Some natural properties of constructive resolution of singularities

These expository notes, addressed to non-experts, are intended to present some of Hironaka's ideas on his theorem of resolution of singularities. We focus particularly on those aspects which have played a central role in the constructive proof of this theorem. In fact, algorithmic proofs of the theorem of resolution grow, to a large extend, from the so called Hironaka's fundamental invariant. Here we underline the influence of this invariant in the proofs of the natural properties of constructive resolution, such as: equivariance, compatibility with open restrictions, with pull-backs by smooth morphisms, with changes of the base field, independence of the embedding, etc.Comment: 43 page

MA-IRRI Industrial Extension Program for Small Farm Equipment

This article is part of the seminar-workshop on the “Consequences of Small Farm Mechanization on Production, Employment and Incomes in the Philippines” sponsored jointly by the Ministry of Agriculture, the National Economic and Development Authority, the Philippine Institute for Development Studies and the International Rice Research Institute (IRRI) held on December 1-2, 1983 at Tagaytay City. It discusses the extension programs implemented by the Ministry of Agriculture and IRRI. It then points out areas where policies and actions are likely to be useful.agriculture sector, mechanization

European Wireless 2019; 25th European Wireless Conference. Aarhus, Denmark

This paper describes a new design of Reed-Solomon (RS) codes when using composite extension fields. Our ultimate goal is to provide codes that remain Maximum Distance Separable (MDS), but that can be processed at higher speeds in the encoder and decoder. This is possible by using coefficients in the generator matrix that belong to smaller (and faster) finite fields of the composite extension and limiting the use of the larger (and slower) finite fields to a minimum. We provide formulae and an algorithm to generate such constructions starting from a Vandermonde RS generator matrix and show that even the simplest constructions, e.g., using only processing in two finite fields, can speed up processing by as much as two-fold compared to a Vandermonde RS and Cauchy RS while using the same decoding algorithm, and more than two-fold compared to other RS Cauchy and FFT-based RS

Singularities of locally acyclic cluster algebras

We show that locally acyclic cluster algebras have (at worst) canonical singularities. In fact, we prove that locally acyclic cluster algebras of positive characteristic are strongly F-regular. In addition, we show that upper cluster algebras are always Frobenius split by a canonically defined splitting, and that they have a free canonical module of rank one. We also give examples to show that not all upper cluster algebras are F-regular if the local acyclicity is dropped.Comment: 24 page

Stellar indices and kinematics in Seyfert 1 nuclei

We present spectra of 6 type 1 Seyfert galaxies, 2 Seyfert 2, a starburst galaxy and a compact narrow line radiogalaxy, taken in two spectral ranges centered around the near--IR CaII triplet (CaT) (at ~8600 Angstroms), and the Mgb stellar feature at 5180 Angstroms. We measured the equivalent width (EWs) of these features and the Fe52 and Fe53 spectral indices. We found that the strength of the CaT in type 1 Seyfert galaxies with prominent central point sources, is larger than what would be expected from the observed strength of the blue indices. This could be explained by the presence of red supergiants in the nuclei of Seyfert 1 galaxies. On the other hand, the blue indices of these galaxies could also be diluted by the strong FeII multiplets that can be seen in their spectra. We have also measured the stellar and gas velocity dispersions of the galaxies in the sample. The stellar velocity dispersions were measured using both, the Mgb and CaT stellar features. The velocity dispersion of the gas in the narrow line region (NLR) was measured using the strong emission lines [OIII] 5007, 4959 and [SIII] 9069. We compare the gas and star velocity dispersions and find that both magnitudes are correlated in Seyfert galaxies. Most of the Seyfert 1 we observe have stellar velocity dispersion somehow greater than that of the gas in the NLR.Comment: To appear in MNRAS, 18 pages, 9 figure

The scar mechanism revisited

Unstable periodic orbits are known to originate scars on some eigenfunctions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically close to the initial point. In the energy domain, these recurrences are seen to accumulate quantum density along the orbit by a constructive interference mechanism when the appropriate quantization (on the action of the scarring orbit) is fulfilled. Other quantized phase space circuits, such as those defined by homoclinic tori, are also important in the coherent transport of quantum density in chaotic systems. The relationship of this secondary quantum transport mechanism with the standard mechanism for scarring is here discussed and analyzed.Comment: 6 pages, 6 figure