Space-time finite element methods stabilized using bubble function spaces

ABSTRACT

In this paper, a stabilized space-time finite element method for solving linear parabolic evolution problems is analyzed. The proposed method is developed on a base of a space-time variational setting, that helps on the simultaneous and unified discretization in space and in time by finite element techniques. Stabilization terms are constructed by means of classical bubble spaces. Stability of the discrete problem with respect to an associated mesh dependent norm is proved, and a priori discretization error estimates are presented. Numerical examples confirm the theoretical estimates.     

Synthesis and characterization of chiral poly(alkyl isocyanates) by coordination polymerization using a chiral half‐titanocene complex

A new chiral half‐titanocene complex, [CpTiCl₂(O‐(S)?2‐Bu)], is synthesized and characterized by ¹H and ¹³C NMR spectroscopy. This complex is employed for the coordination polymerization of n‐butyl and n‐hexyl‐ isocyanate leading to chiral polymers, as revealed by their CD spectra. Only the left‐handed helix is produced, due to the chiral (S)?2‐butoxy group, which is bound to the polymer chain end. The polymerization of 3‐(triethoxysilyl)propyl isocyanate produces less soluble polymers. On the other hand, phenyl isocyanate reacts slowly with the complex leading quantitatively and selectively to triphenyl isocyanurate. 2‐Ethylhexyl isocyanate is slowly and selectively cyclotrimerized in the presence of the half‐titanocene complex. However, a statistical copolymer of 2‐ethylhexyl isocyanate and hexyl isocyanate is produced. The reaction of benzyl isocyanate with the complex leads to a mixture of low molecular weight polymer and cyclotrimer. The polymers are characterized using SEC, NMR, and CD spectroscopy and their thermal properties are investigated by TGA/DSC analysis. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2141–2151     

Chitosan-Based Materials for the Removal of Nickel Ions from Aqueous Solutions

Russian Journal of Physical Chemistry A - Sorption of Ni(II) ions from liquid effluents utilizing chemically modified chitosan; (vanillin, polymer I) and (ortho-vanillin, polymer II) is studied...     

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.     

Prediction of 195Pt NMR chemical shifts of dissolution products of H2[Pt(OH)6] in nitric acid solutions by DFT methods: how important are the counter‐ion effects?

¹⁹⁵Pt NMR chemical shifts of octahedral Pt(IV) complexes with general formula [Pt(NO₃)_n(OH)_{6 ? n}]^2?, [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 1–6), and [Pt(NO₃)_{6 ? n ? m}(OH)_m(OH₂)_n]^{?2 + n ? m} formed by dissolution of platinic acid, H₂[Pt(OH)₆], in aqueous nitric acid solutions are calculated employing density functional theory methods. Particularly, the gauge‐including atomic orbitals (GIAO)‐PBE0/segmented all‐electron relativistically contracted–zeroth‐order regular approximation (SARC–ZORA)(Pt) ∪ 6–31G(d,p)(E)/Polarizable Continuum Model computational protocol performs the best. Excellent second‐order polynomial plots of δ_calcd(¹⁹⁵Pt) versus δ_exptl(¹⁹⁵Pt) chemical shifts and δ_calcd(¹⁹⁵Pt) versus the natural atomic charge Q_Pt are obtained. Despite of neglecting relativistic and spin orbit effects the good agreement of the calculated δ ¹⁹⁵Pt chemical shifts with experimental values is probably because of the fact that the contribution of relativistic and spin orbit effects to computed σ^{iso 195}Pt magnetic shielding of Pt(IV) coordination compounds is effectively cancelled in the computed δ ¹⁹⁵Pt chemical shifts, because the relativistic corrections are expected to be similar in the complexes and the proper reference standard used. To probe the counter‐ion effects on the ¹⁹⁵Pt NMR chemical shifts of the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? and cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 0–3) complexes we calculated the ¹⁹⁵Pt NMR chemical shifts of the neutral (PyH)₂[Pt(NO₃)_n(OH)_{6 ? n}] (n = 1–6; PyH = pyridinium cation, C₅H₅NH⁺) and [Pt(NO₃)_n(H₂O)_{6 ? n}](NO₃)_{4 ? n} (n = 0–3) complexes. Counter‐anion effects are very important for the accurate prediction of the ¹⁹⁵Pt NMR chemical shifts of the cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} complexes, while counter‐cation effects are less important for the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? complexes. The simple computational protocol is easily implemented even by synthetic chemists in platinum coordination chemistry that dispose limited software availability, or locally existing routines and knowhow. Copyright © 2016 John Wiley & Sons, Ltd.     

DFT-calculated structures based on 1H NMR chemical shifts in solution vs. structures solved by single-crystal X-ray and crystalline-sponge methods: Assessing specific sources of discrepancies

DFT calculations of ¹H NMR chemical shifts, using various functionals and basis sets, the conductor-like polarizable continuum model and discrete solute-solvent hydrogen bond interactions have been used to derive the solution structures of methyl salicylate and methyl 2,5-dihydroxybenzoate. We demonstrate that very good agreement between experimental and computed ¹H NMR chemical shifts can be obtained for various basis sets. The DFT structures in solution were compared with the recently reported X-ray structure, solved by the crystalline-sponge method, of the methyl salicylate and the single-crystal X-ray structure of methyl 2,5-dihydroxybenzoate. It is demonstrated that the information provided by ¹H NMR chemical shifts about the solution structure is significantly more precise than that obtained by the single-crystal X-ray and the crystalline-sponge methods.     

Asymptotic Recurrence and Waiting Times for Stationary Processes

Let be a discrete-valued stationary ergodic process distributed according to P and let x=(..., x _–1, x ₀, x ₁,...) denote a realization from X. We investigate the asymptotic behavior of the recurrence time R _n defined as the first time that the initial n-block reappears in the past of x. We identify an associated random walk, on the same probability space as X, and we prove a strong approximation theorem between log R _n and . From this we deduce an almost sure invariance principle for log R _n. As a byproduct of our analysis we get unified proofs for several recent results that were previously established using methods from ergodic theory, the theory of Poisson approximation and the analysis of random trees. Similar results are proved for the waiting time W _n defined as the first time until the initial n-block from one realization first appears in an independent realization generated by the same (or by a different) process.     

Development and validation of an HPLC method for the determination of benzodiazepines and tricyclic antidepressants in biological fluids after sequential SPE

A novel method for the simultaneous determination of six benzodiazepines (BZDs) and four tricyclic antidepressants (TCAs) in biological fluids by HPLC with UV detection at 240 nm has been developed. After a deproteinization step biological fluids were analyzed by direct injection. SPE on Nexus cartridges was also applied. Since two compounds, namely imipramine and diazepam, were coeluting, a sequential SPE protocol has been developed. BZDs were eluted by a mixture of methanol/ACN(1:1), followed by the elution of TCAs with methanol. Separation was performed on a Kromasil C8 column (250 x 64 mm(2) id, 5 microm) using a mobile phase of 0.05 MCH3COONH4/ACN/methanol (initial composition 55:15:30 v/v/v) at a flow rate of 1.0 mL/min delivered by a gradient program within 15 min. Colchicine was used as the internal standard (4 ng/microL). The method was linear for all analytes up to 20 ng/lL, with coefficients of regression between 0.996 and 0.99996. LODs and LOQs were 0.08-1.17 and 0.28-3.91 ng/lL, respectively. Recovery was in the range of 92.8-108.7% for within-day and 91.9-109.9% for between-day assays, with RSD values lower than 10.0% for all matrices.     

Synthesis of conformationally constrained adamantane imidazolines with trypanocidal activity

Aiming at the development of new adamantano building blocks for treating African trypanosomiasis, we report on the synthesis of spiro adamantane 2‐imidazolines 8a‐f and 9a‐c , and their congeneric 5‐(1‐adamantyl)imidazolines 14 and 15 . The potency of these compounds against Trypanosoma brucei was compared to that of rimantadine and found, in the case of compound 14e , to be three fold higher. Together with the other active compounds, 14b and 15b , which were equipotent to rimantadine, the new molecules illustrate the synergistic effect of the lipophilic character of adamantane and the C1 amidine functionality on trypanocidal activity.