Rank one discrete valuations of power series fields

In this paper we study the rank one discrete valuations of the field $k((X_1,..., X_n))$ whose center in k\lcor\X\rcor is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field of coefficients is the residue field of the valuation, and it is given in section 5. The constructions given in these sections are not effective in the general case, because we need either to use the Zorn's lemma or to know explicitly a section $\sigma$ of the natural homomorphism R_v\to\d between the ring and the residue field of the valuation $v$. However, as a consequence of this construction, in section 7, we prove that k((\X)) can be embedded into a field L((\Y)), where $L$ is an algebraic extension of $k$ and the {\em ``extended valuation'' is as close as possible to the usual order function}

Key polynomials for simple extensions of valued fields

Let $\iota:K\hookrightarrow L\cong K(x)$ be a simple transcendental extension of valued fields, where $K$ is equipped with a valuation $\nu$ of rank 1. That is, we assume given a rank 1 valuation $\nu$ of $K$ and its extension $\nu'$ to $L$. Let $(R_\nu,M_\nu,k_\nu)$ denote the valuation ring of $\nu$. The purpose of this paper is to present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo. Namely, we associate to $\iota$ a countable well ordered set $$\mathbf{Q}=\{Q_i\}_{i\in\Lambda}\subset K[x];$$ the $Q_i$ are called {\bf key polynomials}. Key polynomials $Q_i$ which have no immediate predecessor are called {\bf limit key polynomials}. Let $\beta_i=\nu'(Q_i)$. We give an explicit description of the limit key polynomials (which may be viewed as a generalization of the Artin--Schreier polynomials). We also give an upper bound on the order type of the set of key polynomials. Namely, we show that if $\operatorname{char}\ k_\nu=0$ then the set of key polynomials has order type at most $\omega$, while in the case $\operatorname{char}\ k_\nu=p>0$ this order type is bounded above by $\omega\times\omega$, where $\omega$ stands for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519

Memory effect in triglycine sulfate induced by a transverse electric field: specific heat measurement

The influence of a transverse electric field in the specific heat of triglycine sulphate (TGS) has been studied. The specific heat of TGS has been measured heating the sample from ferroelectric to paraelectric phase after prolonged transverse electric field (i.e. perpendicular to the ferroelectric axis). It is shown that the specific heat of TGS can remember the temperature $T_s$ at which the transverse field was previously applied.Comment: ReVTeX4 Twocolumn 4 pages, 4 figure

Information and discrimination in the rental housing market: evidence from a field experiment

This paper investigates the effect of disclosing information on the discriminatory behaviour against immigrants in the Spanish rental market. We conduct a field experiment where emails are sent showing interest on vacant rental apartments. Fictitious applicants whose names represent different ethnic groups send emails with different amount of information about their ability to pay the rent. Our results show that applicants with a Moroccan sounding name are 15 percentage points less likely to be contacted by the property owner than those with a Spanish name. We also find that revealing positive information about the socioeconomic status of the Moroccan candidate increases the probability of being contacted by 8 percentage points. However, the information revealed does not completely eliminate discriminatory behavior, suggesting the presence of negative attitudes towards immigrants.Discrimination, migration, rental market, field experiment

Rental housing discrimination and the persistence of ethnic enclaves

We conduct a field experiment to show that discrimination in the rental market represents a significant obstacle for the geographical assimilation process by immigrants. We employ the Internet platform to identify vacant rental apartments in different areas of the two largest Spanish cities, Madrid and Barcelona. We send emails showing interest in the apartments and signal the applicants’ ethnicity by using native and foreign-sounding names. We find that, in line with previous studies, immigrants face a differential treatment when trying to rent an apartment. Our results also indicate that this negative treatment varies considerably with the concentration of immigrants in the area. In neighbourhoods with a low presence of immigrants the response rate is 30 percentage points lower for immigrants than for natives, while this differential disappears when the immigration share reaches 50%. We conclude that discriminatory practices in the rental housing market contribute to perpetuate the ethnic spatial segregation observed in large cities.immigration, discrimination, spatial segregation.