An introduction to loopoids

We discuss a concept of loopoid as a non-associative generalization of (Brandt) groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.Comment: 9 pages, proceedings of LOOPS'1

Shaft vibrations in turbomachinery excited by cracks

During the past years the dynamic behavior of rotors with cracks has been investigated mainly theoretically. This paper deals with the comparison of analytical and experimental results of the dynamics of a rotor with an artificial crack. The experimental results verify the crack model used in the analysis. They show the general possibility to determine a crack by extended vibration control

Isomorphisms of algebras of smooth functions revisited

It is proved that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms. It is not required that manifolds are second countable nor paracompact. This solves a problem stated by A. Wienstein. Some related results are discussed as well.Comment: 6 pages, minor changes, the final version to appear in Archiv der Mathemati

Irrational l2-invariants arising from the lamplighter group

We show that the Novikov-Shubin invariant of an element of the integral group ring of the lamplighter group Z_2 \wr Z can be irrational. This disproves a conjecture of Lott and Lueck. Furthermore we show that every positive real number is equal to the Novikov-Shubin invariant of some element of the real group ring of Z_2 \wr Z. Finally we show that the l2-Betti number of a matrix over the integral group ring of the group Z_p \wr Z, p>1, can be irrational, and so the groups Z_p \wr Z become the simplest known groups which give rise to irrational l2-Betti numbers.Comment: 26 pages, 11 figures, v4: changes suggested by a referee (including fixing the proof of Lemma 11); To appear in Groups Geom. Dy

Restriction Testing in Binary Choice Model with I(1) Regressors

This paper deals with the problem of nonstationarity of regressors in binary choice model. The limit distribution of the ML-estimator is mixed normal, but restriction testing shall not be based on standard t-statistic. The results of the conducted Monte Carlo experiment demonstrate that the true size of the restriction test is far from the significance level. Therefore, the t -Student statistic should be modified and this paper proposes its modification. The results of the Monte Carlo investigation point to the superiority of the new statistic.nonstationarity, maximum likelihood, restriction testing

The Financial Indicators Leading Real Economic Activity - the Case of Poland

In many research studies it is argued that it is possible to extract useful information about future real economic activity from the performance of financial markets. However, this study goes further and shows that it is not only possible to use expectations derived from financial markets to forecast future economic activity, but that data about the financial system can be used for this purpose as well. This paper sheds light on the ability to forecast real economic activity, based on additional and different financial variables than what have been presented so far. The research is conducted for the Polish emerging economy on the basis of monthly data. The results suggest that, based purely on the data from the financial system, it is possible to construct reasonable measures that can, even for an emerging economy, effectively forecast future real economic activity. The outcomes are proved by two different econometric methods, namely, by a time series analysis and by a probit model. All presented models are tested in-sample and out-of-sample.forecasting, rational expectations, financial system, term spreads, real economic activity

Lie algebraic characterization of manifolds

Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operators, i.e. isomorphisms of such Lie algebras are induced by the appropriate class of diffeomorphisms of the underlaying manifolds.Comment: 15 page