A study of T=1, T=3/2, and T=2 states in some light nuclei using (He^3,n) reactions

The (He³, n) reactions on B¹¹, N¹⁵, O¹⁶, and O¹⁸ targets have been studied using a pulsed-beam time-of-flight spectrometer. Special emphasis was placed upon the determination of the excitation energies and properties of states with T = 1 (in Ne¹⁸), T = 3/2 (in N¹³ and F¹⁷) and T = 2 (in Ne²⁰). The identification of the T = 3/2 and T = 2 levels is based on the structure of these states as revealed by intensities and shapes of angular distributions. The reactions are interpreted in terms of double stripping theory. Angular distributions have been compared with plane and distorted wave stripping theories. Results for the four reactions are summarized below:

1) O¹⁶ (He³, n). The reaction has been studied at incident energies up to 13.5 MeV and two previously unreported levels in Ne¹⁸ were observed at E_x = 4.55 ± .015 MeV (Γ = 70 ± 30 keV) and E_x = 5.14 ± .018 MeV (Γ = 100 ± 40 keV).

2) B¹¹ (He³, n). The reaction has been studied at incident energies up to 13.5 MeV. Three T = 3/2 levels in N¹³ have been identified at E_x = 15.068 ± .008 MeV (Γ ˂ 15 keV), E_x = 18.44 ± .04, and E_x 18.98 ± .02 MeV (Γ = 40 ± 20 keV).

3) N¹⁵ (He³, n). The reaction has been studied at incident energies up to 11.88 MeV. T = 3/2 levels in F¹⁷ have been identified at E_x = 11.195 ± .007 MeV (Γ ˂ 20 keV), E_x = 12.540 ± .010 MeV (Γ ˂ 25 keV), and E_x = 13.095 ± .009 MeV (Γ ˂ 25 keV).

4) O¹⁸ (He³, n). The reaction has been studied at incident energies up to 9.0 MeV. The excitation energy of the lowest T = 2 level in Ne²⁰ has been found to be 16.730 ± .006 MeV (Γ ˂ 20 keV).

Angular distributions of the transitions leading to the above higher isospin states are well described by double stripping theory. Analog correspondences are established by comparing the present results with recent studies (t, p) and (He³, p) reactions on the same targets.

Freshwater survey of the ditches around Hinkley Point Power Station, 20 June 1985

Sampling was concentrated on the North Moor region and the series of ditches which drained this area to the Bristol Channel. Although most ditches were not deep the mud substratum precluded sampling from within the habitat. All samples were taken with a pond net from the banks. Efforts were made to sample each part of the habitat although in some ditches the macrophyte growth was so intense as to make sampling difficult particularly of the sediments. Organisms were identified on the 10 sampling sites.

Beta and gamma vibrational bands in deformed nuclei

Energies and relative intensities of gamma transitions in ¹⁵²Sm, ¹⁵²Gd, ¹⁵⁴Gd, ¹⁶⁶Er, and ²³²U following radioactive decay have been measured with a Ge(Li) spectrometer. A peak fitting program has been developed to determine gamma ray energies and relative intensities with precision sufficient to give a meaningful test of nuclear models. Several previously unobserved gamma rays were placed in the nuclear level schemes. Particular attention has been paid to transitions from the beta and gamma vibrational bands, since the gamma ray branching ratios are sensitive tests of configuration mixing in the nuclear levels. As the reduced branching ratios depend on the multipolarity of the gamma transitions, experiments were performed to measure multipole mixing ratios for transitions from the gamma vibrational band. In ¹⁵⁴Gd, angular correlation experiments showed that transitions from the gamma band to the ground state band were predominantly electric quadrupole, in agreement with the rotational model. In ²³²U, the internal conversion spectrum has been studied with a Si(Li) spectrometer constructed for electron spectroscopy. The strength of electric monopole transitions and the multipolarity of some gamma transitions have been determined from the measured relative electron intensities.

The results of the experiments have been compared with the rotational model and several microscopic models. Relative B(E2) strengths for transitions from the gamma band in ²³²U and ¹⁶⁶Er are in good agreement with a single parameter band mixing model, with values of z₂= 0.025(10) and 0.046(2), respectively. Neither the beta nor the gamma band transition strengths in ¹⁵²Sm and ¹⁵⁴Gd can be accounted for by a single parameter theory, nor can agreement be found by considering the large mixing found between the beta and gamma bands. The relative B(E2) strength for transitions from the gamma band to the beta band in ²³²U is found to be five times greater than the strength to the ground state band, indicating collective transitions with strength approximately 15 single particle units.

On the Cesari fixed point method in a Banach space

In a paper published in 1961, L. Cesari [1] introduces a method which extends certain earlier existence theorems of Cesari and Hale ([2] to [6]) for perturbation problems to strictly nonlinear problems. Various authors ([1], [7] to [15]) have now applied this method to nonlinear ordinary and partial differential equations. The basic idea of the method is to use the contraction principle to reduce an infinite-dimensional fixed point problem to a finite-dimensional problem which may be attacked using the methods of fixed point indexes.

The following is my formulation of the Cesari fixed point method:

Let B be a Banach space and let S be a finite-dimensional linear subspace of B. Let P be a projection of B onto S and suppose Г≤B such that pГ is compact and such that for every x in PГ, P^-1x∩Г is closed. Let W be a continuous mapping from Г into B. The Cesari method gives sufficient conditions for the existence of a fixed point of W in Г.

Let I denote the identity mapping in B. Clearly y = Wy for some y in Г if and only if both of the following conditions hold:

(i) Py = PWy.

(ii) y = (P + (I - P)W)y.

Definition. The Cesari fixed paint method applies to (Г, W, P) if and only if the following three conditions are satisfied:

(1) For each x in PГ, P + (I - P)W is a contraction from P^-1x∩Г into itself. Let y(x) be that element (uniqueness follows from the contraction principle) of P^-1x∩Г which satisfies the equation y(x) = Py(x) + (I-P)Wy(x).

(2) The function y just defined is continuous from PГ into B.

(3) There are no fixed points of PWy on the boundary of PГ, so that the (finite- dimensional) fixed point index i(PWy, int PГ) is defined.

Definition. If the Cesari fixed point method applies to (Г, W, P) then define i(Г, W, P) to be the index i(PWy, int PГ).

The three theorems of this thesis can now be easily stated.

Theorem 1 (Cesari). If i(Г, W, P) is defined and i(Г, W, P) ≠0, then there is a fixed point of W in Г.

Theorem 2. Let the Cesari fixed point method apply to both (Г, W, P₁) and (Г, W, P₂). Assume that P₂P₁=P₁P₂=P₁ and assume that either of the following two conditions holds:

(1) For every b in B and every z in the range of P₂, we have that ‖b=P₂b‖ ≤ ‖b-z‖

(2)P₂Г is convex.

Then i(Г, W, P₁) = i(Г, W, P₂).

Theorem 3. If Ω is a bounded open set and W is a compact operator defined on Ω so that the (infinite-dimensional) Leray-Schauder index i_LS(W, Ω) is defined, and if the Cesari fixed point method applies to (Ω, W, P), then i(Ω, W, P) = i_LS(W, Ω).

Theorems 2 and 3 are proved using mainly a homotopy theorem and a reduction theorem for the finite-dimensional and the Leray-Schauder indexes. These and other properties of indexes will be listed before the theorem in which they are used.

Uma casa, tempo de espera e silêncio: uma leitura de Ontem não te vi em Babilónia e O arquipélago da insónia, de António Lobo Antunes

Este trabalho se propõe a analisar duas obras do escritor português António Lobo Antunes, tendo em vista algumas instâncias narrativas, que, a nosso ver, sobressaem na obra do autor. As obras são Ontem não te vi em Babilónia, romance publicado em 2006, e O arquipélago da insónia, de 2008. Os dois romances compõem o ciclo de produção mais recente do autor, no qual as experimentações formais e estéticas são mais intensas do que nos romances anteriores. Além disso, as obras apresentam convergências temáticas já explicitadas por uma leitura atenta de seus títulos. Ontem não te vi é a representação de um tempo de espera, um tempo de frustração; Babilónia é Babel, símbolo maior da incomunicabilidade para o Ocidente. Já arquipélago é um conjunto de ilhas, reunião marcada pelo isolamento e pela incomunicabilidade; insónia é, igualmente, uma espera frustrada por algo que não vem, no caso, o sono, que nos romances será metáfora para a morte. O trabalho privilegiará, portanto, a análise do espaço, a partir do símbolo da casa; do tempo, insone e de morte; e do texto, que se apresenta, essencialmente, por uma enxurrada discursiva. Assim, pretende-se entrar no universo antuniano e, como parece ser o desejo do autor, desvendar a nós mesmos e a nosso tempo

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

A dinâmica da demanda por serviços de saúde no município de Piraí, RJ, do ponto de vista da medicalização

Apesar da definição da Estratégia de Saúde da Família (ESF) como porta de entrada preferencial do sistema de saúde e estratégia de reorganização da assistência, os usuários do SUS, vêm demonstrando historicamente preferência pelo serviço de urgência/emergência hospitalar. Neste contexto, o campo do presente estudo é a cidade de Piraí e seus habitantes, que desde 2002 contam com 100% de cobertura da ESF, modelo que dá ênfase: à lógica territorial na assistência, no cuidado continuado e transversal, no vínculo e no acesso facilitado pelo acolhimento humanizado e escuta qualificada; ocupando o centro da rede de serviços atuando como ordenador e coordenador do cuidado. Avaliando os dados de produtividade (com foco nas consultas médicas) hospitalar e da ESF notamos que a busca por assistência médica hospitalar, tem aumentado exponencialmente, e pode-se perceber que a grande maioria destes usuários se apresenta ao serviço com demandas de atenção básica, o que é considerado ilógico e contraditório na visão de gestores e profissionais. A prática profissional tem me levado a um processo de reflexão sobre as expectativas dos usuários ao procurarem o sistema de saúde (principalmente a ESF), sobre os caminhos que cada um deles constrói diante de uma questão de saúde e como se dá a tomada de decisão em busca da resolutividade da questão. Dessa forma, o objetivo deste trabalho é compreender como se constrói essa demanda; que critérios estão envolvidos na tomada de decisão desses usuários ao optarem pelo serviço de emergência como porta de entrada preferencial; mesmo em um município que oferece um serviço estruturado, pautado nas diretrizes da ESF e com uma cobertura que alcança toda a sua população. Acreditamos que o processo conhecido como medicalização da vida, que descreve o processo pelo qual problemas não médicos são definidos e tratados como problemas médicos, usualmente em termos de doenças e desordens (CONRAD, 2007); influencie na construção dessa demanda. Quanto a metodologia, foram realizadas entrevistas semiestruturadas, com usuários do SUS, residentes no município e que buscaram espontaneamente o serviço de urgência/emergência hospitalar. Verificou-se que a imagem que o usuário faz dos serviços de saúde se relaciona principalmente com o tempo de espera pelo atendimento, o acesso (interpretado principalmente como a certeza/incerteza do atendimento) e a acessibilidade. Os usuários frequentemente se referem à organização das unidades da ESF com o significado de barreiras ao acesso (principalmente pela necessidade de agendamento) e demonstram ter em relação às USF uma imagem de grande limitação de recursos humanos (quase exclusivamente em relação ao médico) e materiais. Por outro lado, prontos-socorros e hospitais se apresentam para eles, por várias razões, como espaços de acesso garantido. É importante ressaltar que o processo de medicalização da vida aparece como parte importante da engrenagem que move a construção dessa demanda.

Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed.

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.