The Łojasiewicz Exponent at Infinity of Non-negative and Non-degenerate Polynomials

Let f be a real polynomial, non-negative at infinity with non-compact zero-set. Suppose that f is non-degenerate in the Kushnirenko sense at infinity. In this paper we give a formula for the Łojasiewicz exponent at infinity of f and a formula for the exponent of growth of f in terms of its Newton polyhedron

The combinatorics of plane curve singularities. How Newton polygons blossom into lotuses

This survey may be seen as an introduction to the use of toric and tropical geometry in the analysis of plane curve singularities, which are germs $(C,o)$ of complex analytic curves contained in a smooth complex analytic surface $S$. The embedded topological type of such a pair $(S, C)$ is usually defined to be that of the oriented link obtained by intersecting $C$ with a sufficiently small oriented Euclidean sphere centered at the point $o$, defined once a system of local coordinates $(x,y)$ was chosen on the germ $(S,o)$. If one works more generally over an arbitrary algebraically closed field of characteristic zero, one speaks instead of the combinatorial type of $(S, C)$. One may define it by looking either at the Newton-Puiseux series associated to $C$ relative to a generic local coordinate system $(x,y)$, or at the set of infinitely near points which have to be blown up in order to get the minimal embedded resolution of the germ $(C,o)$ or, thirdly, at the preimage of this germ by the resolution. Each point of view leads to a different encoding of the combinatorial type by a decorated tree: an Eggers-Wall tree, an Enriques diagram, or a weighted dual graph. The three trees contain the same information, which in the complex setting is equivalent to the knowledge of the embedded topological type. There are known algorithms for transforming one tree into another. In this paper we explain how a special type of two-dimensional simplicial complex called a lotus allows to think geometrically about the relations between the three types of trees. Namely, all of them embed in a natural lotus, their numerical decorations appearing as invariants of it. This lotus is constructed from the finite set of Newton polygons created during any process of resolution of $(C,o)$ by successive toric modifications.Comment: 104 pages, 58 figures. Compared to the previous version, section 2 is new. The historical information, contained before in subsection 6.2, is distributed now throughout the paper in the subsections called "Historical comments''. More details are also added at various places of the paper. To appear in the Handbook of Geometry and Topology of Singularities I, Springer, 202

Single-phase line start permanent magnet synchronous motor. Construction and parameters

The paper deals with construction of single-phase line start permanent magnet synchronous motor. Circuit-field single-phase line start permanent magnet synchronous motor model based on the mass production single-phase induction motor was applied in Maxwell ver. 14 program. Various rotor constructions were taken into account. Influence of the rotor construction on the motor properties was examined

Two-directional single-phase synchronous motor

The paper deals with constructions of two-directional two-pole single-phase line start permanent magnet synchronous motor. Circuit-field single-phase line start permanent magnet synchronous motor models were applied in Maxwell ver. 16 program. Various rotor constructions were taken into account. Influence of the rotor construction on the motor properties was examined

Single-phase line start permanent magnet synchronous motor

The paper deals with construction of single-phase line start permanent magnet synchronous motor. Circuit-field model based on the mass production single-phase induction motor was applied in Maxwell ver. 14 program. On the basis of obtained simulation results load characteristics: current, power factor and efficiency against load power were examined. Starting properties were also examined Obtained results of the single-phase line start permanent magnet synchronous motor properties were compared with the induction motor properties

Comparison of Single-Phase Induction Motor and Single-Phase Permanent Magnet Synchronous Motor. Experimental Results

The paper deals with comparison of single-phase induction motor and single-phase permanent magnet synchronous motor. The motors have the same stator cores and different rotors and stator windings. The comparison is based on the experimental results.Artykuł przedstawia porównanie jednofazowego silnika indukcyjnego i jednofazowego silnika synchronicznego z magnesami trwałymi o rozruchu bezpośrednim. Silniki posiadają identyczne pakiety blach stojana i różne wirniki oraz uzwojenia stojana. Wyniki dotyczą badań eksperymentalnych

Porównanie właściwości jednofazowych silników synchronicznych z magnesami trwałymi o ułożeniu magnesów w kształcie w i vv. Badania eksperymentalne

Praca przedstawia porównanie właściwości jednofazowych silników synchronicznych z magnesami trwałymi o rozruchu bezpośrednim. Silniki te mają identyczne magnetowody i uzwojenia stojanów, pręty klatki wirników oraz różne ułożenia magnesów trwałych wewnątrz wirników. Porównanie silników wykonano na podstawie badań eksperymentalnych.The paper deals with comparison of properties of single-phase line start permanent magnet synchronous motors with different permanent magnet shapes. The motors have the same stators, stator windings, rotor bars and different permanent magnets arrangements inside the rotor. The comparison is based on the experimental results

Single-phase line start permanent magnet synchronous motor with skewed stator

The article deals with single-phase line start permanent magnet synchronous motor with skewed stator. Constructions of two physical motor models are presented. Results of the motors running properties are analysed

Single-phase line start permanent magnet synchronous motor. Magnetic circuit constructions

Politechnika Wrocławska Instytut Maszyn, Napędow i Pomiarow Elektrycznych Influence of the permanent magnet assembly on the single-phase permanent magnet synchronous motor on the running motor properties was investigated. Field-circuit synchronous motor models were applied in Maxwell ver. 14. EMF, THD and cogging torque were investigated. The optimum permanent magnet assembly motor solution with the best auxiliary winding parameters was presented

Wpływ sposobu ułożenia magnesów trwałych w wirniku jednofazowego silnika synchronicznego z magnesami trwałymi na jego parametry

W artykule przedstawiono konstrukcje jednofazowych silników synchronicznych z magnesami trwałymi. W programie Maxwell zbudowano modele jednofazowych silników synchronicznych z magnesami trwałymi bazujące na jednofazowym silniku indukcyjnym produkcji seryjnej. Zbadano wpływ sposobu ułożenia magnesów na właściwości silnika. Zaprezentowano parametry eksploatacyjne jednofazowego silnika synchronicznego z magnesami trwałymi o rozruchu bezpośrednim