Femtosecond intermolecular electron transfer in condensed systems

We have investigated the ultrafast intermolecular electron transfer (ET) from an electron-donating solvent (aniline (AN) or N, N-dimethylaniline (DMA)) to an excited dye molecule (oxazines (Nile blue and oxazine 1) or coumarins). A non-exponential time dependence was observed in AN and can be explained by solvent reorientation and nuclear motion of the reactants. However, in DMA, a single exponential process was observed for Nile blue (160 fs) and oxazine 1 (280 fs), which can be explained by assuming that the rate of ET is limited mainly by ultrafast nuclear motion. A clear substituent effect on intermolecular ET was observed for the 7-aminocoumarins. When the alkyl chain on the 7-amino group is extended and a hexagonal ring with the benzene moiety is formed, the rate of ET is reduced by three orders of magnitude. This effect can be explained by a change in the free energy difference of the reaction and by the vibrational motion of the amino group.     

A surface containing a line and a circle through each point is a quadric

We prove that a surface in 3-dimensional Euclidean space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point.     

Codimension Two PL Embeddings of Spheres with Nonstandard Regular Neighborhoods

For a given polyhedron K(?)M,the notation RM(K)denotes a regular neigh- borhood of K in M.The authors study the following problem:find all pairs(m,k) such that if K is a compact k-polyhedron and M a PL m-manifold,then R_M(f(K))≌R_M(g(K))for each two homotopic PL embeddings f,g:K→M.It is proved that R_S~(k 2)(S~k)(?)S~k×D~2 for each k(?)2 and some PL sphere S~k(?)S~(k 2)(even for any PL sphere S~k(?)S~(K 2)having an isolated non-locally flat point with the singularity S~(k-1)(?) S~(k 1)such thatπ_1(S~(k 1)-S~(k-1))(?)Z).     

On the deleted product criterion for embeddability of manifolds in $ \Bbb {R}^m $

Commentarii Mathematici Helvetici - For a space N let $ \tilde N = \{(x,y) \in N \times N|x \neq y \} $ . Let $\Bbb {Z}_2 $ act on Ñ and on $ S^{m-1} $ by exchanging factors and antipodes,...     

An Extension of the Conjugate Directions Method With Orthogonalization to Large-Scale Problems With Bound Constraints

In our previous works a new method of conjugate directions for large-scale unconstrained minimization problems has been presented [1, 2]. In the paper this algorithm is extended to minimization problems with bound constraints. Because the linear minimization along the newly found conjugate vector is not needed for constructing the next conjugate vector and one arbitrarily step-size (not necessarily the optimal one) is calculated along this conjugate direction, we are able to incorporate naturally the bound constraints into the algorithm. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Classification of framed links in 3-manifolds

We present a short and complete proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in detail. Let M be a connected oriented closed smooth 3-manifold, L ₁(M) be the set of framed links in M up to a framed cobordism, and deg: L ₁(M) → H ₁(M; ℤ) be the map taking a framed link to its homology class. Then for each α ∈ H ₁(M; ℤ) there is a one-to-one correspondence between the set deg⁻¹ α and the group ℤ_2d(α), where d(α) is the divisibility of the projection of α to the free part of H ₁(M; ℤ).