The Loewner differential equation and slit mappings

We show that the Loewner equation generates slits if the driving term is Hölder continuous with exponent 1/2 and small norm and that this is best possible.

     

Measurements of edge-uncolorability

Cubic bridgeless graphs with chromatic index four are called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other. For k=2,3, let c_k be the maximum size of a k-colorable subgraph of a cubic graph G=(V,E). We consider r₃=|E|−c₃ and . We show that on one side r₃ and r₂ bound each other, but on the other side that the difference between them can be arbitrarily large. We also compare them to the oddness ω of G, the smallest possible number of odd circuits in a 2-factor of G. We construct cyclically 5-edge connected cubic graphs where r₃ and ω are arbitrarily far apart, and show that for each 1c<2 there is a cubic graph such that ωcr₃. For k=2,3, let ζ_k denote the largest fraction of edges that can be k-colored. We give best possible bounds for these parameters, and relate them to each other.     

Variation of the conformal radius

We study the change of the conformal radiusr(U) of a simply connected planar domainU versus the subdomainU _ε consisting of the points of distance at least ε to ∂U. We show that the smallest exponent λ such thatr(U)-r(U _t)=0(e ^λ) satisfies 0.59<λ<0.91. We also show that a well-known conjecture implies . Partially supported by NSF Grant DMS-9970398.     

Petersen Cores and the Oddness of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. We study lists by three 1‐factors, and call with a ‐core of G. If G is not 3‐edge‐colorable, then . In Steffen (J Graph Theory 78 (2015), 195–206) it is shown that if , then is an upper bound for the girth of G. We show that bounds the oddness of G as well. We prove that . If , then every ‐core has a very specific structure. We call these cores Petersen cores. We show that for any given oddness there is a cyclically 4‐edge‐connected cubic graph G with . On the other hand, the difference between and can be arbitrarily big. This is true even if we additionally fix the oddness. Furthermore, for every integer , there exists a bridgeless cubic graph G such that .     

Development of a Miniaturized Energy Converter Without Moving Parts

New developments in portable electrical and mechanical devices have created demand for increasing amounts of energy and thus new ways of supplying energy. The high energy density of hydrocarbon fuels are a possible way to solve this issue. This paper deals with the development of an adapted thermodynamic concept for a micro energy converter based on the thermoelectric effect. Developing a PowerMEMS device that does not contain any moving parts is the main design feature. In the proposed concept liquid hydrocarbon fuel, such as methanol, is evaporated in a micro evaporator, mixed with air, and combusted in a micro combustion chamber. The combustion process is assisted by catalytically coated microfibers. Electrical power can be generated by a thermoelectric generator, which is located between the hot combustion zone and the cold micro evaporator. This arrangement leads to large temperature differences between hot and cold junctions, which is necessary for efficient thermoelectric energy conversion and hence power generation. For a more detailed investigation of thermal boundary conditions and interior thermal management, in-situ temperature measurements of the combustor walls are performed using thermographic phosphors.     

Stable categories of higher preprojective algebras

We introduce (n+1)$(n+1)$-preprojective algebras of algebras of global dimension n$n$. We show that if an algebra is n$n$-representation-finite then its (n+1)$(n+1)$-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)$(n+1)$-preprojective algebra is (n+1)$(n+1)$-Calabi–Yau, and, more precisely, it is the (n+1)$(n+1)$-Amiot cluster category of the stable n$n$-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)$(n+1)$-cluster tilting object. We show that even if the (n+1)$(n+1)$-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}$n\in \{1,2\}$) the results above still hold for the stable category of Cohen–Macaulay modules.     

BSDEs driven by time-changed Lévy noises and optimal control

We study backward stochastic differential equations (BSDEs) for time-changed Lévy noises when the time-change is independent of the Lévy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for linear BSDEs and a comparison principle. BSDEs naturally appear in control problems. Here we prove a sufficient maximum principle for a general optimal control problem of a system driven by a time-changed Lévy noise. As an illustration we solve the mean–variance portfolio selection problem.     

Powder compaction. Experiments,modeling and simulation

Field-assisted sintering technology (FAST) is a combined thermal and mechanical loading process to compact and sinter a powder material within one process step. In this short essay a constitutive model of thermo-viscoplasticity is proposed representing most of the phenomena observed in the experiments. The constitutive model is calibrated to the experimental data and some predicted experiments are compared with constitutive model showing appropriate results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral approximation of Wiener-Hopf operators with almost periodic generating function

The paper deals with spectral approximation of Wiener-Hopf operators acting on L^p -spaces by their

finite sections. The generating functions of the Wiener-Hopf operators are supposed to be continuous plus almost

periodic.While the usual spectra of the finite sections drastically fail to converge to the spectrum of the Wiener-Hopf

operator,it turns out that other spectral approximants, viz. the pseudospectra and the numerical ranges, do converge

perfectly.The proof requires a modified approach to the finite section method for Wiener-Hopf operators. This note

generalizes results obtained by Böttcher, Grudsky and Silbermann for the case of continuous generating

functions.