Construction of noncommutative surfaces with exceptional collections of length 4

Recently de Thanhoffer de V\"olcsey and Van den Bergh classified the Euler forms on a free abelian group of rank 4 having the properties of the Euler form of a smooth projective surface. There are two types of solutions: one corresponding to $\mathbb{P}^1\times\mathbb{P}^1$ (and noncommutative quadrics), and an infinite family indexed by the natural numbers. For $m=0,1$ there are commutative and noncommutative surfaces having this Euler form, whilst for $m\geq 2$ there are no commutative surfaces. In this paper we construct sheaves of maximal orders on surfaces having these Euler forms, giving a geometric construction for their numerical blowups.Comment: 24 pages, see also companion paper arXiv:1811.0881

Embeddings of algebras in derived categories of surfaces

By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some restrictions on those algebras whose derived categories can be embedded into the bounded derived category of a smooth projective surface. This is then applied to obtain explicit results for hereditary algebras.Comment: 13 pages; revised versio

Evaluation, practice and remarks on the IEC 61000-3-2 standard

This paper describes an evaluation,interpretation and discussion of the IEC61000-3-2standard [1]. Since January 2001, this standard isapplied. Some of the directives mentioned in thisreference are liable to interpretations, test conditionsare not well defined and warm up conditions areneglected (except for lamps). In practice, a lot ofsingle phase [2] as well as three phase non linear loadsdo not comply with the standard. All tested devicesshow bad power quality parameters. Using an IEC fullcompliant programmable power source and poweranalyzer, several test set ups are analyzed, withrespect to the IEC61000-3-2 standard.The paper presents some important remarks andconclusions, based on measurements on several singlephase non linear loads

Impact of harmonic voltage distortion on the voltage sag behavior of adjustable speed drives

The behavior of adjustable speed drives under voltage sag conditions and supplied form non-sinusoidal voltage waveforms has received little attention in recent years. This paper shows that voltage harmonic distortion has a major impact on the drive behavior. The impact of voltage sag conditions, including harmonics is represented by means of voltage tolerance curves. To overcome the impact, a fast field weakening control scheme for field oriented induction motor drives is analyzed

Examples violating Golyshev's canonical strip hypotheses

We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomials of polarised varieties. They are given by moduli spaces of rank 2 bundles with fixed odd-degree determinant on curves of sufficiently high genus, hence our Fano examples have Picard rank 1, index 2, are rational, and have moduli. The hypotheses also fail for several other closely related varieties.Comment: 8 pages, 1 table, 1 figur

Advanced nonlinear modelling techniques for switched reluctance machines

This paper gives an overview of different modelling techniques to describe the nonlinear behaviour of both saturated switched reluctance machine (SRM) and power electronic converter. The current research contributes by comparing the de-coupled single-phase superposition method (lookup-tables) with a coupled analysis between drive model in Matlab/Simulink® and finite element model of the SRM motor. Experimental characterization techniques as well as finite element techniques are used to obtain the single-phase flux-linkage data. Transient electromagnetic analysis using the finite element method,coupled with a drive model and optimization strategy in Matlab/Simulink®, results in a more accurate SRM modelling. These results are more accurate because the mutual coupling between different phases is taken into account. Using this direct coupling, a complete analysis of the motor behaviour (local saturation, iron losses, …) can be modelled with the finite element software, keeping the complex drive and control strategy in Matlab/Simulink®.At every time step of the discrete solver, data is exchanged between the drive model and the coupled electric circuit of the finite element analysis.Simulation results are compared with measurements offlux-linkage, torque, phase current and iron losses. Pro’s and contra’s of the coupled and de-coupled modelling technique are discussed

Measuring line parameters of multiconductor cables using a vector impedance meter

In the present paper, a method to measure the parameters of a multiconductor transmission line is given. The method is accurate, straightforward and only needs a single vector impedance meter or equivalent. The method has been applied for frequencies in a range from 20 kHz up to 30 MHz