The Laplace transform on time scales revisited

In this work, we reexamine the time scale Laplace transform as defined by Bohner and Peterson [M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001; M. Bohner, A. Peterson, Laplace transform and Z-transform: Unification and extension, Methods Appl. Anal. 9 (1) (2002) 155-162]. In particular, we give conditions on the class of functions which have a transform, develop an inversion formula for the transform, and further, we provide a convolution for the transform. The notion of convolution leads to considering its algebraic structure—in particular the existence of an identity element—motivating the development of the Dirac delta functional on time scales. Applications and examples of these concepts are given.     

A convenient synthesis of sulfonylureas from carboxylic acids and sulfonamides via an in situ Curtius rearrangement

A one-pot reaction of carboxylic acids with sulfonamides to afford sulfonylureas is described.     

Pseudo-Anosov foliations on periodic surfaces

We study lifts of the stable foliation of a pseudo-Anosov diffeomorphism to abelian covers. Under certain conditions, we show that it is ergodic but not uniquely ergodic and describe the ergodic measures.     

Mean curvature flow with a forcing term in minkowski space

We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending on the boundary conditions at infinity. It is a pleasure to thank my PhD advisors Klaus Ecker and Gerhard Huisken for their assistance and encouragement. I also thank Maria Athanassenas, Oliver Schnürrer and Marty Ross for their interest and useful comments, and the Max Planck Gesellschaft for financial support.     

Synthesis of 2H-pyrroles via the 1,3-dipolar cycloaddition reaction of nitrile ylides with acrylamides

3,4-Dihydro-2H-pyrrole derivatives were synthesized by the 1,3-dipolar cycloaddition reaction of nitrile ylides with acrylamides. Acrylamide substitution patterns and benzimidoyl chloride equilibration were investigated.     

Adhesion studies of latex film surfaces on the meso- and nanoscale

In this paper the effects of surface roughness and annealing temperature (T) of latex coating films on adhesion are discussed for the different stages of the film formation process. The surface free energy of latex films was assessed in terms of practical work of adhesion (W) (or adherence) using a custom-built adhesion-testing device (ATD), atomic force microscopy (AFM), and contact angle measurements. For preannealed latex films surface roughness averages (R_a) were determined from AFM height images and were related to the values of W obtained from ATD measurements at room temperature. The results obtained using these tests exhibiting surface behavior on different length scales indicate a dependence of the measured adhesion on surface roughness and temperature, as well as on the length scale of the measurements.First preannealed samples were studied, which were obtained by heat treatment above the respective glass transition temperatures (T_g). Increasing the temperature of preannealing resulted in a decrease of the adherence observed in ATD experiments at room temperature. However, on the nanoscale, using AFM, no significant variation of the adherence was observed. This observation can be explained by roughness arguments. Preannealing decreases roughness which results in lower adherence values measured by ATD while for essentially single asperity AFM experiments roughness has an insignificant effect. Specimens were also annealed over a constant period of time (90 min) at different temperatures. At the end of the heat treatment, adhesion was measured at the treatment temperature by ATD. The amplified effect of temperature observed in this case on adherence is attributed to the combination of roughness decrease and increasing test temperature. In a third set of experiments completely annealed samples were studied by ATD as well as by AFM as a function of temperature. With increasing T values ATD showed a decrease in adherence, which is attributed to a decreasing surface free energy of the annealed films at elevated T values. AFM, on the other hand, showed an opposite trend which is assigned to increasing penetration of the tip into the tip/wetting polymer samples versus increasing temperature. Finally, annealing isotherms as a function of time were investigated by ATD in situ at different temperatures. This last set of experiments allowed us to optimize annealing time and temperature to achieve complete curing.     

New interpretations of XPS spectra of nickel metal and oxides

A current interpretation of XPS spectra of Ni metal assumes that the main 6 eV satellite is due to a two hole c3d⁹4s² (c is a core hole) final state effect. We report REELS observation in AES at low voltages of losses (plasmons and inter-band transitions) corresponding to the satellite structures in Ni metal 2p spectra. The satellite near 6 eV is attributed to a predominant surface plasmon loss. A current interpretation of Ni 2p spectra of oxides and other compounds is based on charge transfer assignments of the main peak at 854.6 eV and the broad satellite centred at around 861 eV to the cd⁹L and the unscreened cd⁸ final-state configurations, respectively (L is a ligand hole). Multiplet splittings have been shown to be necessary for assignment of Fe 2p and Cr 2p spectral profiles and chemical states. The assignments of Ni 2p states are re-examined with intra-atomic multiplet envelopes applied to Ni(OH)₂, NiOOH and NiO spectra. It is shown that the free ion multiplet envelopes for Ni²⁺ and Ni³⁺ simulate the main line and satellite structures for Ni(OH)₂ and NiOOH. Fitting the NiO Ni 2p spectral profile is not as straightforward as the hydroxide and oxyhydroxide. It may involve contributions from inter-atomic, non-local electronic coupling and screening effects with multiplet structures significantly different from the free ions as found for MnO. A scheme for fitting these spectra using multiplet envelopes is proposed.