Modification of carbon electrodes by vitamin B12-polymers

New types of electroactive polymers consisting of derivatives of vitamin B₁₂ and epoxy resins have been synthesized. Surface modification of carbon (carbon felt or basal plane pyrolytic graphite) has been achieved by thermal curing of the monomers on the electrodes. Electrochemical response from the Co (II)/Co (I) redox couple has been observed from sub-mono to multilayer coverages. The influence of the size of the epoxy spacer on charge propagation in the polymer has been studied. The B₁₂-modified electrodes have been applied to electrosynthesis and electroanalysis: They catalyze the reductive cross-coupling of alkyl halides and activated olefins and they are efficient sensors for alkylating agents.     

On a Microscopic Representation of Space-Time VIII—On Relativity

Physics of Atomic Nuclei - Based on the previous work on the Dirac algebra and su*(4) Lie algebra generators, using Lie transfer we have associated spin to line and Complex reps. Here, we discuss...     

Hyperflock determining line sets and totally regular parallelisms of PG (3, \mathbbR){(3,\,{\mathbb{R}})}

By a totally regular parallelism of the real projective 3-space P₃:=PG(3, \mathbb R){\Pi_3:={{\rm PG}}(3, \mathbb {R})} we mean a family T of regular spreads such that each line of Π ₃ is contained in exactly one spread of T. For the investigation of totally regular parallelisms the authors mainly employ Klein’s correspondence λ of line geometry and the polarity π ₅ associated with the Klein quadric H ₅ (for details see Chaps. 1 and 3). The λ-image of a totally regular parallelism T is a hyperflock of H ₅, i.e., a family H of elliptic subquadrics of H ₅ such that each point of H ₅ is on exactly one subquadric of H. Moreover, {p₅(span  l(X))|X ? T}=:H_T{\{\pi_5({{\rm span}} \,\lambda(\mathcal {X}))\vert\mathcal {X}\in\bf{T}\}=:\mathcal {H}_{\bf{T}}} is a hyperflock determining line set, i.e., a set Z{\mathcal {Z}} of 0-secants of H ₅ such that each tangential hyperplane of H ₅ contains exactly one line of Z{\mathcal {Z}} . We say that dim(span H_T)=:d_T{{{\rm dim}}({{\rm span}}\,\mathcal {H}_{\bf{T}})=:d_{\bf{T}}} is the dimension of T and that T is a d _T - parallelism. Clifford parallelisms and 2-parallelisms coincide. The examples of non-Clifford parallelisms exhibited in Betten and Riesinger [Result Math 47:226–241, 2004; Adv Geom 8:11–32, 2008; J Geom (to appear)] are totally regular and of dimension 3. If G{\mathcal{G}} is a hyperflock determining line set, then {l^-1 (p₅(X) ?H₅) | X ? G}{\{\lambda^{-1}\,{\rm (}\pi_5(X){\,\cap H_5)\,|\, X\in\mathcal{G}\}}} is a totally regular parallelism. In the present paper the authors construct examples of topological (see Definition 1.1) 4- and 5-parallelisms via hyperflock determining line sets.     

Cumulant approach to the two-dimensional magneto-conductivity problem

The validity of assumptions involved in experimental evaluations of the g-factor of electrons in (100) surface inversion layers of p-silicon from Shubnikov-De Haas oscillations of the surface conductivity by the method of tilted megnetic fields is discussed on the basis of the transport theory of a two-dimensional electron-impurity system. The self-consistent Born approximation is shown to be insufficient to this task, and an alternative cumulant approach is discussed. Contrary to recent work, the cumulant approach is introduced in a simple manner, avoiding the path-integral formalism.     

Walking an unknown street with bounded detour

A polygon with two distinguished vertices, s and g, is called a street if the two boundary chains from s to g are mutually weakly visible. For a mobile robot with on-board vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the length of the path created does not exceed 1 + π times the length of the shortest path from s to g. Experiments suggest that our strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate.