Quantum curves and q-deformed Painlevé equations

Letters in Mathematical Physics - We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus...     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Characterization of low molecular weight hydrocarbon oligomers by laser desorption/ionization time-of-flight mass spectrometry using a solvent-free sample preparation method.

A new solvent-free sample preparation method using silver trifluoroacetate (AgTFA) was developed for the analysis of low molecular weight paraffins and microcrystalline waxes by laser desorption/ionization time-of-flight mass spectrometry (LDI-TOFMS). Experiments show that spectral quality can be enhanced by dispersing AgTFA directly in liquid paraffins without the use of additional solvents. This preparation mixture is applied directly to the MALDI probe. Solid waxes could be examined by melting prior to analysis. The method also provides sufficiently reproducible spectra that peak area ratios between mono- and bicyclic alkane peaks indicated variations in the cycloalkane content of paraffin samples. Dehydrogenation of hydrocarbons observed during the desorption/ionization process was studied by analysis of alkane standards.     

Design of neutral, mono- or di-cationic water-soluble trihydrazidophosphoradamantanes

The versatile behavior of a trihydrazidophosphoradamantane allowing the synthesis of a variety of neutral, mono- or di-cationic water-soluble molecules of potential interest for biphasic catalysis is reported.     

On the geometry of infinite cyclic subgroups

In this paper we construct an example of a word metric on an infinite cyclic subgroup. This example shows that subexponential distortion does not obstruct non-trivial growth of connected radii. This answers a question of Gromov [6]. The constructed metric has other pathological properies. Specifically, its asymptotic cone depends on the choice of ultrafilter and scaling sequence. The work has been partially supported by the Swiss National Science Foundation.     

IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.     

Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

Asymptotic Analysis of the Current-Voltage Curve of a pnpn Semiconductor Device

We consider the one-dimensional steady-state semiconductor deviceequations modelling a pnpn device. There are two relevant scalingsof the equations corresponding to small and large applied voltages.In both scalings, the semiconductor equations can be consideredas singularly perturbed. It turns out that the small-voltagescaling breaks down for current values between two saturationcurrents. In that interval, the large-voltage scaling has tobe employed. For both scalings, we derive the first-order termsof an asymptotic expansion and show that the reduced problemhas a solution. An example verifies that the current-voltagecurves obtained have the expected qualitative structure.