty Bay than in the north part. This can be associated with much more alteration in the rocks in the south part compared to the northern one. This finding can contribute to the question of the history of the formation and alteration of volcanic rocks in the border of Antarctica.