On the growth of Betti numbers of locally symmetric spaces

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the Lück Approximation Theorem (Lück, 1994 [10]) which is much stronger than the linear upper bounds on Betti numbers given by Gromov in Ballmann et al. (1985) [3].The basic idea is to adapt the theory of local convergence, originally introduced for sequences of graphs of bounded degree by Benjamini and Schramm, to sequences of Riemannian manifolds. Using rigidity theory we are able to show that when the volume tends to infinity, the manifolds locally converge to the universal cover in a sufficiently strong manner that allows us to derive the convergence of the normalized Betti numbers.     

Electronic structure calculations and optical properties of a new organic-inorganic luminescent perovskite: (C9H19NH3)2PbI2Br2

(C₉H₁₉NH₃)₂PbI₂Br₂ compound is a new crystal belonging to the large hybrid organic-inorganic perovskites compounds family. Optical properties are investigated by optical absorption UV-visible and photoluminescence (PL) techniques. Bands to band absorption peak at 2.44 eV as well as an extremely strong yellow-green photoluminescence emission at 2.17 eV is observed at room temperature. First principle calculations based on the DFT and FLAPW methods combined with LDA approximation are performed as well. Density of state close to the gap is presented and discussed in terms of optical absorption and photoluminescence experimental results. The perfect agreement between experimental data and electronic structure calculations is highlighted.     

Towards a Sustainable Synthesis of Formate Salts: Combined Catalytic Methanol Dehydrogenation and Bicarbonate Hydrogenation

Formate salts are important chemicals widely used in everyday products. The current industrial‐scale manufacture of formates requires CO at high pressure and harsh reaction conditions. Herein, we describe a new process for these products without the utilization of hazardous gases and chemicals. By application of ruthenium pincer complexes, a simultaneous methanol dehydrogenation and bicarbonate hydrogenation reaction proceeds, which provides a green synthesis of formate salts with excellent TON (>18 000), TOF (>1300 h^?1), and yield (>90 %).     

Facile Debromination by Potassium-Graphite Intercalate

The dehalogenation of vic-dihalides can be performed with the easily accessible potassium-graphite intercalate C₈K. The reaction is a convenient one, the yields are good, and the workup us simple.     

On weighted Shapley values

Nonsymmetric Shapley values for coalitional form games with transferable utility are studied. The nonsymmetries are modeled through nonsymmetric weight systems defined on the players of the games. It is shown axiomatically that two families of solutions of this type are possible. These families are strongly related to each other through the duality relationship on games. While the first family lends itself to applications of nonsymmetric revenue sharing problems the second family is suitable for applications of cost allocation problems. The intersection of these two families consists essentially of the symmetric Shapley value. These families are also characterized by a probabilistic arrival time to the game approach. It is also demonstrated that lack of symmetries may arise naturally when players in a game represent nonequal size constituencies.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.     

Electrochemical behavior and analytical detection of Imidacloprid insecticide on a BDD electrode using square-wave voltammetric method

A sensitive square-wave voltammetric method for the determination of Imidacloprid(IMD) was developed using electrochemically pretreated boron-doped diamond(BDD) electrode. Aqueous solutions were prepared with Confidor 200 SL as the commercial formulation of IMD. Sodium sulfate(Na_2SO_4) was used as supporting electrolyte. The influence of operating parameters, such as the p H of the medium, frequency, pulse amplitude, scan increment and the concentration of IMD was investigated. An irreversible cathodic peak, corresponding to the reduction of IMD is observed at 1.21 V(vs. SCE) and the electrode reaction was controlled by adsorption. Under optimized conditions, the square-wave reduction peak current was linear over the concentration range of(30–200 μmol L~(-1)) with a detection and quantification limits of 8.60 μmol L~(-1))and 28.67 μmol L~(-1)), respectively. The results were compared with spectrophotometry and HPLC methods under some conditions and found to be in good agreement.To investigate applicability to real samples, the proposed method was applied to the determination of IMD in plum juice.