Epimorphismen von kommutativen Ringen

Ohne Zusammenfassung     

Über die Nielsensche Kürzungsmethode in freien Produkten mit Amalgam

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Simple curves on surfaces and an analog of a theorem of Magnus for surface groups

Magnus proved that, if is a free group and u, v are elements of with the same normal closure, u is a conjugate of v or v^–1 [9]. We prove the analogous result in the case that is the fundamental group of a closed surface S and u,v are elements of ₁(S) containing simple closed two-sided curves on S. As a corollary we prove that, if S is not a torus and is not a Klein bottle, each automorphism of ₁(S) which maps every normal subgroup of ₁(S) into itself is an inner automorphism.Mathematical Subject Classification (2000): 50F34, 57M07, 57M99The first two authors were supported by the DFG-Projekt Niedrigdimensionale Topologie und geometrisch-topologische Methoden in der Gruppentheorie. The first author was supported by the RFFI grant 02-01-99252 and the grant N7 of RAS in the 6-th competition of projects of young scientists. The second author was partially supported by the Support of Leading Scientifical Schools, 00-15-96059 (2000–2002) and by the RFFI grant 01-01-00583 (2001–2003). This work was partially done during the visits of the first and the second authors to the Fakultät für Mathematik, Ruhr-Universität Bochum, Germany in August 2001, and the visit of the third author to the mathematical department of the Moscow State University in 2001/02. This visit was supported by the Johann Gottfried Herder Stiftung.in final form: 18 July 2003     

Any 3-manifold 1-dominates at most finitely many 3-manifolds of -geometry

Any 3-manifold 1-dominates at most finitely many 3-manifolds supporting geometry.

     

The minimal number of roots of surface mappings and quadratic equations in free groups

Let be a continuous mapping between orientable closed surfaces of genus h and g and let c denote the constant map with . Let be the minimal number of roots of f' among all maps f' homotopic to f, i.e. . We prove that where and denotes the Euler characteristic. In addition, certain quadratic equations in free groups closely related to the coincidence problem are solved. Received January 26, 1999; in final form November 8, 1999 / Published online February 5, 2001     

Overcoming Kinetic Limitations of Electron Injection in the Dye Solar Cell via Coadsorption and FRET

A new, extremely simple concept for the use of energy transfer as a means to the enhancement of light absorption and current generation in the dye solar cell (DSC) is presented. This model study is based upon a carboxy‐functionalized 4‐aminonaphthalimide dye (carboxy‐fluorol) as donor, and (NBu₄)₂[Ru(dcbpy)₂(NCS)₂] (N719) as acceptor chromophores. A set of three different devices is assembled containing either exclusively carboxy‐fluorol or N719, or a mixture of both. This set of transparent devices is characterized via IV‐measurements under AM1.5G and monochromatic illumination and their light‐harvesting and external quantum efficiencies (LHE and EQE, respectively) are determined as well. It is shown that the device containing only the donor chromophore has a marginal power conversion efficiency, thus indicating that carboxy‐fluorol is a poor sensitizer for the DSC. Cyclovoltametric measurements show that the poor sensitization ability arises from the kinetic inhibition of electron injection into the TiO₂ conduction band. Comparing the spectral properties of the DSCs assembled presently, however, demonstrates that light absorbed by carboxy‐fluorol is almost quantitatively contributing to the photocurrent if N719 is present as an additional sensitizer. In this case, N719 acts as a catalyst for the sensitization of TiO₂ by carboxy‐fluorol in addition to being a photosensitizer. Evaluation of the maximum output power under blue illumination shows that the introduction of an energy‐donor moiety via coadsorption, leads to a significant increase in the monochromatic maximum output power. This result demonstrates that energy transfer between coadsorbed chromophores could be useful for the generation of current in dye‐sensitized solar cells.     

On finding compromise solutions in multicriteria problems using the fuzzy min-operator

This paper presents an application of fuzzy approaches to the linear vectormaximum problem. It shows that using the fuzzy min-operator together with linear as well as special nonlinear membership functions the obtained solutions are always compromise solutions of the original multicriteria problem.