Hadamard’s formula and couplings of SLEs with free field

The relation between level lines of Gaussian free fields (GFF) and SLE₄-type curves was discovered by O. Schramm and S. Sheffield. A weak interpretation of this relation is the existence of a coupling of the GFF and a random curve, in which the curve behaves like a level line of the field. In the present paper we study these couplings for the free field with different boundary conditions. We provide a unified way to determine the law of the curve (i.e. to compute the driving process of the Loewner chain) given boundary conditions of the field and to prove existence of the coupling. The proof is reduced to the verification of two simple properties of the mean and covariance of the field, which always relies on Hadamard’s formula and properties of harmonic functions. Examples include combinations of Dirichlet, Neumann and Riemann–Hilbert boundary conditions. In doubly connected domains, the standard annulus SLE₄ is coupled with a compactified GFF obeying Neumann boundary conditions on the inner boundary. We also consider variants of annulus SLE coupled with free fields having other natural boundary conditions. These include boundary conditions leading to curves connecting two points on different boundary components with prescribed winding as well as those recently proposed by C. Hagendorf, M. Bauer and D. Bernard.     

Potentiometric monitoring DNA hybridization with polyaniline/Nylon-6 working electrode

Electrically conducting polymers are useful in various applications such as transistors and sensors. A potentiometric pH meter has been developed using polyaniline based working electrode and with improved selectivity using ionophores, the polyaniline based potentiometer has been applied to monitor various ions mainly in environmental applications. The polyaniline working electrode can be used to monitor not only the binding of a biological ionic macromolecules on polyaniline surface but also the binding of the adsorbed macromolecule with another macromolecule. We present first how the working electrode was prepared by polymerization of aniline in Nylon-6 matrix to provide the mechanical strength and then how single strand oligonucleotide probe binds with polyaniline surface. We then present how an electrode modification with mercaptoethanol results in a surface protected against non-specific binding and then finally we present the results of monitoring the complimentary strand binding leading to the formation of the double strand DNA. The text was submitted by the authors in English.     

Ring-substituted polyaniline copolymers combining high solubility with high conductivity

Poly(aniline-co-phenetidine)s were synthesized by the copolymerization of aniline and o-phenetidine (o-ethoxyaniline). The molar feed ratio of the starting aniline monomers was varied to result in copolymers with different compositions. The actual composition was deduced by integrated proton NMR spectroscopy. The copolymers exhibit excellent solubility characteristics. It was particularly interesting to find that the 20% ethoxyaniline containing copolymer exhibits excellent solubility and yet retains the high conductivity characteristic of the unsubstituted homopolymer. The conductivity of the hydrochloride salt of this par-ticular copolymer is identical to that of the unsubstituted derivative. However, the copolymer solubility greatly exceeds that of the unsubstituted homopolymer. The copolymer in the base form exhibits very high solubility in NMP and the resulting solutions are exceedingly more stable than those of the unsubstituted derivative. A 10% by weight solution of the 20% ethoxy copolymer in NMP is stable for ? 50 days at room temperature afterwhich a gel is formed as compared to previous reports of ? 3–10 h stability for corresponding solutions of the unsubstituted derivative. © 1995 John Wiley & Sons, Inc.     

On varieties generated by functionally complete algebras

In [4] A. F. Pixley stated a problem due to A. L. Foster: is a functionally complete algebra having no non-trivial subalgebras necessarily categorical? In this paper we show that, in general, the answer to this question is negative. However the answer becomes affirmative, if we replace the word “non-trivial” by the word “proper”.     

Hard Lefschetz theorem for nonrational polytopes

The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it. We prove the Hard Lefschetz theorem for the intersection cohomology of a general polytope.     

N‐Heterocyclic Phosphenium,Arsenium, and Stibenium Ions as Ligands in Transition Metal Complexes: A Comparative Experimental and Computational Study

Reaction of 2‐chloro‐1,3,2‐diazaarsolenes and ‐diazaphospholenes with Tl[Co(CO)₄] gives instable complexes of type [Co(ER₂)(CO)₄] which decarbonylated to yield [Co(ER₂)(CO)₃]. Spectroscopic and X‐ray diffraction studies revealed that the tetracarbonyl complexes can be formulated as ion pair for E = P and as covalent metalla‐arsine for E = As, and the tricarbonyl complexes as carbene‐like species with a formal E=Co double bond. A similar reactivity towards Tl[Co(CO)₄] was also inferred for 1,3,2‐diazastibolenes although the products were not isolable and their constitution remained uncertain. Evaluation of structural and computational data suggests that the weak and polarized Co–As bond in [Co(AsR₂)(CO)₄] can be characterized as an “inverse” M→L donor‐acceptor bond. The computational studies disclosed further η²(EN)‐coordination of the EN₂C₂ heterocycle as an alternative to the formation of a carbene‐like structure for [Co(ER₂)(CO)₃]. The η²‐complex is less stable for E = P but close in energy for E = As and more stable than the carbene‐like complex for E = Sb.     

Doping of polyaniline with polymeric dopants in solid state,gel state and solutions

Polystyrene with different degrees of sulfonation was empolyed as a polymeric dopant for polyaniline. The purpose of using a polymeric dopant is to avoid the migration of a small molecule dopant to increase stability of the doped complex. We applied the polymeric dopant to polyaniline in three different ways: in solid state, in solution and in gel state. In solid state, the conducting form was achieved only through a novel thermal doping method with the increase in temperature and pressure. In solution, the doping process was shown to be dependent on the nature of the solution and also on the molecular weight of the polymer. In the gel form of polyaniline, a polymeric dopant with a surprising low degree of sulfonation was found to be successful in the doping process.     

Multiple-stage mass spectrometry in structural characterization of organophosphorus compounds

Multiple-stage mass spectrometry involving consecutive collision-activated dissociation reactions was used to examine the structures of fragment ions commonly formed on electron ionization of organophosphorus esters. The compounds studied include several aryl thiophosphates, some of which are analogs of common pesticides. Energy-resolved collisionactivated dissociation experiments allow the dissociation of the molecular ions of these compounds in such a manner that only a few fragment ions dominate the spectrum. An abundant fragment ion of m/z 109, formed from all of the compounds studied, can have at least four different stable structures: (CH₃O)₂PO⁺, CH₃CH₂OP(O)OH⁺, CH₂ =CHOP(H)(OH)₂ ⁺, and (CH₂O)₂P(H)OH⁺. The structure of the fragment ion of m/z 109 was found to reflect the phosphorus-containing part of the compounds studied. Another abundant fragment ion obtained for all the aryl esters studied is structurally characteristic of the aromatic moiety of the molecule. This fragment ion is the result of a complex rearrangement involving transfer of an alkylene group to the aromatic ring from the phosphoruscontaining part of the molecular ion. The utility of these fragment ions in the structural characterization of unknown organophosphorus esters is discussed.     

Electrochemical Generation of Hot Electrons in Fully Aqueous Solutions at Tetrahedral Amorphous Carbon Thin Film Electrodes and Electrochemiluminescence Immunoassay of Serum Amyloid A

Electrochemistry of hot electrons in fully aqueous solutions at tetrahedral amorphous carbon thin film electrodes is discussed. The generation of these highly reducing chemical species was confirmed by normal pulse voltammetry and several electrochemiluminescent systems. Electron transfer into pre-existing solvent cavities was observed at approximately −2.65 V vs. Ag/AgCl (sat.). Electrogenerated hot electrons were utilized as chemiluminescent mediators in heterogeneous sandwich immunoassay of Serum Amyloid A. The calibration curve was linear over four orders of magnitude and the detection limit was 85 ng L⁻¹ that demonstrates the efficiency of hot electron generation at this electrode material.     

Shear‐induced delocalization of polarons in polyaniline‐zinc salt complexes

A zinc salt of the acid dopant has been into a doped polyaniline in order to improve the processing conditions. The complex shows viscoelastic behavior at elevated temperatures when manual shear for the sample was applied. The ratios between polyaniline, the dopant and the zinc‐salt of the dopant was controlled in order to understand the optimal conditions for the shearing experiments. The initial samples are not birefringent, but the samples become birefringent and liquid crystalline after the shear. Additionally, the application of UV‐spectroscopy revealed strong delocalization of the polarons after the shear process.