Classification of Riemannian manifolds in nonlinear potential theory

The classification theory of Riemann surfaces is generalized to Riemanniann-manifolds in the conformally invariant case. This leads to the study of the existence ofA-harmonic functions of typen with various properties and to an extension of the definition of the classical notions with inclusionsO _G O _HP O _HB O _HD . In the classical case the properness of the inclusions were proved rather late, in the 50's by Ahlfors and Tôki. Our main objective is to show that such inclusions are proper also in the generalized case.This research was supported in part by grants from the Academy of Finland and the U.S. National Science Foundation (NSF DMS 9003438).     

Towardsab Initio simulations of concentrated suspensions

Determination of many-body interactions between particles of arbitrary shape in a viscous fluid is a key problem in the simulation of concentrated suspensions. Three-dimensional flows involving such complex fluid-solid boundaries are beyond the scope of spatial methods, even on supercomputers. Boundary integral methods convert the three-dimensional PDE to a two-dimensional integral equation. Unfortunately, conventional boundary methods yield Fredholm integral equations of the first kind, and dense linear systems which are too large for accurate solution. We have pursued a different boundary integral formulation, which yields Fredholm integral equations of the second kind; these arc amenable to iterative solution. The velocity representation involves a compact operator, so a discrete spectrum results. Wielandt deflations give dramatic reductions in the spectral radius and accurate solutions are obtained after only a few iterations (typically less than 10). An analytic construction of the spectrum for sphere sphere interactions confirms these numerical results. The mathematics is similar to that encountered in the mixing ofd-atomic orbitals to form bonding/antibonding molecular orbitals in transition metals. The memory-saving version of our code can be implemented directly on a dedicated MicroVAX to solve problems involving clusters of less than a dozen particles. For a fixed number of processors, the algorithm grows essentially asN ², whereN is the system size, so computational times are readily estimated on more powerful super-minicomputers and supercomputers using standard dot-product benchmarks. The algorithm is especially ideal for gigaflop and teraflop parallel array processors under construction in a number of computer companies; an analysis of the spectrum reveals that asynchronous iterative methods will converge, leading the way to a rigorous formulation of screening concepts for suspended particles of arbitrary shape.     

Sulphur Kβ X-ray emission spectra of SO2−3 and SO3F− ions

The SK_β X-ray emission spectra of the SO^2?₃ and SO₃F^? ions are studied in detail and the observed fine structures are interpreted with the aid of existing molecular orbital (MO) calculations. The different MO methods are compared with regard to success and the effect of d-orbitals is discussed. The spectrometer is a double-crystal type with an instrument fwhm resolution of 0.25 eV for SK_β X-rays.     

On-line process monitoring of water-soluble ions in pulp and paper machine waters by capillary electrophoresis

In this study, capillary electrophoresis (CE) was used for separation of inorganic and organic ions from waters of paper and paperboard machines at mills. The instrument was constructed for on-line measurements by building a batch-type sample feeding unit. Chloride, thiosulphate, sulphate, oxalate, sulphite, hydrogen sulphide, formate, carbonate, phosphate and acetate in the process water samples were separated using an ion-specific separation system in CE with dicarboxylic acid buffer (pH 8.2), with pyridinium-2,3-dicarboxylic acid modified with commercial NICE-Pak OFM-OH solution (pH 12.0) or with a cetyltrimethylammonium bromide solution modified with chromate (pH 10.6). In addition, Analis CEofix Anions 8 electrolyte solution was tested in on-line studies at mills. It allowed 5 min separation time for the anions. Aluminium was determined at pH 3.6 in 10 min by using a laboratory-made imidazole buffer modified with 18-crown 6-ether. The developed CE systems were used to monitor the concentrations of sulphur species in dithionite degradation, to estimate corrosion degree in the water tanks, to monitor formaldehyde as the biocide chemical in wire washing and, in general, to observe process disturbances resulting from chemical feedings and their sites. The CE combination was on-line coupled to eight different process machines for continuous monitoring of concentrations for periods between two weeks and one month at paper and pulp mills in Finland.     

Quantitative determination of acetylcholine in microdialysis samples using liquid chromatography/atmospheric pressure spray ionization mass spectrometry

A fast, simple and sensitive liquid chromatography/tandem mass spectrometry (LC/MS/MS) method was developed for the determination of acetylcholine in rat brain microdialysis samples. The chromatographic separation was achieved in 3 min on a reversed-phase column with isocratic conditions using a mobile phase containing 2% (v/v) of acetonitrile and 0.05% (v/v) of trifluoroacetic acid (TFA). A stable isotope-labeled internal standard was included in the analysis and detection was carried out with a linear ion trap mass spectrometer using selected reaction monitoring (SRM). Analyte ionization was performed with an atmospheric pressure chemical ionization (APCI) source without applying discharge current (atmospheric pressure spray ionization). This special ionization technique offered significant advantages over electrospray ionization for the analysis of acetylcholine with reversed-phase ion-pairing chromatography. The lower limit of quantification was 0.15 nM (1.5 fmol on-column) and linearity was maintained over the range of 0.15-73 nM, providing a concentration range that is significantly wider than that of the existing LC/MS methods. Good accuracy and precision were obtained for concentrations within the standard curve range. The method was validated and has been used extensively for the determination of acetylcholine in rat brain microdialysis samples.     

Mass spectrometric characterization of a series of adenosylated peptides acting as bisubstrate analogs of protein kinases

We are currently developing strategies to synthesize bisubstrate analogs as potential inhibitors of serine and tyrosine protein kinases; several such analogs have been synthesized. The initial target proteins were the cAMP dependent protein kinase (cAPK) and the Ca⁺²/calmodulin dependent protein kinase (CaM kiiase II). These bisubstrate analogs were based on either known peptide substrates such as kemptide, a seven amino acid peptide substrate of cAPK, or on inhibitory peptides such as a seventeen amino acid peptide encompassing the autoinhibitory domain of CaM kinase II. Peptides containing a single phosphoserine group were first synthesized and then adenosine 5′-monophosphate (AMP), adenosine 5′-diphosphate (ADP), or adenosine 5′-triphosphate (ATP) was coupled through the serine phosphate with prior activation by 1,1-carbonyldiimidazole using either a solution or solid phase reaction scheme. In this current study, we report the characterization of the bisubstrate analogs by liquid secondary ionization mass spectrometry (LSIMS), matrix-assisted laser desorption mass spectrometry (MALDI), and tandem mass spectrometry (MS/MS). In the positive-ion mode, the LSIMS spectra of the bisubstrate analogs yielded a series of molecular ions containing mono-, di-, and trivalent cation adducts. Cation adducts were absent in the negative-ion mode where the dominant species were deprotonated molecular ions, [M ? H]^?, making this latter technique more useful for confirming product identity and assessing purity. Analysis of these compounds by MALDI in both the positive- and negative-ion modes yielded molecular ions which also contained metal ion adducts, although they were limited primarily to Fe⁺² adducts. Unlike LSIMS, the MALDI spectra showed no evidence for the elimination of the phosphoadenosine or other structural moieties. When these compounds were subjected to high energy collision-induced dissociation (CID), the dominant fragmentation pathways under positive-ion MS/MS conditions resulted from cleavage of the phosphate linkages to the adenosine moiety with charge retention on the peptide, although a major peak for 5′-deoxyadenosine was also seen at m/z 250. Charge retention in the negative-ion mode was most pronounced for ion fragments containing the highly acidic phosphate moieties and yielded phosphoadenosine related ions, for example, (AMP-H)^?, (AMP-H-H₂O)^?, (ADP-H)^?, etc., as well as ions originating from the phosphate linker such as PO₃ ^?, H₂PO₄ ^?, HP₂O₆ ^?, H₃P₂O₇ ^?, and H₂P₃O₉ ^?. The largest phosphoadenosine ion in the negative-ion CID spectra for each bisubstrate analog, for example, m/z 426 (ADP-H)^?, m/z 506 (ATP-H)^?, or m/z 586 (AP₄-H)^?, indicated that the desired covalent modification had been formed between the phosphoserine and AP_n moieties.     

Past and future impact of electroactive polymers on the electronics sector

A broad review of the field of applications of electroactive polymers, defined as inherently conductive, charged, piezoelectric and pyroelectric, and systems made electroactive by addition of conductive additives, in the field of electronics and microelectronics. Applications mentioned include the use of polymers for electrodes for rechargeable batteries, electret microphones, hydrophones, vidicons, EMI and ESD protection, and conductor and resistor tracks as thick films on printed circuit boards. Future trends as the development of supermolecular assemblies for parallel processing are also highlighted.     

Controlled grafting of acetylated starch by atom transfer radical polymerization of MMA

Graft copolymers of acetylated starch oligomer (AS) and poly(methyl methacrylate) (PMMA) were polymerized by atom transfer radical polymerization (ATRP). AS was converted to an ATRP macroinitiator by converting a part of the hydroxyl groups of AS to 2-bromoisobutyryl groups. Macroinitiators with varying degrees of substitution for the 2-bromoisobutyryl group were prepared. The polymerizations were conducted using CuBr/BiPy catalyst system, either in bulk or in 1:1 v/v THF solution. They proceeded with first-order kinetics and the molecular weights of the polymers increased linearly with conversion. Graft copolymers with different graft densities and graft lengths were prepared in a controlled manner. The hydrophobicity of these copolymers was studied by contact angle measurements.     

A characterization of semibounded selfadjoint operators

For a class of closed symmetric operators with defect numbers it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator is semibounded if and only if each one-dimensional restriction of has a generalized Friedrichs extension.

     

Uniqueness and existence results for ordinary differential equations

We establish some uniqueness and existence results for first-order ordinary differential equations with constant-signed discontinuous nonlinear parts. Several examples are given to illustrate the applicability of our work.