Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Global review of permian Tyloplecta muir-wood and cooper, 1960 (Brachiopoda): morphology, palaeobiogeographical and palaeogeographical implications

A global review of the stratigraphical and geographical distribution of Tyloplecta reveals that the genus ranges in age from Kungurian to Changhsingian (Middle to Late Permian). Tyloplecta first evolved in South China in the Kungurian (late Early Permian). The genus went through its first diversification in the Guadalupian, suffered a major extinction at the end of the Guadalupian, and re-diversified in the Wuchiapingian. T. yangtzeensis persisted into the Changhsingian as the only survivor of the genus involved in the end-Permian mass extinction. Palaeogeographically, South China is not only the centre of origin for the genus but also an area of diversification and evolution. In addition to South China, Tyloplecta has also been recorded from the Far East Russia, Japan, central Thailand, Laos, Cambodia, Qiangtang Terrane of Tibet, Salt Range, Iran, Armenia, Hungary, Yugoslavia, and Slovenia. This geographic spread suggests that Tyloplecta was primarily restricted to the Palaeotethys and is indicative of warm-water palaeoequatorial conditions. Its presence in some of the northeast Asian terranes (e.g., parts of Japan and Far East Russia) and in the Salt Range (Pakistan) and central and north Iran (part of the Cimmerian microcontinents) demonstrate that the genus invaded the middle palaeolatitudinal regions in both hemispheres during the late Middle Permian in response to increased shallow marine biotic communications between Cathaysia in the eastern Palaeotethys and southern Angaraland, and between Cathaysia and Peri-Gondwanaland. The invasion of Tyloplecta (and some other taxa) into the southern shore waters of Angaraland may be explained by assuming ocean surface current connections and close palaeogeographical proximities between the South China, Sino-Korea and Bureya blocks. In comparison, the invasion of Tyloplecta into the Peri-Gondwanaland region is more likely a result of reduced palaeogeographical distance between South China and Peri-Gondwanaland and the appearance of the Cimmerian microcontinents as migratory stepping stones.

Oligomethylene-bridged dinuclear triorganotin triflates and diphenylphosphinates. Ion pairing in the solid state and electrolytic dissociation in solution of [Ph2Sn(CH2)nSnPh2X](O3SCF3) (X = OH, O2PPh2; n = 1-3)

The condensation of [Ph₂(OH)Sn(CH₂)_nSn(OH)Ph₂] (1-3; n = 1-3) with HO₃SCF₃ and HO₂PPh₂ provided [Ph₂Sn(CH₂)_nSnPh₂(OH)](O₃SCF₃) (4-6; n = 1-3) and [Ph₂(O₂PPh₂)Sn(CH₂)_nSn(O₂PPh₂)Ph₂] (10-12; n = 1-3), respectively. The reaction of [Ph₂Sn(CH₂)_nSnPh₂(OH)](O₃SCF₃) (4-6; n = 1-3) with HO₂PPh₂ and NaO₂PPh₂ gave rise to the formation of [Ph₂Sn(CH₂)_nSnPh₂(O₂PPh₂)](O₃SCF₃) (7-9; n = 1-3) and [Ph₂(OH)Sn(CH₂)_nSn(O₂PPh₂)Ph₂] (13-15; _n = 1-3), respectively. In the solid state, compounds 4-9 comprise ion pairs of cationic cyclo-[Ph₂SnCH₂SnPh₂(OH)]₂²⁺, cyclo-[Ph₂Sn(CH₂)_nSnPh₂(OH)]⁺ (n = 2, 3), and cyclo-[Ph₂Sn(CH₂)_nSnPh₂(O₂PPh₂)]⁺ (n = 1-3) and triflate anions. In MeCN, the eight-membered-ring system cyclo-[Ph₂SnCH₂SnPh₂(OH)]₂²⁺ appears to be in equilibrium with the four-membered-ring system cyclo-[Ph₂SnCH₂SnPh₂(OH)]⁺. In contrast, compounds 10-15 show no ionic character. Compounds 1-15 were characterized by multinuclear NMR spectroscopy in solution and in the solid state, IR spectroscopy, conductivity measurements, electrospray mass spectrometry, osmometric molecular weight determinations, and X-ray crystallography (4, 5, 7, and 12).

Ftir study of ion-pairing effects in plasticized polymer electrolytes

The effect of plasticizer on the ubiquitous ion-pairing observed in polymer electrolytes has been investigated using FTIR as a probe of the local environment of the triflate ion in sodium and lithium triflate based electrolytes. Plasticizers having a range of properties, such as, propylene carbonate, and dimethyl formamide (DMF), have been investigated in the pure state for comparison with the polymer (a random copolymer of ethylene oxide at propylene oxide (mol ratio 3: 1)). The different plasticizers exhibited strikingly different effects on the triflate ion bands normally observed in polyether salt systems. In particular, the cation associated triflate ion bands at 1288 and 1248 cm⁻¹ and the band at 1272 cm⁻¹ which has variously been assigned to the free ion and also to the strongly aggregated anion, are different. PC produces a rapid disappearance of the “free” ion band in favour of the monodentate ion pair. On the other hand, DMF strongly enhances the band near 1270 cm⁻¹ at salt concentrations higher than 0.7 mol kg⁻¹. These observations are discussed in terms of recent ab initio calculations of the triflate vibrational bands.

Juvenile social experience affects pairing success at adulthood: Congruence with the loser effect?

Social interactions with adults are often critical for the development of mating behaviours. However, the potential role of other primary social partners such as juvenile counterparts is rarely considered. Most interestingly, it is not known whether interactions with juvenile females improve males’ courtship and whether, similar to the winner and loser effects in a fighting context—outcome of these interactions shapes males’ behaviour in future encounters. We investigated the combined effects of male quality and juvenile social experience on pairing success at adulthood in zebra finches (Taeniopygia guttata). We manipulated brood size to alter male quality and then placed males in either same- or mixed-sex juvenile dyads until adulthood. We found that males from reduced broods obtained more copulations and males from mixed-sex dyads had more complete courtships. Furthermore, independent of their quality, males that failed to pair with juvenile females, but not juvenile males, had a lower pairing success at adulthood. Our study shows that negative social experience with peers during adolescence may be a potent determinant of pairing success that can override the effects of early environmental conditions on male attractiveness and thereby supports the occurrence of an analogous process to the loser effect in a mating context.

Sequential polyandry through divorce and re-pairing in a cooperatively breeding bird reduces helper-offspring relatedness

Polyandry is an important component of both sexual selection and kin structuring within cooperatively breeding species. A female may have multiple partners within a single reproductive attempt (simultaneous polyandry) or across multiple broods within and/or across years (sequential polyandry). Both types of polyandry confer a range of costs and benefits to individuals and alter the genetic structure of social groups over time. To date, many molecular studies of cooperative breeders have examined the evolution of cooperative breeding in relation to simultaneous polyandry. However, cooperatively breeding vertebrates are iteroparous, and thus sequential polyandry is also likely, but more rarely considered in this context. We examined sequential polyandry in a cooperatively breeding bird that has a low level of within-brood polyandry. Over a 5-year period (2006–2010), we monitored individual mating relationships using molecular markers in a population of individually marked apostlebirds (Struthidea cinerea). Divorce occurred between reproductive seasons in 17 % (8/48) of pairs and appeared to be female-driven. The level of sequential polyandry was also driven by the disappearance of males after breeding, and over 90 % of females, for whom we had suitable data, bred with multiple males over the period of study. This sequential polyandry significantly altered the relatedness of group members to the offspring in the nest. However, in about half of the cases, the second male was related (first- or second-order relative) to the first male of a sequentially polyandrous female and this alleviated the reduction in relatedness caused by polyandry. Our findings suggest that even in species with high within-brood parentage certainty, helper-offspring relatedness values can quickly erode through sequential polyandry.

O grau zero da organização: diálogos entre Deleuze e Robert Cooper

O objetivo do presente trabalho é reconstituir o conceito de grau zero da organização formulado por Robert Cooper a partir de um diálogo entre os escritos desse autor e a filosofia de Gilles Deleuze. Para alcançar este objetivo, primeiramente explicitaremos nosso compromisso epistemológico com o pós-estruturalismo, buscando situar este fenômeno do pensamento em termos de seu posicionamento nos estudos organizacionais. Nesta seção teremos o primeiro contato com o pensamento de Deleuze e Robert Cooper e, de antemão, apresentaremos a noção de grau zero como um conceito capaz de levantar possíveis pontos de convergência/divergência presentes nos trabalhos destes autores bem como de suscitar uma problematização do conceito de organização em seu nível ontológico e a própria ruptura do pós-estruturalismo com o estruturalismo no âmbito do estudo das organizações. Na segunda parte do trabalho analisaremos os escritos de Robert Cooper buscando realizar um apanhado geral de sua obra (que tratou do tema da organização), situaremos o conceito de grau zero da organização na mesma justificando sua escolha como o ponto de partida para o diálogo que buscaremos traçar entre Cooper e Deleuze. Após isso, faremos uma leitura ampla da filosofia deleuzeana e buscaremos compreender alguns de seus elementos fundamentais para, então, aproximar o pensamento de ambos os autores e desenhar possíveis aproximações e/ou afastamento. Foi possível identificar aproximações entre os pensamentos de Deleuze e Cooper: por um lado, destacamos que a primazia do devir, a proposta de um pensamento aberto e plural, uma preocupação com a linguagem e com materialidades, bem como fortes traços de influências vindas do estruturalismo e da psicanálise são pontos de aproximação marcantes entre os pensamentos destes autores. Por outro lado, também destacamos alguns possíveis pontos de divergência: a crítica à representação enquanto instância de limitação/negação; diferentes concepções de inconsciente (o inconsciente freudiano em Cooper/forjamento de noção própria do inconsciente em Deleuze); e, finalmente, no engajamento político da visão crítica proposta por seus trabalhos. Destacamos, finalmente, que a noção de grau zero da organização de Cooper ainda é passível de questionamentos quando deparada com a crítica ao estruturalismo e à representação conforme presente na filosofia de Deleuze. Concluímos que a filosofia de Deleuze impõe a necessidade reconstituir este conceito de forma a fazer com que ele afaste-se da possibilidade de ser tomado como uma visão estruturalista (uma esfera meramente linguística) e/ou oposicional (o grau zero enquanto mera desorganização) da organização.

Classification of states in S0(8) proton-neutron pairing model

lsoscalar (T = 0) plus isovector (T = 1) pairing Hamiltonian in LS-coupling. which is important for heavy N = Z nuclei, is solvable in terms of a SO(8) Lie algebra for three special values of the mixing parameter that measures the competition between the T = 0 aid T = 1 pairing. The SO(8) algebra is generated, amongst others, by the S = 1, T = 0 and S = 0, T = 1 pair creation and annihilation operators and corresponding to the three values of the mixing parameter, there are three chains of subalgebras: SO(8) superset of SOST (6) superset of SOS(3) circle times SOT(3), SO(8) superset of [SOS(5) superset of SOS(3)] circle times SOT(3) and SO(8) superset of [SOT(5) superset of SOT(3)] circle times SOS(3). Shell model Lie algebras, with only particle number conserving generators, that are complementary to these three chains of subalgebras are identified and they are used in the classification of states for a given number of nucleons. The classification problem is solved explicitly tor states with SO(8) seniority nu = 0, 1, 2, 3 and 4. Using them, hand structures in isospin space are identified for states with nu = 0, 1, 2 and 3. (c) 2005 Elsevier B.V. All rights reserved.

Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

We establish universal behaviour in the temperature dependencies of some observables in (s + id)-wave BCS superconductivity in the presence of a weak a wave. We find also a second second-order phase transition. As temperature is lowered-past the usual critical temperature T-c, a less ordered superconducting phase is created in the d wave, which changes to a more ordered phase in a (s + id) wave at T-c1 (

Cooper pair dispersion relation in two dimensions

The Cooper pair binding energy vs. center-of-mass-momentum dispersion relation for Bose-Einstein condensation studies of superconductivity is found in two dimensions for a renormalized attractive delta interaction. It crosses over smoothly from a linear to a quadratic form as coupling varies from weak to strong.