Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Maximum and mean diameter record of Orbulina universa from DSDP Hole 47-397 of Cape Bojador, eastern North Atlantic

Measurements of the diameter of O. universa carried out on 30 specimens from 39 samples covering a sediment thickness of 78 m and going back in time to approximately 750 000 y resulted in the construction of a curve of the mean diameter and a curve of the maximum diameter. Both curves, as well as those calculated with the running-averages technique, display cyclic fluctuations with durations of the order of 100 000 y and downwards decreasing amplitudes. These curves are compared with a carbonate curve (on bulk sediment) and an isotopic curve (on benthic foraminifers) obtained from the same set of samples. Correlations are fair to good, but a timelag is noticed between the isotopic curve and the faunal (O. universa mean diameter) curve, with the isotopic signal coming first, in the middle part of the Brunhes Epoch. Biostratigraphic calibration to the paleomagnetic record is provided by four datum planes (two based on calcareous nannofossils, two on diatoms) identified in the succession. Changes recorded in test porosity seem to be less meaningful than changes in test size.

(Table 4) Mean diameter of Orbulina universa d'Orbigny at DSDP Leg 54 Holes

On Deep Sea Drilling Project Leg 54, we recovered upper Pliocene (Globigerinoides obliquus: PL6 zone) to Pleistocene sediments from the equatorial East Pacific Rise (EPR) and Galapagos spreading center (GSC). Progressively older sediments were drilled at increasing distances from the crest, with the exception of the sediment drilled in the deepest trough known in the Siqueiros fracture zone. The anomalous age obtained at the latter site suggests that the basalt which was drilled may represent fracture zone volcanism. Paleoenvironmental analysis using the planktonic foraminifers at the EPR sites indicated the presence of environmental cycles of shorter wave length during the interval from 0 to 0.24 Ma, whereas cycles of longer wave length occurred from 0.43 to 2.17 Ma. The planktonic foraminiferal taphocoenoses at the EPR sites were strongly affected by selective dissolution which indicated that these EPR sites have been near either the lysocline or carbonate compensation surface since the upper Pliocene. The planktonic foraminiferal thanatocoenoses at the GSC sites were preserved better than those at the EPR sites. The number of planktonic foraminiferal species generally was greatly reduced in the green mud associated with the GSC hydrothermal mounds. More species were found in older than in younger green mud; this suggests that there probably was an increase in the rate of production of green mud sometime after the initiation of the hydrothermal system.

Characterization of expiration air jets and droplet size distributions immediately at the mouth opening

Size distributions of expiratory droplets expelled during coughing and speaking and the velocities of the expiration air jets of healthy volunteers were measured. Droplet size was measured using the Interferometric Mie imaging (IMI) technique while the Particle Image Velocimetry (PIV) technique was used for measuring air velocity. These techniques allowed measurements in close proximity to the mouth and avoided air sampling losses. The average expiration air velocity was 11.7 m/s for coughing and 3.9 m/s for speaking. Under the experimental setting, evaporation and condensation effects had negligible impact on the measured droplet size. The geometric mean diameter of droplets from coughing was 13.5m and it was 16.0m for speaking (counting 1 to 100). The estimated total number of droplets expelled ranged from 947 – 2085 per cough and 112 – 6720 for speaking. The estimated droplet concentrations for coughing ranged from 2.4 - 5.2cm-3 per cough and 0.004 – 0.223 cm-3 for speaking.

Study of new particle formation in subtropical urban environment in Brisbane, Australia

Atmospheric ultrafine particles play an important role in affecting human health, altering climate and degrading visibility. Numerous studies have been conducted to better understand the formation process of these particles, including field measurements, laboratory chamber studies and mathematical modeling approaches. Field studies on new particle formation found that formation processes were significantly affected by atmospheric conditions, such as the availability of particle precursors and meteorological conditions. However, those studies were mainly carried out in rural areas of the northern hemisphere and information on new particle formation in urban areas, especially those in subtropical regions, is limited. In general, subtropical regions display a higher level of solar radiation, along with stronger photochemical reactivity, than those regions investigated in previous studies. However, based on the results of these studies, the mechanisms involved in the new particle formation process remain unclear, particularly in the Southern Hemisphere. Therefore, in order to fill this gap in knowledge, a new particle formation study was conducted in a subtropical urban area in the Southern Hemisphere during 2009, which measured particle size distribution in different locations in Brisbane, Australia. Characterisation of nucleation events was conducted at the campus building of the Queensland University of Technology (QUT), located in an urban area of Brisbane. Overall, the annual average number concentrations of ultrafine, Aitken and nucleation mode particles were found to be 9.3 x 103, 3.7 x 103 and 5.6 x 103 cm-3, respectively. This was comparable to levels measured in urban areas of northern Europe, but lower than those from polluted urban areas such as the Yangtze River Delta, China and Huelva and Santa Cruz de Tenerife, Spain. Average particle number concentration (PNC) in the Brisbane region did not show significant seasonal variation, however a relatively large variation was observed during the warmer season. Diurnal variation of Aitken and nucleation mode particles displayed different patterns, which suggested that direct vehicle exhaust emissions were a major contributor of Aitken mode particles, while nucleation mode particles originated from vehicle exhaust emissions in the morning and photochemical production at around noon. A total of 65 nucleation events were observed during 2009, in which 40 events were classified as nucleation growth events and the remainder were nucleation burst events. An interesting observation in this study was that all nucleation growth events were associated with vehicle exhaust emission plumes, while the nucleation burst events were associated with industrial emission plumes from an industrial area. The average particle growth rate for nucleation events was found to be 4.6 nm hr-1 (ranging from 1.79-7.78 nm hr-1), which is comparable to other urban studies conducted in the United States, while monthly particle growth rates were found to be positively related to monthly solar radiation (r = 0.76, p <0.05). The particle growth rate values reported in this work are the first of their kind to be reported for the subtropical urban area of Australia. Furthermore, the influence of nucleation events on PNC within the urban airshed was also investigated. PNC was simultaneously measured at urban (QUT), roadside (Woolloongabba) and semi-urban (Rocklea) sites in Brisbane during 2009. Total PNC at these sites was found to be significantly affected by regional nucleation events. The relative fractions of PNC to total daily PNC observed at QUT, Woolloongabba and Rocklea were found to be 12%, 9% and 14%, respectively, during regional nucleation events. These values were higher than those observed as a result of vehicle exhaust emissions during weekday mornings, which ranged from 5.1-5.5% at QUT and Woolloongabba. In addition, PNC in the semi-urban area of Rocklea increased by a factor of 15.4 when it was upwind from urban pollution sources under the influence of nucleation burst events. Finally, we investigated the influence of sulfuric acid on new particle formation in the study region. A H2SO4 proxy was calculated by using [SO2], solar radiation and particle condensation sink data to represent the new particle production strength for the urban, roadside and semi-urban areas of Brisbane during the period June-July of 2009. The temporal variations of the H2SO4 proxies and the nucleation mode particle concentration were found to be in phase during nucleation events in the urban and roadside areas. In contrast, the peak of proxy concentration occurred 1-2 hr prior to the observed peak in nucleation mode particle concentration at the downwind semi-urban area of Brisbane. A moderate to strong linear relationship was found between the proxy and the freshly formed particles, with r2 values of 0.26-0.77 during the nucleation events. In addition, the log[H2SO4 proxy] required to produce new particles was found to be ~1.0 ppb Wm-2 s and below 0.5 ppb Wm-2 s for the urban and semi-urban areas, respectively. The particle growth rates were similar during nucleation events at the three study locations, with an average value of 2.7 ± 0.5 nm hr-1. This result suggested that a similar nucleation mechanism dominated in the study region, which was strongly related to sulphuric acid concentration, however the relationship between the proxy and PNC was poor in the semi-urban area of Rocklea. This can be explained by the fact that the nucleation process was initiated upwind of the site and the resultant particles were transported via the wind to Rocklea. This explanation is also supported by the higher geometric mean diameter value observed for particles during the nucleation event and the time lag relationship between the H2SO4 proxy and PNC observed at Rocklea. In summary, particle size distribution was continuously measured in a subtropical urban area of southern hemisphere during 2009, the findings from which formed the first particle size distribution dataset in the study region. The characteristics of nucleation events in the Brisbane region were quantified and the properties of the nucleation growth and burst events are discussed in detail using a case studies approach. To further investigate the influence of nucleation events on PNC in the study region, PNC was simultaneously measured at three locations to examine the spatial variation of PNC during the regional nucleation events. In addition, the impact of upwind urban pollution on the downwind semi-urban area was quantified during these nucleation events. Sulphuric acid was found to be an important factor influencing new particle formation in the urban and roadside areas of the study region, however, a direct relationship with nucleation events at the semi-urban site was not observed. This study provided an overview of new particle formation in the Brisbane region, and its influence on PNC in the surrounding area. The findings of this work are the first of their kind for an urban area in the southern hemisphere.

Updated correlation between aircraft smoke number and black carbon concentration

Aircraft emissions of black carbon (BC) contribute to anthropogenic climate forcing and degrade air quality. The smoke number (SN) is the current regulatory measure of aircraft particulate matter emissions and quantifies exhaust plume visibility. Several correlations between SN and the exhaust mass concentration of BC (CBC) have been developed, based on measurements relevant to older aircraft engines. These form the basis of the current standard method used to estimate aircraft BC emissions (First Order Approximation version 3 [FOA3]) for the purposes of environmental impact analyses. In this study, BC with a geometric mean diameter (GMD) of 20, 30, and 60 nm and filter diameters of 19 and 35 mm are used to investigate the effect of particle size and sampling variability on SN measurements. For BC with 20 and 30 nm GMD, corresponding to BC emitted by modern aircraft engines, a smaller SN results from a given CBC than is the case for BC with 60 nm GMD, which is more typical of older engines. An updated correlation between CBC and SNthat accounts for typical size of BC emitted by modern aircraft is proposed. An uncertainty of ±25% accounts for variation in GMD in the range 20-30 nm and for the range of filter diameters. The SN-CBC correlation currently used in FOA3 underestimates by a factor of 2.5-3 for SN <15, implying that current estimates of aircraft BC emissions derived from SN are underestimated by the same factor. Copyright © American Association for Aerosol Research.

Moisture-dependent physical properties of locust bean (Parkia biglobosa) seeds

Seed moisture content is significant in the handling and processing of seeds. This work therefore determined the physical properties of Locust bean seeds as functions of seed moisture content in the moisture range of 5.9 – 28.2% dry basis. Mohsenin, Stepanoff and ASAE standard methods were used in determining the properties. Increases in seed dimensions vitz length = 10.2±1.0 – 11.3±0.9 mm; width = 8.5±0.8 – 9.1±0.6 mm; surface area = 191.2±24.6 – 208.3±26.3 mm2 ; geometric mean diameter = 7.78±0.49 – 8.12±0.03 and arithmetic mean diameter = 8.06±0.56 – 8.34±0.49 mm were recorded. Seed thickness = 5.49±0.43 – 5.26±0.62 mm; sphericity = 0.75±0.04 – 0.71±0.03; true density = 1251.96±55.5 - 1222±62.16 kgm-3 and porosity = 48.4±2.14 – 41.9±3.78 decreased. Static coefficient of friction increased on plywood (0.5±0.02 – 0.6±0.01), glass (0.4±0.05 – 0.5±0.01) and decreased on aluminium (0.5±0.02 – 0.5±0.04). A data of the physical properties of Locust bean; Parkia biglobosa was developed. This is useful for the design and development of equipment necessary for its handling and processing.

Effect of moisture content on the physical properties of fibered flaxseed

The physical properties of fibered flaxseed were investigated within moisture content varying from 6.21 to 16.29%. The length, width, thickness and geometric mean diameter increased from 4.20 to 4.44mm, 1.99 to 2.13mm, 0.91 to 0.95mm, and 1.95 to 2.06mm, respectively in the moisture content range. One thousand seed weight increased linearly from 4.22 to 4.62g. The bulk density decreased from 726.783 to 611.872kg/m3, while the true density increased from 1165.265 to 1289.341kg/m3 in the moisture content range. The porosity values of flaxseed increased linearly from 37.67 to 52.54%. The highest static coefficient of friction was found on the plywood surface, while the lowest on the stainless steel surface. The static coefficient of friction increased from 0.467 to 0.972, 0.442 to 0.864, 0.492 to 0.927, and 0.490 to 0.845 for plywood, stainless steel, aluminum sheet and galvanized iron, respectively. The angle of repose increased linearly from 25.7° to 33.8° in the moisture content range. The results are necessary for design of equipment to handling, transportation, processing, and the storage of flaxseed.

Spatial variability of aggregate stability in latosols under sugarcane

Solos submetidos ao mesmo sistema de manejo manifestam variabilidade espacial diferenciada de seus atributos. A variabilidade espacial da estabilidade de agregados foi caracterizada em um Latossolo Vermelho distrófico e Latossolo Vermelho eutroférrico, sob cultivo de cana-de-açúcar. Foram realizadas amostragens de terra nos pontos de interseção de uma malha de 10 x 10 linhas, espaçadas de 10 m, totalizando 100 pontos de amostragem por área, coletadas nas camadas de 0,0-0,2 e 0,2-0,4 m de profundidade, para determinação de diâmetro médio geométrico (DMG), diâmetro médio ponderado (DMP), agregados na classe >2,0 mm e teor de matéria orgânica do solo. O Latossolo Vermelho eutroférrico apresenta maior estabilidade de agregados quando comparado com o Latossolo Vermelho distrófico, condizente com o maior teor de argila, matéria orgânica e mineralogia gibbsítica. A evolução diferenciada dos Latossolos estudados explica os maiores alcances, o menor coeficiente de variação (CV) e a menor variabilidade, observados no Latossolo Vermelho eutroférrico para todos os atributos estudados.

Agregação de um argissolo sob pomar de goiabeiras após aplicação de resíduos da indústria processadora de goiaba

A utilização de resíduos da indústria de processamento de frutas na agricultura pode proporcionar melhorias à qualidade do solo. Dessa forma, objetivou-se com este estudo avaliar o efeito da aplicação de resíduos de sementes de goiaba na agregação e no estoque de carbono orgânico do solo (EC). O experimento esteve inserido em um pomar comercial irrigado de goiabeiras (cv. Paluma), com sete anos de idade, sobre um Argissolo Vermelho-Amarelo distrófico típico. O delineamento experimental foi em blocos casualizados e parcelas subdivididas, sendo cinco tratamentos (doses de: 0;9;18;27 e 36 Mg ha-1 de resíduo) e duas camadas de solo (0-0,10 e 0,10-0,20 m). Foi avaliado o mesmo tipo de solo sobre mata nativa adjacente à área experimental. As análises realizadas foram a distribuição do tamanho dos agregados estáveis em água, o diâmetro médio ponderado, o diâmetro médio geométrico, os agregados maiores que 2 mm e o EC. Os dados foram submetidos à análise de variância (Teste F), seguindo o delineamento em blocos casualizados com parcelas subdivididas (5 doses x 2 camadas). As médias dos tratamentos foram comparadas pelo teste de Tukey, a 5% de probabilidade, e as médias das camadas foram comparadas pelo teste F, a 5% de probabilidade. Os dados coletados no solo sob mata foram utilizados apenas como referência de um solo em estado natural e, portanto, não foram considerados como fator de variação nas análises de variância. Os valores dos índices de agregação com o estoque de carbono orgânico do solo foram submetidos à correlação de Pearson (p < 0,05). O efeito das doses de resíduo de sementes de goiaba sobre o estoque de carbono orgânico, na camada de 0-0,20 m do solo, foi avaliado por análise de regressão. Os tratamentos não diferiram em relação à agregação do solo, contudo EC foi diretamente relacionado à quantidade de resíduo aplicado ao solo. Houve correlação positiva e significativa entre os índices de agregação e o EC. A aplicação de resíduos de sementes de goiaba proporcionou melhoria da qualidade do solo.

Limestone and oyster shell for brown layers in their second egg production cycle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effects of corn particle size and physical form of the diet on the gastrointestinal structures of broiler chickens

The objective of this experiment was to investigate the effects of different particle sizes, expressed as Geometric Mean Diameter (GMD) of corn (0.336mm, 0.585mm, 0.856mm and 1.12mm) of mash and pelleted broiler chicken diets on the weight of the gizzard, duodenum and jejunum+ileum; on the pH of the gizzard and small intestine and on the characteristics of the duodenal mucous layer (number and height of villi and crypt depth) in 42-day-old broilers. The physical form and the particle size of the diet had no significant effect on gizzard and intestine pH (p > 0.05). A greater gizzard weight was seen in the birds receiving pelleted diet and particle size of 0.336mm (p < 0.008). However, for the particle sizes of 0.856 and 1.12 mm, a greater weight was found in birds that received mash diet (p < 0.039 and p < 0.006, respectively). Also, gizzard weight was greater with increasing corn GMD independent of the physical form of the diet. In the mash diet, the increase in particle size promoted a quadratic response in the weight of duodenum and jejunum + ileum. The pelleted diet promoted a greater number of villi per transverse duodenum cut (p < 0.007) and greater crypt depth (p < 0.05). As the particle size increased, there was a linear increase of villus height and crypt depth in the duodenum, irrespective of the physical form of the diet.

Agregação de ume nitossolo vermelho distroférrico sob sistemas de plantio direto, preparo convencional e mata nativa

This study aimed to evaluate the effect of time since the adoption of the no-till system, in comparison with a native forest area and a conventional tillage area, using the distribution of soil aggregates in a Distroferric Red Nitosol. Treatments were as follows: native forest (NF), conventional tillage (CT), no-till for one year (NT1), no-till for four years (NT4), no-till for five years (NT5), and no-till for 12 years (NT12). Aggregate samples were collected randomly within each treatment at depths of 0-5 and 10-15 cm. After sifting the aggregates in water they were separated into the following aggregate classes > 2 mm; < 2 mm; 2-1 mm, and < 1 mm. The adoption time in the no-till system favored soil aggregation. The mean weighted diameter (MWD) of the soil aggregates and the percentage of aggregates greater than 2 mm increased with adoption time in the no-till system at the 0-5 cm depth. The NF and NT12 treatments had higher MWD values in the 0-5 cm layer. CT had the highest percentage of aggregates smaller than 1 mm.

Agregados em um Latossolo sob sistema plantio direto e rotação de culturas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)