Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we are able to obtain complete agreement with the results obtained in intrinsic coordinates. In particular, we have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.Comment: Extended version of GRG publication, with some typos etc correcte

2-Engel relations between subgroups

In this paper we study groups G generated by two subgroups A and B such that is nilpotent of class at most 2 for all a¿. A and b¿. B. A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups

Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators

Using the generalised invariant formalism we derive a class of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.Comment: 29 page

Acoustic assessment and distribution of anchovy, sardine and chub mackerel in ICES Subdivision 9a South during the ECOCADIZ-RECLUTAS 2021-10 Spanish survey (October 2020) with notes on the distribution of other pelagic species. Preliminary information.

The present working document summarises a part of the main results obtained during the ECOCADIZ-RECLUTAS 2021-10 Spanish (pelagic ecosystem-) acoustic survey. The survey was conducted by IEO between 21st October and 07th November 2021 in the Portuguese and Spanish shelf waters (20-200 m isobaths) off the Gulf of Cadiz (GoC) onboard the R/V Ramón Margalef. The survey suffered a ten-day delay in relation to the usual starting dates, resulting in ending dates very close to the starting ones of the WGACEGG meeting. Therefore, no acoustic estimates were available at the time of WG meeting. The survey’s main objective is the acoustic assessment of anchovy and sardine juveniles (age 0 fish) in the recruitment areas of the GoC. The 21 foreseen acoustic transects were sampled. A total of 18 valid fishing hauls were carried out for echo-trace ground-truthing purposes. This working document only provides information on the results of these hauls in terms of species-specific occurrences, yields in numbers and weight, size ranges, mean size and mean weight in catches

Products of finite connected subgroups

For a non-empty class of groups L, a finite group G = AB is said to be an L-connected product of the subgroups A and B if e L for all a e A and b e B. In a previous paper, we prove that, for such a product, when L = S is the class of finite soluble groups, then [A, B] is soluble. This generalizes the theorem of Thompson that states the solubility of finite groups whose two-generated subgroups are soluble. In the present paper, our result is applied to extend to finite groups previous research about finite groups in the soluble universe. In particular, we characterize connected products for relevant classes of groups, among others, the class of metanilpotent groups and the class of groups with nilpotent derived subgroup. Additionally, we give local descriptions of relevant subgroups of finite groups

Characterization of the soil of peach orchards in the region of Beira Interior

A cultura do pessegueiro na região da Beira Interior representa 23% da área total de pessegueiro de Portugal continental e 16% da área de culturas permanentes da região. Para a caracterização do potencial edáfico onde se desenvolve a cultura, foi efectuado um trabalho de sistematização dos dados referentes às análises de terra, através das Organizações de Agricultores reconhecidas para a prática da Protecção Integrada e Produção Integrada de Prunóideas (AAPIM, APPIZÊZERE e Cooperativa dos Fruticultores da Cova da Beira). O total das 117 análises disponíveis diz respeito ao conjunto de agricultores que exploram uma área de pessegueiros de 463 ha, o que corresponde a um terço da área total ocupada pela cultura na região (1500 ha). O conjunto dos dados analisados permitiu concluir que os solos são maioritariamente ácidos, apresentando textura grosseira, baixo teor de matéria orgânica e elevados teores de fósforo e potássio assimiláveis na camada superficial.info:eu-repo/semantics/publishedVersio

Continuous and binary sets of responses differ in the field

This paper conducts a pre-registered study aimed to compare binary and continuous set of responses in survey questionnaires. Binary responses consist of two possible opposing response options (Yes/No). Continuous responses are numerical, where respondents can indicate an option on a 0–10 horizontal blind line. We study whether feasible sets of binary and continuous responses yield the same outcome (distribution) and have the same cost (duration in minutes). We collect data from 360 households in Honduras that were randomly assigned to Yes/No questions or given a slider (0–10 visual scale) to mark their responses, therefore, we provide causal evidence. We find that respondents are 13% more likely to respond “Yes” and spend 2.1 min less in the binary setting. Additionally, the results suggest that the type of question matters