Boosting the feasibility pump

The feasibility pump (FP) has proved to be an effective method for finding feasible solutions to mixed integer programming problems. FP iterates between a rounding procedure and a projection procedure, which together provide a sequence of points alternating between LP feasible but fractional solutions, and integer but LP infeasible solutions. The process attempts to minimize the distance between consecutive iterates, producing an integer feasible solution when closing the distance between them. We investigate the benefits of enhancing the rounding procedure with a clever integer line search that efficiently explores a large set of integer points. An extensive computational study on benchmark instances demonstrates the efficacy of the proposed approach.     

Interval methods as a simulation tool for the dynamics of biological wastewater treatment processes with parameter uncertainties

This paper presents sophisticated interval algorithms for the simulation of discrete-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Since naive implementations of interval algorithms might lead to guaranteed enclosures of all system states which are too conservative to be practically useful, we present algorithmic extensions of classical approaches which are applicable to the simulation of non-cooperative systems with time-varying uncertain parameters. Overestimation arising in the interval evaluation of dynamical system models due to the wrapping effect is reduced by an exact pseudo-linear transformation of nonlinear state equations and by new heuristics for the subdivision of interval enclosures which especially prefer splitting of unstable intervals. To highlight the typical procedure for parameterization of interval-based simulation routines and to demonstrate their efficiency, a nonlinear model of biological wastewater treatment processes is discussed. For this application, we consider the maximum specific growth rate of substrate consuming bacteria as a time-varying uncertain parameter. Only worst-case bounds are assumed to be available for the range of this parameter while no information is provided about its actual variation rate.     

On Hardy’s uncertainty principle for connected nilpotent Lie groups

In (Kaniuth and Kumar in Math. Proc. Camb. Phil. Soc. 131, 487–494, 2001) Hardy’s uncertainty principle for was generalized to connected and simply connected nilpotent Lie groups. In this paper, we extend it further to connected nilpotent Lie groups with non-compact centre. Concerning the converse, we show that Hardy’s theorem fails for a connected nilpotent Lie group G which admits a square integrable irreducible representation and that this condition is necessary if the simply connected covering group of G satisfies the flat orbit condition.     

On the Eigenvalues of Half‐Linear Boundary Value Problems

We consider the half‐linear boundary value problem where and the weight function q is assumed to change sign. We prove the existence of two sequences , of eigenvalues and derive asymptotic estimates for as .     

On permutations of central quadrics which preserve an inner distance

Letq be a regular quadratic form on a vector space (V, $\mathbb{F}$ ) and assume dimV ≥ 4 and ¦ $\mathbb{F}$ ¦ ≥ 4. We consider a permutation ? of the central affine quadric $\mathcal{F}$ := {x εV ¦q(x) = 1} such that $$(*)x \cdot y = \mu \Leftrightarrow x^\varphi \cdot y^\varphi = \mu \forall x,y\varepsilon \mathcal{F}$$ holds true, where μ is a fixed element of $\mathbb{F}$ and where “·” is the scalar product associated withq. We prove that ? is induced (in a certain sense) by a semi-linear bijection (σ,?): (V, $\mathbb{F}$ ) → (V, $\mathbb{F}$ ) such thatq o ?o q, provided $\mathcal{F}$ contains lines and the pair (μ, $\mathbb{F}$ ) has additional properties if there ar no planes in $\mathcal{F}$ . The cases μ,≠ 0 and μ = 0 require different techniques.     

Phase-locked ultrashort pulse trains at separate and independently tunable wavelengths

The generation and characterization of femtosecond pulses at three independently tunable visible wavelengths is reported. Selected spectral portions of a common continuum generated in sapphire are amplified in noncollinear optical parametric amplifiers. The phase relation of the pulse trains is analyzed with a nonlinear interferometer based on coherent anti-Stokes Raman scattering and is found to be locked to better than 250 mrad rms. Small spectral shifts of the pulses lead to interference behavior that is consistent with 1 kHz frequency combs.     

Über Eigenwerte und Eigenfunktionen einer Klasse von nichtselbstadjungierten Randwertproblemen

Ohne Zusammenfassung