On a Volume‐Constrained Variational Problem

. Existence of minimizers for a volume-constrained energy $ E(u) := \int_{\Omega} W(\nabla u)\, dx Existence of minimizers for a volume-constrained energy E(u) : = ò_W W(?u) dx E(u) := \int_{\Omega} W(\nabla u)\, dx where L^N({u = z_i}) = a_i, i = 1, ?, P, {\cal L}^N(\{u = z_i\}) = \alpha_i, i = 1, \ldots, P, is proved for the case in which z_iz_i are extremal points of a compact, convex set in \Bbb R^d\Bbb R^d and under suitable assumptions on a class of quasiconvex energy densities W. Optimality properties are studied in the scalar-valued problem where d=1d=1, P=2P=2, W(x)=|x|²W(\xi)=|\xi|^2, and the &-limit as the sum of the measures of the 2 phases tends to \L(W)\L(\Omega) is identified. Minimizers are fully characterized when N=1N=1, and candidates for solutions are studied for the circle and the square in the plane.     

Über ebene affine Inzidenzgruppen

For a translation plane P with respect to f we consider the group of collineations generated by all elations fixing f and a point F of f. All subgroups or are determined which operate regularly on the points of the affine plane P. Group-theoretic and operating properties of the groups are stated especially for the finite and the Desarguesian cases. In the latter case the companion NL-near modules are constructed. Finally we characterize the groups within PGL(3, K) with commutative field K of finite characteristic.     

Direct 23Na NMR observation of mixed cations residing inside a G-quadruplex channel

We report direct (23)Na NMR observation for the presence of mixed cations (Na(+)/K(+), Na(+)/Rb(+), Na(+)/Sr(2+)) inside the G-quadruplex channel formed by the self-association of guanosine 5'-monophosphate at pH 8.     

New 4-(benzotriazol-1-yl)-1,2,3-triazole derivatives

A new 4-(benzotriazol-1-yl)-1,2,3-triazole structure was obtained by the diazotization reaction of either of 1-(2-aminophenyl)-4-carboxamido-5-amino-1H-1,2,3-triazole ( 1c ) or of the corresponding Dimroth isomer 1d . It underwent some common reactions to evaluate its chemical behaviour and structure. An analogous reaction sequence was carried out from the 2-nitro-4-methylphenyl azide, to assign the structure to the nitro derivatives prepared. The structure of the new compounds prepared was confirmed by chemical and spectroscopic methods.     

New 1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidine derivatives II

The 7‐chloro‐3‐(2‐chlorobenzyl)‐ and 7‐chloro‐3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐d]pyrimidines ( 1 and 4 ), by nucleophilic replacement with some hydrazides, gave the corresponding 7‐hydrazidoderivatives ( 2a‐e and 5a‐e ). These, by heating in Dowtherm, underwent an intramolecular cyclization to form the new tricyclic 7‐substituted‐3‐(2‐chlorobenzyl)‐ and 3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidines ( 3a‐d and 6a‐d ). The 7‐hydrazino‐3‐(2‐chlorobenzyl)‐ and 7‐hydrazino‐3‐(2‐fluorobenzyl)‐triazolo‐pyrimidines ( 9a and 9b ) were also prepared via the corresponding mercapto ( 7a and 7b ) and thiomethyl ( 8a and 8b ) derivatives.     

Thermal analysis of glasses for proecological applications

Thermal behaviour and biochemical activity of potassium-silicate-phosphate glasses modified by addition of Ca, Mg, acting as ecological fertilisers of controlled release rate of the nutrients for plants were studied. It has been found that the biochemical activity of silicate-phosphate glasses depends on the nature and the number of components forming the glassy framework and is related to the thermal stability of glass demonstrated by the formation of new compounds during the process of crystallisation. It is proved that these seemingly different properties are determined by the same parameters which are the strengths bonds of glass network-formers and modifiers as well as their chemical affinity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Monitoring of di-(2-ethylhexyl)phthalate,nonylphenol, nonylphenol ethoxylates,and polychlorinated biphenyls in anaerobic and aerobic sewage sludge by gas chromatography–mass spectrometry

The occurrence of di-(2-ethyhexyl)phthalate (DEHP), nonylphenol and nonyphenol mono- and diethoxylates (NPEs) and seven polychlorinated biphenyl (PCB) congeners in different types of sludge samples is reported. The analysis of these compounds was carried out by sonication-assisted extraction and analytical determination by gas chromatography coupled with a mass spectrometry detector, following a previously described method. The applicability of the method was tested by monitoring the organic pollutants in primary, secondary, mixed, and digested-dehydrated sludge samples from two wastewater treatment plants (WWTPs) based on aerobic and on anaerobic biological stabilization. The occurrence of these compounds in sewage sludge and the influence of sludge stabilization process on the further farmland application of the sludge were evaluated. DEHP and NPEs were detected in all analysed sludge samples from both WWTPs at concentration levels in the range of 22.3–601?mg?kg^?1 and 136–2357?mg?kg^?1 dm (dry matter), respectively. PCBs were detected in all types of sludge analysed from the anaerobic WWTP but was not detected in any sludge sample from the aerobic WWTP. Concentration levels of the sum of the seven PCBs congeners were up to 1.5?mg?kg^?1 dm. The concentration of DEHP, sum of NPEs, and sum of the seven PCB congeners were higher than the limits fixed in the third draft of the future Sludge Directive for land application of sludge in the 67%, 100%, and 11% of samples from the anaerobic WWTP and in the 83%, 92%, and 0% of samples from the aerobic WWTP, respectively.     

Coordination Compounds of Palladium(II) and 4‐Amino‐1,2,4‐triazole

Mononuclear coordination compounds of the type [Pd(NH₂trz)₄]²⁺ with the counterions chloride, nitrate, trifluoromethanesulfonate, and methanesulfonate were synthesized and their structures identified with single‐crystal X‐ray diffraction. In case of the synthesis with methanesulfonate as the counterion the dominant product was of the generic formula [Pd₂(NH₂trz)₃](CH₃SO₃)₄, and the complex [Pd(NH₂trz)₄](CH₃SO₃)₂ only emerged as a byproduct. While the structure of the byproduct could be analyzed by single‐crystal X‐ray diffraction, suitable crystals of the main product [Pd₂(NH₂trz)₃](CH₃SO₃)₄ could not be obtained. However, stoichiometry implies a polynuclear nature with NH₂trz present in the rare μ₃‐η¹:η¹:η¹ coordination type, i.e. with NH₂trz molecules coordinating to three palladium atoms. Accordingly, identification of solids by single‐crystal analysis alone can be misleading in particular with NH₂trz as a ligand due to its versatile coordination behavior. Finally, analysis by differential scanning calorimetry (DSC) revealed that the complexes were thermally stable (the onset of decomposition well above 100 °C), with [Pd₂(NH₂trz)₃](CH₃SO₃)₄ being the most stable compound (onset of decomposition at 204 °C).     

Affinity capillary electrophoresis study of the linkage existing between proton and zinc ion binding to bacitracin A1

Measurements by capillary electrophoresis (CE) of bacitracin A(1) effective mobility at different pH values permitted to estimate the five acidic dissociation constants and the Stokes radii at different protonation stages of the macrocyclic dodecapeptide. The pK(a) values were 3.6 and 4.4 for the two carboxylic groups of the lateral chains of D-Asp-11 and D-Glu-4, respectively, 6.4 for the aza-atom of the imidazole ring of His-10, 7.6 for the amino group of N-terminal Ile-1 and 9.7 for the delta-amino group of D-Orn-7, very close to the values obtained by other researchers by titration experiments. In agreement with a rigid macrocyclic structure the Stokes radii of different protonated forms ranged only between 14.3 and 14.8 A. Best fitting procedures performed on experimental mobility measured at two different pH values (5.50 and 6.72) in the presence of increasing Zn(+2) concentration allowed confirming the model that assumes the binding of Zn(+2) to P(0) peptide form with a 1.5 x 10(3) M(-1) intrinsic association constant. Following to Zn(+2) binding, the pK(a) of the amino group of N-terminal Ile-1 is shifted from 7.6 to 5.9 and the Stokes radius is reduced of about 3 A. The mean charge of the bacitracin A(1)-Zn(+2) complex resulted +1.67 and +1.12 at pH 5.50 and 6.72, respectively. These results suggest that the amino group of N-terminal Ile-1 is not essential for Zn(+2) binding.