Polyhedral <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">2</Emphasis></Subscript>

 Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional case provides interesting classes of groups. Received: 13 December 2001 / Revised version: 24 June 2002 The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107 Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20     

Simulation of aerated lagoon using artificial neural networks and multivariate regression techniques

The aim of this study was to develop an empirical model that provides accurate predictions of the biochemical oxygen demand of the output stream from the aerated lagoon at International Paper of Brazil, one of the major pulp and paper plants in Brazil. Predictive models were calculated from functional link neural networks (FLNNs), multiple linear regression, principal components regression, and partial least-squares regression (PLSR). Improvement in FLNN modeling capability was observed when the data were preprocessed using the PLSR technique. PLSR also proved to be a powerful linear regression technique for this problem, which presents operational data limitations.     

Donor—acceptor interactions of substituted benzenes with molecular chlorine and carbon disulfide

CNDO molecular orbital calculations have been performed to analyze donor—acceptor interactions between molecular chlorine and benzene, toluene, mesitylene and hexamethylbenzene and the, as yet, unreported chlorine—hexafluorobenzene and carbon disulfide—benzene pairs. The stabilization energy and the dipole moment and its derivative (?p/?R_CICI) calculated for the benzene—chlorine complex are in good agreement with the estimated experimental values. The trends in the experimental stabilization energies and the Cl-Cl vibrational frequencies with increasing methyl substitution appear to be well reproduced by the calculations. The charge transferred from the benzene donor is polarized toward the outer chlorine atom or sulfur atom. For hexafluorobenzene-chlorine the direction of electronic charge polarization is reversed from that of the benzene and methylbenzene complexes. The calculated results are discussed within the framework of Muliiken's simplified resonance theory for complexes.     

Isolation, primary structure characterization and identification of the glycosylation pattern of recombinant goldfish neurolin, a neuronal cell adhesion protein

Neurolin is a growth-associated cell surface glycoprotein from goldfish and zebra fish which has been shown to be involved in axonal path-finding in the goldfish retina and suggested to function as a receptor for axon guidance molecules. Being a member of the immunoglobulin superfamily of cell adhesion proteins, neurolin consists of five N-terminal extracellular immunoglobulin (Ig)-like domains, a transmembrane and a short cytoplasmatic domain. Repeated injections of polyclonal Fab fragments against neurolin and of monoclonal antibodies against either Ig domains cause path-finding errors and disturbance of axonal fasciculation. In order to obtain a complete structural characterization and a molecular basis for structure-function determination, recombinant neurolin with the complete extracellular part but lacking the transmembrane and cytoplasmatic domain was expressed in Chinese hamster ovary (CHO) cells (CHO-neurolin). The isolation of CHO-neurolin was carried out by Ni-affinity chromatography and subsequent high-performance liquid chromatography (HPLC). An exact molecular mass determination was obtained by matrix-assisted laser desorption/ionization mass spectrometry (MALDI/MS) and revealed 60.9 kDa, which suggested that approximately 10 kDa are due to glycosylation. The predicted molecular mass is 51.5 kDa, whereas sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE) yielded an apparent molecular mass of 72 kDa. Gel shift assays using SDS-PAGE and Western blot analysis with anti-neurolin antibodies provided consistent molecular mass data. The complete primary structure and N-glycosylation patterns were identified using specific lectin assays, MALDI/MS peptide mapping analysis by proteolytic and in-gel digestion, electrospray ionization MS and MALDI/MS in combination with specific glycosidase degradation. HPLC isolation of glycosylated peptide fragments and MS after selective deglycosylation revealed heterogeneous glycosylations at all five N-glycosylation consensus sites. All attached N-glycans are of the complex type and show a mainly biantennary structure; they are fucosylated with alpha(2,3)-terminal neuraminic acid. These data serve as a first detailed model to characterize the molecular recognition structures exhibited by the extracellular domains.     

Combinatorial invariance of Stanley-Reisner rings

In this short note we show that Stanley—Reisner rings of simplicial complexes, which have had a dramatic application in combinatorics [2, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.     

New Factorial Designs to Evaluate Chemisorption of Divalent Metals on Aminated Silicas

Adsorption processes of Cu(II), Co(II), and Hg(II) on two aminated silica gel surfaces with immobilized ethylenediamine and diethylenediamine groups were studied by a new 2(3) full factorial design. Two metal quantity levels, temperatures of 25 and 50 degrees C, and silica amounts of 100 and 200 mg were employed. Our study indicates that higher factorial design levels increase adsorption for all metals evaluated, with the exception of the mass parameter. Adsorption is also significantly affected by important antagonistic and synergistic effects involving all factors. Both functionalized silica gel surfaces present higher interactions and good perspectives in preconcentration studies for mercury. The factorial design results are also discussed in terms of some solvation properties for each of the metals studied. Copyright 2001 Academic Press.     

Zur Längenberechnung der Torsion äusserer Potenzen

Let R be a noetherian ring of dimension d and M a finitely generated R-module of homologic dimension less or equal to one. Assume further that M has a rank r, which equals d or (in case d>0) d?1 and that the r-th Fitting-ideal \(\vartheta _r (M)\) of M has grade ?d. Then the torsion-submodule of the d-th exterior power of M and the module \(R/\vartheta _r (M)\) are equivalent.     

Reaction with SO3 in Ionic Liquids: The Example of K2(S2O7)­(H2SO4)

The ionic liquid 1‐butyl‐3‐methylimidazolium hydrogensulfate, [bmim]HSO₄, turned out to be resistant even to strong oxidizers like SO₃. Thus, it should be a suitable solvent for the preparation of polysulfates at low temperatures. As a proof of principle we here present the synthesis and crystal structure of K₂(S₂O₇)(H₂SO₄), which has been obtained from the reaction of K₂SO₄ and SO₃ in [bmim]HSO₄. In the crystal structure of K₂(S₂O₇)(H₂SO₄) (orthorhombic, Pbca, Z = 8, a = 810.64(2) pm, b = 1047.90(2) pm, c = 2328.86(6) pm, V = 1978.30(8) ų) two crystallographically unique potassium cations are coordinated by a different number of monodentate and bidentate‐chelating disulfate anions as well as by sulfuric acid molecules. The crystal structure consists of alternating layers of [K₂(S₂O₇)] slabs and H₂SO₄ molecules. Hydrogen bonds between hydrogen atoms of sulfuric acid molecules and oxygen atoms of the neighboring disulfate anions are observed.