Discrete groups of slow subgroup growth

It is known that the subgroup growth of finitely generated linear groups is either polynomial or at least $n^{\frac{{\log n}}{{\log \log n}}} $ . In this paper we prove the existence of a finitely generated group whose subgroup growth is of type $n^{\frac{{\log n}}{{(\log \log n)^2 }}} $ . This is the slowest non-polynomial subgroup growth obtained so far for finitely generated groups. The subgroup growth typen ^logn is also realized. The proofs involve analysis of the subgroup structure of finite alternating groups and finite simple groups in general. For example, we show there is an absolute constantc such that, ifT is any finite simple group, thenT has at mostn ^{c logn} subgroups of indexn.     

Synthesis and structure of a dithioether-substituted butene-2-olide-4-ylidene-4 cobalt carbonyl complex

The complex (1) has been prepared and its structure determined. Complex1 is the first stable thioether derivative of a metal carbonyl containing only cobalt as metal. It crystallizes in the monoclinic P2₁/c space group, witha = 13.975( 4 ),b = 11.363( 3 ),c = 14.686(2)A, = 112.25(2)°,V = 2158.5(7)A³.Z = 4. The solution using direct methods and the anisotropic refinement of all nonhydrogen atoms led toR = 0.039,wR = 0.041 for 3296 reflections with F> 4.0(F) Analogous but less stable complexes are formed with 1,6-diphenyl-2,5-dithiahexane and the crown thioether 1,4,7-trithiacyclonane, the latter functioning either as a bidenlate or a tridentate ligand.     

Experimental determination of the flame expansion factor

The flame expansion factor (ratio of volumes of flame gases before and after burning) has been determined by mercury vapour introduction. The method is based on the determination of atomic concentration ratio in the flame and the flameless gas jet using the same sample introduction rate. A good agreement has been found between the expansion factors determined by the proposed method and those calculated by the gas law.     

On the cube problem of Las Vergnas

We prove a conjecture of Las Vergnas in dimensions d7: The matroid of the d-dimensional cube C ^d has a unique reorientation class. This extends a result of Las Vergnas, Roudneff and Salaün in dimension 4. Moreover, we determine the automorphism group G ^d of the matroid of the d-cube C ^d for arbitrary dimension d, and we discuss its relation to the Coxeter group of C ^d . We introduce matroid facets of the matroid of the d-cube in order to evaluate the order of G ^d . These matroid facets turn out to be arbitrary pairs of parallel subfacets of the cube. We show that the Euclidean automorphism group W ^d is a proper subgroup of the group G ^d of all matroid symmetries of the d-cube by describing genuine matroid symmetries for each Euclidean facet. A main theorem asserts that any one of these matroid symmetries together with the Euclidean Coxeter symmetries generate the full automorphism group G ^d . For the proof of Las Vergnas' conjecture we use essentially these symmetry results together with the fact that the reorientation class of an oriented matroid is determined by the labeled lower rank contractions of the oriented matroid. We also describe the Folkman-Lawrence representation of the vertex figure of the d-cube and a contraction of it. Finally, we apply our method of proof to show a result of Las Vergnas, Roudneff, and Salaün that the matroid of the 24-cell has a unique reorientation class, too.     

Construction of Rank 2 Semistable Torsion Free Sheaves Which Are Not Limit of Vector Bundles

We show the following theorem of compensated compactness type: Ifu _n ⇁u weakly in the spaceH ^1,p (Ω, ℝ ^k ) and if also in the sense of distributions then ∂_α(∣∇u∣ ^p-2∂_α u)=0. This result has applications in the partial regularity theory ofp-stationary mappings Ω→S ^k −1.     

Flow-through optical fiber sensor for automatic sulfide determination in waters by multisyringe flow injection analysis using solid-phase reflectometry

A software-controlled flow-through optical fiber diffuse reflectance sensor capitalized on the implementation of disk-based solid-phase pre-concentration schemes in a multisyringe flow injection analysis (MSFIA) set-up is proposed for the trace determination of sulfide in environmental waters and wastewaters. The fully automated flowing methodology is based on Fischer's coupling reaction of sulfide with N,N-dimethyl-p-phenylenediamine (DMPD) in the presence of Fe(iii) as oxidizing reagent in a 0.5 M HCl medium. The on-line generated methylene blue dye is subsequently delivered downstream to a dedicated optode cell furnished with an octadecyl-chemically modified (C(18)) disk, while continuously recording the diffuse reflectance spectrum of the pre-concentrated compound. A double regeneration protocol is finally executed to warrant minimum background noise and negligible baseline. Under the optimized chemical and hydrodynamic conditions, the optosensing MSFIA method features coefficients of variation better than 0.7%(n= 10) at 50 microg l(-1) concentration, a linear working range of 20-200 microg l(-1) sulfide, a 3sigma(blank) detection limit of 2.9 microg l(-1) sulfide and an injection throughput of 8 h(-1) for a pre-concentration sample volume of 2.9 ml. The interfacing of the robust and versatile multisyringe flow injection-based optode with a plug-in spectrophotometer furnished with a light emitting diode assures the miniaturization of the overall flow analyzer, which is, thus, readily adaptable to real-time monitoring schemes. The potential of the multisyringe flow method was assessed via the determination of sulfide traces in water samples of different complexity (namely, freshwater, seawater and wastewater).