Two 1-substituted 4-nitro­imidazoles

Crystalline 4-nitro-1-phenyl­imidazole, C₉H₇N₃O₂, (I), and 4′-­nitro-1-phenyl-4,1′-bii­imidazole, C₁₂H₉N₅O₂, (II), contain C—H⃛O and C—H⃛N hydrogen bonds, connecting the mol­ecules into infinite chains. The aromatic fragments in both compounds are nearly planar. The dihedral angles between the benzene and imidazole rings are 26.78 (5)° in (I) and 29.36 (8)° in (II).     

Two-Sided Optimal Bounds for Green Functions of Half-Spaces for Relativistic <Emphasis Type="Italic">α</Emphasis>-Stable Process

The purpose of this paper is to find optimal estimates for the Green function of a half-space of the relativistic α -stable process with parameter m on ℝ ^d space. This process has an infinitesimal generator of the form mI–(m ^2/α I–Δ) ^α/2, where 0<α<2, m>0, and reduces to the isotropic α-stable process for m=0. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and we provide two-sided sharp estimates for the Green function for a half-space. As a byproduct we obtain some improvements of the estimates known for bounded sets. Our approach combines the recent results obtained in Byczkowski et al. (Bessel Potentials, Hitting Distributions and Green Functions (2006) (preprint). ), where an explicit integral formula for the m-resolvent of a half-space was found, with estimates of the transition densities for the killed process on exiting a half-space. The main result states that the Green function is comparable with the Green function for the Brownian motion if the points are away from the boundary of a half-space and their distance is greater than one. On the other hand for the remaining points the Green function is somehow related the Green function for the isotropic α-stable process. For example, for d≥3, it is comparable with the Green function for the isotropic α-stable process, provided that the points are close enough. Research supported by KBN Grants.     

Insight into the mechanism of three component condensation leading to aminomethylenebisphosphonates

Three-component reaction of a primary amine, diethyl phosphite and triethyl orthoformate followed by acid hydrolysis of the adduct provides N-substituted aminomethylenebisphosphonic acids in good yields. Being extremely versatile, it is commonly utilized for preparation of compounds possessing potential antiosteoporotic, antibacterial, anticancer, antiparasitic or herbicidal activity. However, the mechanism of the reaction remains unknown. p-Nitroaniline has been found an interesting tool to shed light on this matter. Its use allowed to separate and identify four intermediates, both non-phosphorus and phosphorus containing, and subsequently suggest the mechanism of the whole process. The acquired knowledge was helpful in explanation the route and the final product structure obtained for more complex reaction proceeding with the use of 4-aminopyridine. Additional alkylation of the pyridine nitrogen atom, leading to unexpected N-(1-alkylpyridinium-4-amino)methylenebisphosphonic acids was unambiguously proved.     

The LIL for <Emphasis Type="Italic">U</Emphasis>-Statistics in Hilbert Spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest. R. Adamczak’s research partially supported by MEiN Grant 2 PO3A 019 30. R. Latała’s research partially supported by MEiN Grant 1 PO3A 012 29.     

A 2-approximation algorithm for interval data minmax regret sequencing problems with the total flow time criterion

In this paper we discuss a minmax regret version of the single-machine scheduling problem with the total flow time criterion. Uncertain processing times are modeled by closed intervals. We show that if the deterministic problem is polynomially solvable, then its minmax regret version is approximable within 2.     

Novel Approach to Two-Component Analysis Based on the Generalized Calibration Strategy

The generalized calibration strategy (GCS), developed and previously applied to chemical analysis, has been adapted to two-component (2C) analysis. According to the 2C-GCS procedure, a set of 10 calibration solutions containing a sample and standards of two analytes in well-defined composition was diluted. The measurements performed at a given dilution stage allow the concentration of both analytes in a sample to be evaluated with six apparent concentrations calculated with various mathematical approaches. As a result, the method allows the detection, examination, and elimination of nonlinear and interference effects with multiplicative and additive characteristics. To perform 2C-GCS automatically and effectively, a dedicated flow sequential injection system was designed to be fully controlled by a computer. Caffeine and paracetamol were determined in synthetic and pharmaceutical samples using this calibration approach. The analytes were determined with good precision and accuracy with low consumption of sample and standard solutions. On the basis of this experimental model, the influence of effects and tendencies in the examined analytical system was detected and evaluated.     

Analytical Strategy for the Determination of Selenium in Biological Materials by Inductively Coupled Plasma-Mass Spectrometry with a Dynamic Reaction Cell

Selenium was determined in serum, hair, and tobacco by inductively coupled plasma-mass spectrometry using ⁷⁷Se, ⁷⁸Se, and ⁸²Se. The set of standards method (SSM) and the standard addition method (SAM) were applied to calibration with and without the use of internal standards (⁷²Ge and ¹⁰³Rh). In addition, the usefulness of the dynamic reaction cell (DRC) with methane as the reaction gas was characterized. The results obtained in different conditions were evaluated in terms of precision and accuracy. It was demonstrated theoretically and experimentally that an internal standard is a potential source of systematic errors as it can be influenced multiplicatively and additively by its own interferents (independently of selenium). Furthermore, it was shown that—against common opinion—an internal standard can fail in elimination of chemical interference effects influencing selenium and in increasing of precision of selenium determinations. The DRC was shown to be effective in the elimination of additive effects, although the results obtained by both SSM and SAM with DRC were systematically positively erroneous. Finally, selenium was determined accurately in each examined sample when SAM was applied to calibration, and signals were measured either for ⁸²Se without the use of the DRC, or for ⁷⁷Se or ⁷⁸Se with the use of the DRC. In addition, it has also been shown that samples should be diluted prior to analysis to the greatest acceptable extent.     

Solid state NMR spectroscopy as a precise tool for assigning the tautomeric form and proton position in the intramolecular bridges of o-hydroxy Schiff bases

Two analogous Schiff bases, (S,E)-2-((1-hydroxy-3-methyl-1,1-diphenylbutan-2-ylimino)methyl)phenol (1) and (S,Z)-2-hydroxy-6-((1-hydroxy-3-methyl-1,1-diphenylbutan-2-ylamino)methylene)cyclohexa-2,4-dienone (2), exist in the solid state as phenol-imine and keto-amine tautomers, respectively. Their crystal structures were solved using the X-ray diffraction method. Sample 1 forms orthorhombic crystals of space group P2(1)2(1)2(1), while 2 forms monoclinic crystals of space group P2(1). In each sample, one molecule is in the asymmetric unit of the crystal structure. One-dimensional and two-dimensional solid state NMR techniques were used for structure assignment and for inspection of the (13)C and (15)N δ(ii) of the chemical shift tensor (CST) values. NMR study indicates that the span (Ω = δ(11)-δ(33)) and the skew (κ = 3(δ(22)-δ(iso)/Ω) are extremely sensitive to change in the tautomeric form of the Schiff bases. Theoretical calculations of NMR shielding parameters for 1 and 2 and a model compound with reduced aliphatic residue were performed using the GIAO method with B3LYP functional and 6-311++g(d,p) basis sets. From comparative analysis of the experimental and theoretical parameters, it was concluded that the position of hydrogen in the intramolecular bridge has tremendous influence on (13)C and (15)N CST parameters. Inspection of Ω and κ parameters allowed for the establishment of the nature of the hydrogen bonding and the assignment of the equilibrium proton position in the intramolecular bridges in the solid state.     

All nonclassical correlations can be activated into distillable entanglement

We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.