Extension theorems for functions of vanishing mean oscillation

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in R^d converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.

We consider the similar extension problem pertaining to BMO(ρ) functions; that is, those VMO functions whose mean oscillation over any cube is O(ρ(l(Q))) where l(Q) is the length of Q and ρ is a positive, non-decreasing function with ρ(0⁺) = 0.

We apply these results to obtain sufficient conditions for a Blaschke sequence to be the zeros of an analytic BMO(ρ) function on the unit disc.

Observação do transporte de sedimentos em suspensão ao longo do Canal Norte do rio Amazonas durante condições de baixa descarga (outubro 2008)

The Amazon river, located in northernBrazil, discharges between 80,000 and 250,000 m3s-1 of water onto the adjacent shelf, creating a plume of brackish water that extends hundreds of kilometers away from the river mouth. This river also carries a large amount of fine sediments to the ocean where fluid mud has been found in the topset and upper foreset layers of the subaqueous delta formed on the mid-shelf. One of the main goals of this dissertation is to describe how turbulence and suspended sediment concentration vary along the Northern Channel of the Amazon river. Water column measurements were carried out in October 2008 at six anchor stations (P1, P3, P5, P6, P8 e P9) located seaward of the river mouth; P1 and P9 were 125 km apart. Each station was occupied during 13 hours during which current speed and direction were continuously sampled with a 600 kHz Teledyne-RDI ADCP; hourly profiles of temperature, salinity, turbidity and depth were also obtained. Water samples were collected for determination of Suspended Particulate Matter (SPM) concentration and calibration of the turbidity sensor. Current speed reached values above 1.5 m s1 in the along-channel direction (NE-SW); a remarkable ebb-flood asymmetry was observed and flows were strongly ebb-dominated. Throughout the water column, SPM concentration at stations P1 and P3 varied between 100 and 300 mg L1 in association with the presence of freshwater. In contrast, a strong salinity gradient was observed between stations P6 and P9, coinciding with the occurrence of concentrations of SPM above 10 g L-1 (fluid mud). At stations P3, P5 and P6, interface between freshwater from the Amazon river and salt water from the continental shelf, shear stresses wereestimated through four diferents methods: Reynolds, Turbulent Kinetic Energy (TKE), modified TKE and Quadratic Law; in the nearbed region (3 mab) the computed values varied between 0 and 3 Pa. At the three stations (P3, P5 and P6) the lowest and the highest shear stress values were obtained through, respectively, the Reynolds and the TKE methods. Over the whole water column turbulence intensity was estimated through the standard deviation of the turbulent component of the along-channel current velocity (root-mean square of u); from these values, it was estimated the turbulent dissipation of energy (G), whose values at 3 mab varied between zero and 20 s1.

Surface water temperature of Windermere. Monthly and yearly totals of degree-days centigrade and monthly mean temperatures, 1933 to 1975

The surface temperature of Windermere has been recorded by the staff of the Freshwater Biological Association on every weekday (with a few minor exceptions) since 11 January 1933. This publication presents this information in a form which can easily be used by individual research workers. There are 43 tables (1 for each year, 1933-1975) which give the data, expressed as degree-days centigrade. The tables show for each month the number of degree-days above each temperature from 0 degree C to the highest recorded, at 1 degree C intervals. Mean temperatures are obtained by dividing the number of degree-days over 0 degree C by the relevant number of days. The advantage of degree-days rather than mean temperatures is that degree-days are additive so data for any desired periods may be combined quickly and simply. Seasonal results for spring, summer, autumn and winter are presented in tabular form, as are selected totals for comparisons between years. Further tables give the mean temperature in each month of the year, and the frequency distributions of monthly mean temperatures.

Intensity-moments characterization of general pulsed paraxial beams with the Wigner distribution function

On the basis of the space-time Wigner distribution function (STWDF), we use the matrix formalism to study the propagation laws for the intensity moments of quasi-monochromatic and polychromatic pulsed paraxial beams. The advantages of this approach are reviewed. Also, a least-squares fitting method for interpreting the physical meaning of the effective curvature matrix is described by means of the STWDF. Then the concept is extended to the higher-order situation, and what me believe is a novel technique for characterizing the beam phase is presented. (C) 1999 Optical Society of America [S0740-3232(99)001009-1].

Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order

A set of recursive formulas for diffractive optical plates design is described. The pure-phase plates simulated by this method homogeneously concentrate more than 96% of the incident laser energy in the desired focal-plane region. The intensity focal-plane profile fits a lath-order super-Gaussian function and has a nearly perfect flat top. Its fit to the required profile measured in the mean square error is 3.576 x 10(-3). (C) 1996 Optical Society of America

Transverse intensity distributions of a broadband laser modulated by a hard-edged aperture

By means of the Huygens-Fresnel diffraction integral, the field representation of a laser beam modulated by a hard-edged aperture is derived. The near-field and far-field transverse intensity distributions of the beams with different bandwidths are analyzed by using the representation. The numerical calculation results indicate that the amplitudes and numbers of the intensity spikes decrease with increasing bandwidth, and beam smoothing is achieved when the bandwidth takes a certain value in the near field. In the far field, the radius of the transverse intensity distribution decreases as the bandwidth increases, and the physical explanation of this fact is also given. (c) 2005 Optical Society of America.

Influence of the chirp on the intensity distributions of an apertured pulse

Starting from the Huygens-Fresnel diffraction integral and the Fourier transform, the propagation expression of a chirped pulse passing through a hard-edged aperture is derived. Using the obtained expression, the intensity distributions of the pulse with different chirp in the near and far fields are analyzed in detail. Due to the modulation of the aperture, many intensity peaks emerge in the intensity distributions of the chirped pulse in the near field. However, the amplitudes of the intensity peaks decrease on increasing the chirp, which results in the smoothing effect in the intensity distributions. The beam smoothing brought by increasing the chirp is explained physically. Also, it is found that the radius of the intensity distribution of the chirped pulse decreases when the chirp increases in the far field. (c) 2005 Elsevier GmbH. All rights reserved.

Ecologia térmica e comportamento de construção de abrigos de Liolaemus lutzae (Lacertilia, Liolaemidae) em três áreas de restinga no estado do Rio de Janeiro, sudeste do Brasil: os efeitos de fatores extrínsecos e intrínsecos

Fatores extrínsecos afetam a ecologia térmica e o comportamento de lagartos no habitat, com as características ambientais locais podendo ocasionar alterações na temperatura corpórea (Tc) e no comportamento destes animais. Entretanto, fatores intrínsecos também representam uma importante influência para sua biologia, assim como fatores filogenéticos (históricos). Liolaemus lutzae (Liolaemidae) é uma espécie de lagarto com ocorrência restrita a restingas do estado do Rio de Janeiro (entre a Restinga da Marambaia no município do Rio de Janeiro e a restinga da Praia do Peró no município de Cabo Frio), vivendo exclusivamente na zona de vegetação halófila-psamófila-reptante a chamada área-de-praia da restinga (sujeita a altas temperaturas ambientais e ventos intensos constantes). Nessa área, onde vivem restritos a uma faixa de poucos metros de restinga, os indivíduos se abrigam escavando abrigos no substrato arenoso. Avaliei a importância de fontes ambientais de calor, da intensidade dos ventos, do sexo, da ontogenia, do comprimento rostro-cloacal (CRC) e da massa corpórea para a Tc e a taxa de atividade de lagartos L. lutzae (observando a ocorrência de variações sazonais), em estudos conduzidos no município de Arraial do Cabo, estado do Rio de Janeiro, sudeste do Brasil. Além disso, eu analisei se o comportamento de L. lutzae, direcionando as aberturas de seus abrigos foi afetado por fatores ambientais nas restingas da Reserva Ecológica Estadual de Jacarepiá e do Parque Natural Municipal de Grumari, ambas no estado do Rio de Janeiro. A atividade dos lagartos se estendeu durante o dia (0600h às 1800h), com máximo entre 1100h e 1300h (com variações sazonais). A Tc dos indivíduos foi 31,7  3,4 C, e variou ao longo do dia e sazonalmente. Em ambas as estações a Tc dos lagartos relacionaram-se às temperaturas do microhabitat (substrato e ar). A intensidade do vento influenciou a Tc dos lagartos (causando seu decréscimo), e a intensidade média do vento afetou o número de lagartos ativos (causando redução da atividade). Houve diferenças intersexuais no CRC, com os machos maiores do que as fêmeas, embora as fêmeas tenham tido maior massa corpórea relativa ao CRC correspondente, comparado aos machos. A Tc também diferiu inter-sexualmente (com machos mais quentes do que fêmeas) e ontogeneticamente (com jovens mais quentes do que adultos depois de removido o efeito do tamanho corpóreo). Houve relações entre a Tc e o CRC e entre a Tc e a massa corpórea, com lagartos maiores tendo Tc mais elevada (causada pela inércia térmica dos corpos). A variabilidade na Tc dos lagartos parece refletir a interação entre características ambientais locais, fatores intrínsecos e a filogenia da espécie. As aberturas dos abrigos foram localizadas principalmente próximas à linha de praia (possivelmente devido ao substrato menos compacto), predominantemente em terrenos inclinados e tiveram uma tendência de orientação influenciada pela inclinação do terreno. O comportamento de L. lutzae de orientar a entrada de seus abrigos para a direção descendente das inclinações pode ser vantajoso para torná-los menos vulneráveis a potenciais ameaças e distúrbios vindos da superfície.

Uptake and factors that influence the use of 'sit less, move more' occupational intervention strategies in Spanish office employees

Background: Little is known about the types of 'sit less, move more' strategies that appeal to office employees, or what factors influence their use. This study assessed the uptake of strategies in Spanish university office employees engaged in an intervention, and those factors that enabled or limited strategy uptake. Methods: The study used a mixed method design. Semi-structured interviews were conducted with academics and administrators (n = 12; 44 +/- 12 mean SD age; 6 women) at three points across the five-month intervention, and data used to identify factors that influenced the uptake of strategies. Employees who finished the intervention then completed a survey rating (n = 88; 42 +/- 8 mean SD age; 51 women) the extent to which strategies were used [never (1) to usually (4)]; additional survey items (generated from interviewee data) rated the impact of factors that enabled or limited strategy uptake [no influence (1) to very strong influence (4)]. Survey score distributions and averages were calculated and findings triangulated with interview data. Results: Relative to baseline, 67% of the sample increased step counts post intervention (n = 59); 60% decreased occupational sitting (n = 53). 'Active work tasks' and 'increases in walking intensity' were the strategies most frequently used by employees (89% and 94% sometimes or usually utilised these strategies); 'walk-talk meetings' and ` lunchtime walking groups' were the least used (80% and 96% hardly ever or never utilised these strategies). 'Sitting time and step count logging' was the most important enabler of behaviour change (mean survey score of 3.1 +/- 0.8); interviewees highlighted the motivational value of being able to view logged data through visual graphics in a dedicated website, and gain feedback on progress against set goals. 'Screen based work' (mean survey score of 3.2 +/- 0.8) was the most significant barrier limiting the uptake of strategies. Inherent time pressures and cultural norms that dictated sedentary work practices limited the adoption of 'walk-talk meetings' and ` lunch time walking groups'. Conclusions: The findings provide practical insights into which strategies and influences practitioners need to target to maximise the impact of 'sit less, move more' occupational intervention strategies.