On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

Singularidades do tipo D(q,p)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dr. A.L. Crelle's calculating tables giving the products of every two numbers from one to one thousand and their application to the multiplication and division of all numbers above one thousand.

Mode of access: Internet.

Properties of photo-cured poly(D,L-lactide) networks

Poly(D,L-lactide) is a degradable polymer with a long history of use in medical applications. It is strong and stiff and degrades over the course of months into lactic acid, a body-own substance. In the field of tissue engineering it is commonly used to fabricate scaffolds. Stereolithography is a high resolution rapid prototyping technique by which designed 3D objects can be built using photo-initiated radical polymerisations. Poly(D,Llactide) (PDLLA) networks can be obtained by photopolymerisation of oligomers functionalised with unsaturated groups. In this work, PDLLA oligomers of varying architectures (arm lengths, numbers of arms) were synthesised and end-functionalised with methacrylate groups. These macromers were photo-crosslinked in solution to yield PDLLA networks of different architectures. The influence of the network architecture on its physical properties was studied.

Occurrence of LINE, gypsy-like, and copia-like retrotransposons in the clonally propagated sweet potato (Ipomoea batatas L.)

Retrotransposons are a class of transposable elements that represent a major fraction of the repetitive DNA of most eukaryotes. Their abundance stems from their expansive replication strategies. We screened and isolated sequence fragments of long terminal repeat (LTR), gypsy-like reverse transcriptase (rt) and gypsy-like envelope (env) domains, and two partial sequences of non-LTR retrotransposons, long interspersed element (LINE), in the clonally propagated allohexaploid sweet potato (Ipomoea batatas (L.) Lam.) genome. Using dot-blot hybridization, these elements were found to be present in the ~1597 Mb haploid sweet potato genome with copy numbers ranging from ~50 to ~4100 as observed in the partial LTR (IbLtr-1) and LINE (IbLi-1) sequences, respectively. The continuous clonal propagation of sweet potato may have contributed to such a multitude of copies of some of these genomic elements. Interestingly, the isolated gypsy-like env and gypsy-like rt sequence fragments, IbGy-1 (~2100 copies) and IbGy-2 (~540 copies), respectively, were found to be homologous to the Bagy-2 cDNA sequences of barley (Hordeum vulgare L.). Although the isolated partial sequences were found to be homologous to other transcriptionally active elements, future studies are required to determine whether they represent elements that are transcriptionally active under normal and (or) stressful conditions.

On the oscillatory behavior of transient Rayleigh Benard convection of air for 2D channel flow at moderate Rayleigh numbers

Unsteady numerical simulation of Rayleigh Benard convection heat transfer from a 2D channel is performed. The oscillatory behavior is attributed to recirculation of ascending and descending flows towards the core of the channel producing organized rolled motions. Variation of the parameters such as Reynolds number, channel outlet flow area and inclination of the channel are considered. Increasing Reynolds number (for a fixed Rayleigh number), delays the generation of vortices. The reduction in the outflow area leads to the later and the less vortex generation. As the time progresses, more vortices are generated, but the reinforced mean velocity does not let the eddies to enter the core of the channel. Therefore, they attach to the wall and reduce the heat transfer area. The inclination of the channel (both positive and negative) induces the generated vortices to get closer to each other and make an enlarged vortex.

Letters and numbers in Excel : fostering student engagement in fundamentals of maths & computing

The television quiz program Letters and Numbers, broadcast on the SBS network, has recently become quite popular in Australia. This paper considers an implementation in Excel 2010 and its potential as a vehicle to showcase a range of mathematical and computing concepts and principles.

J. L. Runebergs samlade skrifter i textkritisk belysning

The Collected Works of J. L. Runeberg from the Viewpoint of Textual Scholarship The theoretical framework of this dissertation builds on textual scholarship. The dissertation explores the history of Runeberg’s publications and his relations with his publishers, from his debut and the first editions, through the editions of collected works published during the course of his life, to the later commercial editions, including the critical edition, published in 1933–2005 by the Svenska Vitterhetssamfundet (The Swedish Society for Belles Lettres) and The Svenska litteratursällskapet i Finland (The Society of Swedish Literature in Finland). The various editions of Runeberg’s collected works are situated in their respective critical traditions, from the 19th century German Ausgabe letzter Hand, to the influence of Anglo-American bibliography on Swedish textual criticism in the late 20th century. By making use of primary material previously not used for research purposes, the author is able to present a new view on Runebergian publishing history, including Runeberg’s fees and his relations with the censor authorities. There are indications that his Finnish publishers could not bear the cost of his sizable fees, that were in proportion neither with the book market in Finland nor with the numbers of copies sold. Apart from a certain body of editions the primary material is comprised of correspondences, publishing contracts, printing house invoices, as well as censor authority records. One of the conclusions drawn is that the early and detailed biography, Biografiska anteckningar om Johan Ludvig Runeberg (Biographical Notes on …) by J. E. Strömborg is not reliable in matters concerning publishing history, and that this work has been used far too uncritically. The history of the critical edition gets a chapter of its own, based on primary material in Swedish and Finnish archives. Finally, the author analyses the critical choices, made primarily in the critical edition, and uses examples from the commercial editions to study the editors’ interventions over time, from the 1850s to the 1920s. The changes to the text are usually small and subtle, but cumulative – and in some cases, crucial for the interpretation of the work. One objective of textual scholarship should be to examine the publishing history of a single work or of an author’s œuvre, and another to pay attention both to changes in a work as such and to the shifts of meaning they might entail.