Arithmetic Groups,Base Change,and Representation Growth

Consider an arithmetic group \({\mathbf{G}(O_S)}\), where \({\mathbf{G}}\) is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of S-integers O _S of a number field K with respect to a finite set of places S. For each \({n \in \mathbb{N}}\), let \({R_n(\mathbf{G}(O_S))}\) denote the number of irreducible complex representations of \({\mathbf{G}(O_S)}\) of dimension at most n. The degree of representation growth \({\alpha(\mathbf{G}(O_S)) = \lim_{n \rightarrow\infty}\log R_n(\mathbf{G}(O_S)) / \log n}\) is finite if and only if \({\mathbf{G}(O_S)}\) has the weak Congruence Subgroup Property. We establish that for every \({\mathbf{G}(O_S)}\) with the weak Congruence Subgroup Property the invariant \({\alpha(\mathbf{G}(O_S))}\) is already determined by the absolute root system of \({\mathbf{G}}\). To show this we demonstrate that the abscissae of convergence of the representation zeta functions of such groups are invariant under base extensions \({K{\subset}L}\). We deduce from our result a variant of a conjecture of Larsen and Lubotzky regarding the representation growth of irreducible lattices in higher rank semi-simple groups. In particular, this reduces Larsen and Lubotzky’s conjecture to Serre’s conjecture on the weak Congruence Subgroup Property, which it refines.     

Compression of CdCu3Ti4O12 perovskite to 55 GPa

Synchrotron x-ray diffraction measurements of CdCu₃Ti₄O₁₂ (CDCTO) were performed up to 55.5 GPa. There is no structural phase transformation in this pressure range. The irregular curvature shifts of the P-V curve are attributed to the grain surface effect. Analysis indicates that the grain surface of CDCTO is stiffer than the grain interior at higher pressures. We point out that the atoms on grain surfaces must be either densely packed or have a strong correlation with the gain interior in order to have a high dielectric constant, as in CaCu₃Ti₄O₁₂. The derived bulk modulus of CDCTO is approximately 235±7 GPa with K^′=5.1±0.4.     

Development of a cloud point extraction and preconcentration method for determination of trace aluminum in mineral waters by FAAS

A cloud point extraction (CPE) method has been developed for the preconcentration of trace aluminum prior to its determination by flame atomic absorption spectrometry (FAAS). The CPE method is based on the complex of Al(III) with Xylidyl Blue (XB) and then entrapped in non-ionic surfactant Triton X-114. The main factors affecting CPE efficiency, such as pH of sample solution, concentration of XB and Triton X-114, equilibration temperature and time, were investigated in detail. An enrichment factor of 50 was obtained for the preconcentration of Al(III) with 50 mL solution. Under the optimal conditions, the detection limit of this method for Al(III) is 1.43 μg L^− 1, and the relative standard deviation is 2.7% at determination of 100 μg L^− 1 Al(III). The proposed method has been applied for determination of trace amount of aluminum in mineral water samples with satisfactory results. Also, the proposed method was applied to the certified reference materials. The results obtained were in good agreement with certified values.     

Soil radon monitoring and anomalies in East Anatolian Fault System (Turkey)

On-line monitoring of soil radon (²²²Rn) concentration system was constructed on one of the main active fault zone of East Anatolian Fault System (EAFS) in Turkey. The preliminary results, observed during the second part of 2004 and first part of 2005 is presented. During the monitoring of soil radon concentration, numerous anomalies that equal or twice standard deviation were observed. In addition, the variation of the radon concentration was examined between the mean values and plus/minus two standard deviations and any increase in radon concentration above this limit was assumed to be ²²²Rn anomalies. These anomalies usually appeared between a few days or weeks before the earthquakes occurrence. The obtained data were also compared as considered respect to the earthquakes occurred in a 100 km radius of the fault system.     

A selection theorem in metric trees

In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set-valued mapping of a metric tree with convex values has a selection for which for each . Here by we mean the Hausdroff distance. Many applications of this result are given.

     

On commensurator growth

We study a new asymptotic invariant of a pair consisting of a group and a subgroup, which we call the commensurator growth. We compute the commensurator growth for several examples, concentrating mainly on the case of a locally compact topological group and a lattice inside it.     

Performance and emission characteristics of a diesel engine operating on safflower seed oil methyl ester

Applied Biochemistry and Biotechnology - This study focused on the evaluation and testing of safflower seed oil methyl ester as a diesel fuel alternative. The kinematic viscosity and ASTM fuel...