Primes in quadratic progressions on average

In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.     

Finite temperature QCD coupling constant —imaginary versus real time framework

The correspondence between the imaginary time and real time thermal running coupling constant is discussed. The temperature dependence is derived in pure QCD at one-loop order in a generalized momentum subtraction (MOM) renormalization scheme.     

Neue Oxozincate mit Inselstruktur: K4[ZnO3] Mit einem Anhang über Rb7Na[ZnO3]2

New Nesozincates: K₄[ZnO₃], Rb₇Na[ZnO₃]₂ For the first time A) K₄[ZnO₃] and B) Rb₇Na[ZnO₃]₂ have been prepared (from the binary oxides). They represent the first oxozincates of the alkali metals in which the coordination number of Zn²⁺ is exclusively 3 (carbonate-like groups [ZnO₃]). Both oxides crystallize triclinic, space group P1 with A): a = 1103.3(3), b = 881.3(3), c = 698.2(2) pm, α = 109.65(2)°, β = 89.56(2)°, γ = 102.41(3)° and Z = 4, and B): a = 1128.3(3), b = 974.5(3), c = 711,8(2) pm, α = 114.12(2)β, = = 88.46(3)°,γ = 106.48(2)° and Z = 4. Their crystal structures have been determined from single crystal data (four circle diffractometer) and refined to R = 10.1%, R_w = 7.8% (2905 unique I₀(hkl)) and R = 19.5%, R_w = 17.3% (2269 unique I₀(hkl)), respectively. The Madelung Part of Lattice Energy (MAPLE), Effective Coordination Numbers (ECoN) and Mean Fictive Ionic Radii (MEFIR) have been calculated.     

Die Deprotonierung von Metallaquoionen II: Aquochrom(III)-ion. Zur Struktur aktiver Chromhydroxide

On alkalinization of solutions of the chromiun(III)-aquo ion simple deprotonation takes place first. The degree of hydroxylation n _OH however can be brought up to only about 1 (the exact value depending on the total concentration [Cr]_t), before the uncharged complex Cr(OH)₃(OH₂)₃ is precipitated. The structure of the very sparingly soluble complex (solubility ～10^?7M ) is held together by hydrogen bonds of type I between the molecules, so that its formula may be written as Cr(OH)₂H_6/2-lattice. The formation of the well ordered structure is extremely fast. On aging, the metallic centers become connected by μ-hydroxo-bridges (type II) and the substances become amorphous and very insoluble. The dinuclear (H₂O)₄Cr(OH)₂Cr(OH₂)₄⁴⁺ behaves similar on deprotonation. Concerning the various equilibria constants see Table 1.     

A multitechnique surface analytical study of a segmented block copolymer poly(ether-urethane) modified through an H2O radio frequency glow discharge

Recent work in our laboratories has fully characterized the surface region of a segmented poly(ether-urethane) (PEU) extending from the air/polymer interfacial region through bulk depths in the micron range. This characterization utilized energy and angle dependent Electron Spectroscopy for Chemical Analysis (ESCA), Attenuated Total Reflectance–Fourier Transform Infrared Spectroscopy (ATR–FTIR), and Comprehensive Wettability Profiling (contact angle using a homologous series of liquids) as defined by Zisman. In this study this same multi-analytical-technique approach is used to elucidate changes in these PEU surfaces induced through an H₂O Radio Frequency Glow Discharge (RFGD) plasma. This investigation reports both qualitative and quantitative changes due to the modification treatments as well as the permanency of the changes effected on these surfaces through the plasma treatment. From our analyses, the amount of surface residing polyurethane (hard segment) is observed to increase due to a proposed plasma etching mechanism. Further, the addition of oxygen containing functionality is detected at the modified surfaces unique with respect to the unmodified PEU. These surface modifications which show large increases in wettability, are finally observed to be semi-permanent over a time period of 6 months.     

Time-resolved investigations of singlet oxygen luminescence in water, in phosphatidylcholine, and in aqueous suspensions of phosphatidylcholine or HT29 cells

Singlet oxygen was generated by energy transfer from the photoexcited sensitizer, Photofrin or 9-acetoxy-2,7,12,17-tetrakis-(beta-methoxyethyl)-porphycene (ATMPn), to molecular oxygen. Singlet oxygen was detected time-resolved by its luminescence at 1270 nm in an environment of increasing complexity, water (H2O), pure phosphatidylcholine, phosphatidylcholine in water (lipid suspensions), and aqueous suspensions of living cells. In the case of the lipid suspensions, the sensitizers accumulated in the lipids, whereas the localizations in the cells are the membranes containing phosphatidylcholine. By use of Photofrin, the measured luminescence decay times of singlet oxygen were 3.5 +/- 0.5 micros in water, 14 +/- 2 micros in lipid, 9 +/- 2 micros in aqueous suspensions of lipid droplets, and 10 +/- 3 micros in aqueous suspensions of human colonic cancer cells (HT29). The decay time in cell suspensions was much longer than in water and was comparable to the value in suspensions of phosphatidylcholine. That luminescence signal might be attributed to singlet oxygen decaying in the lipid areas of cellular membranes. The measured luminescence decay times of singlet oxygen excited by ATMPn in pure lipid and lipid suspensions were the same within the experimental error as for Photofrin. In contrast to experiments with Photofrin, the decay time in aqueous suspension of HT29 cells was 6 +/- 2 micros when using ATMPn.     

On a new method for constructing good point sets on spheres

We use quadrature formulas with equal weights in order to constructN point sets on spheres ind-space (d 3) which are almost optimal with respect to a discrepancy concept, based on distance functions (potentials) and distance functionals (energies). By combining this approach with the probabilistic method, we obtain almost best possible approximations of balls by zonotopes, generated byN segments of equal length.Editors' note: We learned with sadness of Gerold Wagner's untimely death as a result of an avalanche in the Alps shortly after the submission of this paper. When one of the referees, Joram Lindenstrauss, suggested that Wagner's results might be extended to dimensions >6, we invited Professor Lindenstrauss to submit a paper containing that extension which we would publish alongside the Wagner paper. The result is the paper by Bourgain and Lindenstrauss that follows the present one.