Milnor algebras could be isomorphic to modular algebras

We find and describe unexpected isomorphisms between two very different objects associated to hypersurface singularities. One object is the Milnor algebra of a function, while the other object associated to a singularity is the local ring of the flatness stratum of the singular locus in a miniversal deformation, an invariant of the contact class of a defining function. Such isomorphisms exist for unimodal hypersurface singularities. However, for the moment it is badly understood, which principle causes these isomorphisms and how far this observation generalises. Here we also provide an algorithmic approach for checking algebra isomorphy.Comment: 15 pages, 1 table Correction of the proof of lemma/proposition 4.2. Elimination of some inaccuracies and errors in section 5 (Now Appendix B

Closure and commutability results for Gamma-limits and the geometric linearization and homogenization of multi-well energy functionals

Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family. Its $\Gamma$-limit is the limit of the $\Gamma$-limits of the original problems. This result not only provides a common basic principle for a number of linearization and homogenization results in elasticity theory. It also allows for new applications as we exemplify by proving that geometric linearization and homogenization of multi-well energy functionals commute

Nearest Points on Toric Varieties

We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the $A$-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.Comment: 20 page

Nach 1995 deutliche Wachstumsschwäche der deutschen Wirtschaft im internationalen Vergleich

Im Folgenden werden ausgewählte Ergebnisse einer neuen Datenquelle zur Messung von Wachstum und Produktivität im internationalen Vergleich präsentiert. Die Informationen decken den Zeitraum von 1970 bis 2004 ab. Sie zeigen, dass Deutschland seine langjährige Wachstumsführerschaft in Europa im Laufe der 90er Jahre verloren hat. Die aktuellen gesamtwirtschaftlichen Daten für 2006 sowie die Schätzungen für 2007 und 2008 deuten allerdings darauf hin, dass Deutschland mittlerweile wieder Anschluss an die Entwicklung in den übrigen Ländern der EU gewonnen hat.Growth, Productivity, European Union

Germany 2007: Undiminished High Construction Production and Increased Construction Prices

After the high growth of 2006, the first quarter of 2007 also shows undiminished high construction production. Evidence of this is provided by the number of hours worked, which see growth rates in double figures in all fields of civil and structural engineering; yet it is surprising that growth in industrial construction lagged somewhat. It remains to be seen to what extent the extremely strong increase in the performance of the construction industry reflects demand or simply consistently favourable weather conditions, for there was actually no real winter in the two quarters preceding and following the new year. Data on the finishing industry in the first quarter indicates a lower dynamics - the number of hours worked increased by almost 8%, compared with 24% in the construction industry. This means that the demand for construction work and services related to existing buildings, particularly in housing construction, is not continuing at the high level last achieved.Housing demand, Construction industry, Forecast 2007

Intangibles, Can They Explain the Dispersion in Return Rates?

It is argued that the observed return rates on capital at firm-level have an upward bias if firms are producing with unobserved intangible capital. Using EUKLEED, a comprehensive firm level data base for Germany, this theoretical preposition is proved empirically. Furthermore, making unobserved capital observable the dispersion in return rates reduces dramatically. The results clearly support the assumption that a considerable part of the observed dispersion in return rates among firms can be contributed to unobserved capital formation in intangible capital. Firms with high input in intangibles also have an above average observed rate of return. However, the question to what extent a more intense use of intangibles can be the cause for higher return rates in the sense of both the monopoly-based and the innovation-based explanations is not answered.Intangible capital, Rate of return, Firm-level profitability

Germany's Construction Industry: Stabilization on the Horizon

The construction volume this year will reach a value of just under euro 230 billion _ a drop as compared to 2004 of close to 3%. At approximately 1.5%, the price increase should turn out somewhat higher than the previous year, which means the real construction volume will thus shrink by a good 4%. While the development during the first six months of this year was clearly on the decline, improved demand in the second half of the year makes a recovery likely. After many years of a downward trend, the construction industry could bottom out next year. Even if real construction of new buildings probably will not grow, at least the shrinking process is likely to come to an end. In particular commercial construction is a motor for growth.