Acknowledgements My deepest thanks go to Tim Römer for his guidance into mathematics and mathematical life since many years now, his support and encouragement during all that time. I wish to thank Winfried Bruns for his interest and many warm and refreshing conversations. I thank Christof and Jochen for always listening to my more or more often less exigent problems. I would also like to thank ...

The possibility of obtaining intervillous blood from pregnant women has made it feasible to study the placental exchange of various substances. Those which are perhaps most vital, i.e. oxygen and carbon dioxide, have already been studied to some extent (Prystowsky, 1957, 1958, 1959, 1960; Prystowsky, Hellegers and Bruns, 1960; Walker, 1959; Sjostedt, Rooth and Caligara, 1960; Rooth, Sjostedt an...

Mycoheterotrophic plants provide fascinating evolutionary narratives. Examples include convergent evolution of traits such as miniscule seeds, shortened and thickened roots, narrow mycorrhizal speci fi city, and self-fertilization (Leake 1994 ) . Another example is provided by the patterns of decay of the photosynthetic machinery (DePamphilis and Palmer 1990 ; Barrett and Freudenstein 2008 ; De...

ectomycorrhizal community change over a nitrogen deposition gradient in Alaska. Ecology 83: 104–115. Lumbsch HT, Buchanan PK, May TW, Mueller GM. 2008. Phylogeography and biogeography of fungi. Mycological Research 112: 423–424. Matheny PB, Aime MC, Bougher NL, Buyck B, Desjardin DE, Horak E, Kropp BR, Lodge DJ, Soytong K, Trappe JM et al. 2009. Out of the palaeotropics? Historical biogeography...

Given a minimal set of generators x of an ideal I of height d in a regular local ring (R,m, k) we prove several cases for which the map Kd(x;R) ⊗ k → Tord (R/I, k) is the 0-map. As a consequence of the order ideal conjecture we derive several cases for which Kd+i(x;R)⊗ k → Tord+i(R/I, k) are 0-maps for i ≥ 0. In order to solve the syzygy problem in the equicharacteristic case Evans and Griffith...

This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

Let sν ◦ sµ denote the plethystic product of Schur functions and sµ. In this article we define an explicit polynomial representation corresponding to with basis indexed by certain ‘plethystic’ semistandard tableaux. Using these representations prove generalizations four results on plethysms due Bruns–Conca–Varbaro, Brion, Ikenmeyer authors. particular, give a sufficient condition for multiplici...

This article presents a discussion of the literary fragment and introduces work Olivia Dresher, an American anthologist, musician, diarist, who has adopted Twitter as support for her intimate writings 2009. preamble works background to exclusive interview with writer reproduced here, through which we learn about Dresher’s formative years, thoughts fragment, implications writing on social media....