Structure of 2-{2-[3-methyl-3-(2,4,6-trimethylphenyl) cyclobutyl]-2-oxoethyl}isoindole-1,3-dione

2-{2-[3-Methyl-3-(2,4,6-trimethylphenyl)cyclobutyl]-2-oxoethyl}isoindole-1,3-dione (C₂₄ H₂₅NO₃) was synthesized, and its crystal structure was determined by X-ray crystallographic techniques. The compound crystallizes in the triclinic space group P-1, with unit cell parameters: a = 14.109(9) Å, b = 14.130(8) Å, c = 12.152(6) Å, = 105.62(5)°, = 113.75(4)°, = 98.78(5)°, V = 2039.8(19) ų, D _c= 1.223 g/cm³, and Z = 4. The crystal structure has two crystallographically independent molecules, I and II. These molecules are held together by weak intermolecular C—H···O interactions, forming a continuous chain. The dihedral angles between the N-substituted phthalimide moiety and cyclobutane ring in molecules I and II are 60.37(14) and 68.18(18)°, respectively.     

QSAR based modeling of inhibitory activity of alkenyldiarylmethane derivatives

A series of alkenyldiarylmethanes (ADAMs) were subjected to QSAR analysis by using linear free energy relationship model of Hansch. QSAR has been developed using steric, electronic and topological parameters along with appropriate dummy variable. Statistical techniques were applied to identify the structural and physicochemical requirements for ADAMs. The results are critically discussed on the basis of regression data and cross-validation techniques.     

Thickness and angular dependence of the L‐edge X‐ray absorption of nickel thin films

We report on the near‐edge X‐ray absorption fine structure spectroscopy of the L₃ (2p_3/2) and L₂ (2p_1/2) edges for ferromagnetic pure nickel transition metal and show that the L_2,3 edge peak intensity and satellite feature at ~6 eV above the L₃ edge in nickel increase with increasing nickel film thickness both in the total electron yield and transmission modes. The absorption spectra of nickel metal, however, exhibit strong angular‐dependent effects when measured in total electron yield mode. In addition, we calculated the mean electron escape depth of the emitted electrons (λ_e), which was found for pure nickel metal to be λ_e=25 ± 2 Å. We point out the advantages of the total electron yield technique for the study of the L‐edge of 3d transition metals. Copyright © 2011 John Wiley & Sons, Ltd.     

A.V. Bitsadze's observation on bianalytic functions and the Schwarz problem

According to an observation of A.V. Bitsadze from 1948 the Dirichlet problem for bianalytic functions is ill-posed. A natural boundary condition for the polyanalytic operator, however, is the Schwarz condition. An integral representation for the solutions in the unit disc to the inhomogeneous polyanalytic equation satisfying Schwarz boundary conditions is known. This representation is extended here to any simply connected plane domain having a harmonic Green function. Some other boundary value problems are investigated with some Dirichlet and Neumann conditions illuminating that just the Schwarz problem is a natural boundary condition for the Bitsadze operator.     

Diagnostics of microwave-induced plasmas and polymerization of gaseous hydrocarbons

The microwave plasmas of gaseous mixtures of methane-argon and propyleneargon were analyzed along the flow stream by the electrical double floating probe system, optical spectroscopy, and quadrupole mass spectrometry. The plasma variables measured and considered were current density, electric field strength, electron temperature, positive ion and electron concentrations, and concentration of pyrolyzed and polymerized species. The results indicate that an irreversible process of polymerization of the hydrocarbons takes place in the plasma. The polymerization process reaches its maximum conversion downstream beyond the microwave cavity. The extent of polymerization was correlated to the concentration of positive ions and electrons in the plasma.Presented in part at ISPC 4, Zurich, 1979, S. Veprek and J. Hertz, eds., Vol. II (University of Zurich, 1979), p. 390.     

Complexes of chromium(III) with 2,3-dihydroxynaphthalene-6-sulfonic acid and 4,5-dihydroxynaphthalene-2,7-disulfonic acid in aqueous solution

The chromium(III) complex species formed, in acidic and basic solutions at 25.0+/-0.1 degrees C, between Cr(III) and 2,3-dihydroxynaphthalene-6-sulfonic acid (2,3-DHN-6-SA, H(2)L(2-)) and 4,5-dihydroxynaphthalene-2,7-disulfonic acid (4,5-DHN-2,7-DSA, H(2)L(-)) were determined. Over the acidic pH range, the coordination of 2,3-DHN-6-SA and 4,5-DHN-2,7-DSA to Cr(III) in 1 : 1 mole ratio occurs, and CrL and CrL(-) type complexes are formed. At near neutral pH, CrL(OH)(-) and CrL(OH)(2-) type hydroxo complexes are formed. The acid-dissociation constants of ligands and the formation constants of chromium(III) complexes were determined in 0.1 m KNO(3) ionic medium by potentiometric titration using the BEST computer program. Thus, the removing capacities of these ligands could be examined by calculating the equilibrium concentration of Cr(III) that exists in the discharge water of various industries since Cr(III) ions are the main pollutants present during waste water treatment in our city, Bursa.     

Erdős Type Problems in Modules over Cyclic Rings

In the present paper, we study various Erd?s type geometric problems in the setting of the integers modulo q, where \(q=p^l\) is an odd prime power. More precisely, we prove certain results about the distribution of triangles and triangle areas among the points of \(E\subset \mathbb {Z}_q^2\).     

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.