Remarks on principal factors in a relative cubic field

AbstractThis work supplements an earlier paper in this journal (Vol. 2, 1970, pp. 7–21) on “principal factors” (essentially principal ramified ideals) in the pure cubic k3 = Q(n13) over Q. The ideas are extended to the Kummer field k6 = k3(ϱ) over the cyclotomic cubic k2 = Q(ϱ). Here the Hilbert theory brings in the nonexistence of a unit in k6 of relative norm ϱ. As a typical result, for n = q (prime) ≡ 2,5 (mod 9), the principal factor must exist in k6 and k3, leading to the solvability of the norm equation x3 + qy3 + q2z3 − 3qxyz = 3. Also for n = q ≡ −1 (mod 9), there is a unit of relative norm ϱ when the class number of k3 is not ≡ 0 (mod 3)

Tame kernels and further 4-rank densites

There has been recent progress on computing the 4-rank of the tame kernel $K_2(\mathcal{O}_F)$ for $F$ a quadratic number field. For certain quadratic number fields, this progress has led to "density results'' concerning the 4-rank of tame kernels. These results were first mentioned in \cite{CH} and proven in \cite{RO}. In this paper, we consider some additional quadratic number fields and obtain further density results of 4-ranks of tame kernels. Additionally, we give tables which might indicate densities in some generality.Comment: 20 page

Mean winter conditions and quasi-stationary Rossby waves associated with the winter frequency of warm and cold nights in subtropical Argentina

El estudio busca definir las condiciones medias de la circulación troposférica y posibles forzantes asociados a la frecuencia de ocurrencia de noches frías (TN10) y noches cálidas (TN90) durante el invierno austral (JJA) sobre Argentina subtropical, al norte de 40°S y adyacencias (ASA) a partir de datos de estaciones meteorológicas y de reanálisis (NCEP/DOE AMIP-II y ECMWF ERA-interim). Se encuentra que la frecuencia de noches cálidas (Tmin superiores al percentil 90, TN90) está modulada interanualmente por la propagación de ondas cuasi-estacionarias (OCE) de Rossby inducidas por anomalías de convección en el Índico y el Pacífico. La alta frecuencia de noches cálidas está asociada a calentamiento anómalo del Pacífico central ecuatorial (fase positiva del El Niño-Oscilación del Sur, ENOS). La baja frecuencia de noches cálidas está relacionada con convección anómala sobre el área monzónica de la India y el Índico sur tropical occidental. Esto favorece la propagación de actividad de OCE de Rossby sobre el Índico, el Pacífico y el sur de Sudamérica. Tal teleconexión a su vez favorece la alta frecuencia de noches frías (Tmin inferiores al percentil 10, TN10). En cambio la baja frecuencia de noches frías está vinculada a variabilidad de baja frecuencia del modo de variabilidad de altas latitudes del hemisferio sur (el MAS). Se encuentra que el fortalecimiento (debilitamiento) del jet subtropical sobre Sudamérica y océanos adyacentes caracteriza los inviernos con alta (baja) frecuencia de noches frías (cálidas) en ASA. Los forzantes remotos encontrados involucran procesos atmosféricos/oceánicos que se interconectan interestacionalmente, lo cual podría permitir desarrollar el pronóstico estadístico-dinámico para invierno de alta o baja frecuencia de noches frías o cálidas en invierno.The study aims to examine the mean conditions of the tropospheric circulation and possible forcing associated with the occurrence frequency of cold nights (TN10) and warm nights (TN90) during winter (JJA) over subtropical Argentina, to the north of 40°S and surrounding areas (ASA) from meteorological stations and (NCEP/DOE AMIP-II and ECMWF ERA-interim) reanalysis data. It is found that the frequency of warm nights (Tmin over percentile 90, TN90) is modulated at interannual scales by quasi-stationary wave propagation induced by convection anomalies in the Indic and Pacific. The high frequency of warm nights is associated with anomalous warming over the central equatorial Pacific (positive phase of El Niño-Southern Oscillation, ENSO). The low frequency of warm nights is linked to anomalous convection over the monsoon Indian area and the western tropical southern Indic. Hence quasi-stationary Rossby wave activity propagation is favored over the Indic, Pacific and southern South America. Such a teleconnection favors in turn the high fequency of cold nights (Tmin below percentile 10, TN10). Instead, the low frequency of cold nights is linked to the low-frequency variability of the Southern Hemisphere high-latitude mode (SAM). It is found that winters with high (low) frequency of cold (warm) nights are characterized by a strengthening (weakening) of the subtropical jet over southern South America and adjacent areas. The current remote forcings are related with atmospheric/oceanic processes that are interconnected at seasonal-interseasonal scales, which could allow us to develop statistical-dynamical forecasts for the higher or lower occurrence of warm or cold nights in winter.Fil: Agosta Scarel, Eduardo Andres. Pontificia Universidad Católica Argentina "Santa María de Los Buenos Aires"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Barrucand, Mariana Graciela. Pontificia Universidad Católica Argentina "Santa María de Los Buenos Aires"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Long-lasting floods buffer the thermal regime of the Pampas

This work was funded by grants from the National Research Council of Argentina (CONICET), the International Research Development Centre [IDRC-Canada, Project 106601-001], ANPCyT [PRH 27 [PICT 2013-2973; PICT 2014-2790], and the Inter-American Institute for Global Change Research [IAI, CRN II 2031], which is supported by the US National Science Foundation[Grant number 448 GEO-0452325]. We thank Dr. Horacio Zagarese from INTECH for the lagoon temperature dataset provided. We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.Peer reviewedPostprin

Summer seasonal predictability of warm days in Argentina: statistical model approach

Predicting extreme temperature events can be very useful for different sectorsthat are strongly affected by their variability. The goal of this study is toanalyze the influence of the main atmospheric, oceanic, and soil moistureforcing on the occurrence of summer warm days and to predict extremetemperatures in Argentina northern of 40°S by fitting a statistical model. In apreliminary analysis, we studied trends and periodicities. Significant positivetrends, fundamentally in western Argentina, and two main periodicities ofsummer warm days were detected: 2?4 years and approximately 8 years.Lagged correlations allowed us to identify the key predictors: ElNiño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), andStandardized Precipitation Indices (SPI). We also noticed that the frequency ofwarm days in spring acts as a good predictor of summer warm days. Due to thecollinearity among many predictors, principal component regression was usedto simulate summer warm days. We obtained negative biases (i.e., the modeltends to underestimate the frequency of summer warm days), but the observedand simulated values of summer warm days were significantly correlated,except in northwest Argentina. Finally, we analyzed the predictability of thesummer warm days under ENSO neutral conditions, and we found newpredictors: the geopotential height gradient in 850 hPa (between the AtlanticAnticyclone and the Chaco Low) and the Atlantic Multidecadal Oscillation(AMO), while the PDO and SPI lost some relevance.Fil: Collazo, Soledad Maribel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; ArgentinaFil: Barrucand, Mariana Graciela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; ArgentinaFil: Rusticucci, Matilde Monica. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentin

Variability and predictability of winter cold nights in Argentina

Extreme cold events can cause crop damage as well as an increase in energy demand and even in the mortality rate. Identifying the atmospheric processes associated with the occurrence of these extremes would allow decision-makers to implement preventive and mitigation actions. The goal of this study is to identify predictors of cold extremes of minimum temperature during winter in Argentina (north of 40 °S), and their modulation by the different El Ni~no-Southern Oscillation (ENSO) phases for the period 1970?2015. Lagged correlation analysis between winter cold nights and several global and regional climate indices identified ENSO, subtropical jet intensity, position and intensity of the South Pacific Anticyclone (SPA), and a blocking index as the dominating forcings. The El Niño phase is associated with a decrease in the occurrence of cold extremes. In addition, an increase in the number of blocking events together with a weaker subtropical jet and, a less intense and northward shift of the SPA also inhibit the occurrence of cold extremes of the minimum temperature. Our results indicate persistence in the winter cold nights series compared with the previous season in eastern Argentina. Twowinters with opposite extreme conditions (high and low frequency of cold nights) were selected as case studies. Since both cases occurred under ENSO neutral conditions, we also searched for cold nights predictors consideringonly neutral years. We detected the presence of an equivalent barotropic structure located in southeastern Pacific in both events, which confirmed the importance of the SPA intensity and blocking events as predictors in absenceof an active El Niño.Fil: Collazo, Soledad Maribel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Barrucand, Mariana Graciela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rusticucci, Matilde Monica. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Association between El Niño and extreme temperatures in southern South America in CMIP5 models. Part 1: model evaluation in the present climate

Climate variability might temporarily improve or mitigate the effects of increasingglobal warming. Understanding and estimating internal variability is just as important as understandingthe role of anthropogenic forcing, as the combination of both drives climate events in thereal world. The objective of this work is to analyze the relationship between the SST of the equatorialPacific and 4 extreme temperature indices in southern South America considering griddedobservational data (HadEX3), reanalyses (ERA-Interim, NCEP1, NCEP2), and global climatemodels participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5) in the historicalperiod 1979−2005. For this, correlations and quantile regression for the 90th percentilewere estimated between the variables. Moreover, to assess the performance of the reanalysis andCMIP5 models, multiple metrics were calculated. The observations showed that warm conditionsin the equatorial Pacific are mainly associated with a higher occurrence of warm nights in thenorth and center of Argentina and Chile in winter and spring. However, the different reanalysesconsidered in this study showed discrepancies in representing these relationships. Several CMIP5models were generally able to simulate correlation patterns for the warm extremes of the minimumand maximum temperature in comparison to HadEX3. These types of studies are critical tounderstanding whether climate models simulate temperature extremes in association with physicalprocesses, providing greater confidence in their future projections.Fil: Collazo, Soledad Maribel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Barrucand, Mariana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; ArgentinaFil: Rusticucci, Matilde Monica. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Predictibilidad estacional de los extremos de temperatura en Argentina a partir de la circulación atmosférica de gran escala

Las variaciones en la temperatura de la superficie del mar (SST), en particular del Océano Atlántico y Pacifico, tienen influencia sobre el sistema climático provocando cambios en los patrones de circulación atmosférica. El Niño – Oscilación del Sur (ENSO), es el mayor modo de variabilidad en el Pacifico Tropical, causando variaciones interanuales en el clima de todo el mundo. Sin embargo, existen otros modos de variabilidad que también son importantes ya que influyen sobre la temperatura y precipitación de Sudamérica. En el presente trabajo se analizó la habilidad para predecir extremos de temperatura en la Argentina al norte de 40°S de los siguientes modos de variabilidad climáticos: Modo anular del Sur (SAM), Dipolo del Océano Indico (IOD), Oscilación Decadal del Pacífico (PDO) y la Oscilación Multidecádica del Atlántico (AMO). Para ello, se calcularon y testearon estadísticamente las correlaciones desfasadas entre cada uno de los modos climáticos y distintos índices representativos de los extremos de temperatura promediados trimestralmente en el periodo 1970-2015. Estos índices de extremos de temperatura, globalmente utilizados, son: noches frías (TN10), noches cálidas (TN90), días fríos (TX10), días cálidos (TX90) y el número de días con heladas (NDH).Eje: Ciencias de la Atmósfera y los Océanos.Facultad de Ciencias Astronómicas y Geofísica

Threefield identities and simultaneous representations of primes by binary quadratic forms

Kaplansky [2003] proved a theorem on the simultaneous representation of a prime $p$ by two different principal binary quadratic forms. Later, Brink found five more like theorems and claimed that there were no others. By putting Kaplansky-like theorems into the context of threefield identities after Andrews, Dyson, and Hickerson, we find that there are at least two similar results not on Brink's list. We also show how such theorems are related to results of Muskat on binary quadratic form