942 resultados para One-point Quadrature


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Given two independent Poisson point processes Phi((1)), Phi((2)) in R-d, the AB Poisson Boolean model is the graph with the points of Phi((1)) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Phi((2)). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d >= 2 and derive bounds fora critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and tau n in the unit cube. The AB random geometric graph is defined as above but with balls of radius r. We derive a weak law result for the largest nearest-neighbor distance and almost-sure asymptotic bounds for the connectivity threshold.

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We study Majorana modes and transport in one-dimensional systems with a p-wave superconductor (SC) and normal metal leads. For a system with an SC lying between two leads, it is known that there is a Majorana mode at the junction between the SC and each lead. If the p-wave pairing Delta changes sign or if a strong impurity is present at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the sub-gap conductance between the leads and the SC. We derive an analytical expression as a function of Delta and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the shifts oscillate and decay exponentially as L is increased. The energy shifts exactly match the location of the peaks in the conductance. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on Delta and the strengths of an impurity inside the SC or the barriers between the SC and the leads; this in turn affects the Majorana modes and the conductance. Finally, we propose a novel experimental realization of these systems, in particular of a system where Delta changes sign at one point inside the SC.

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In 2006 the UK-based charity, Global Ocean, with local support from the Third Millennium Foundation, convened a Conversation among specialists about the problems facing the conservation of whales. Called "A consultation on whaling", this gathering was held in the ancient village of Paciano, in Umbria near the border with Tuscany, 15 – 17 October 2006. There were 15 participants from 11 countries. Dr Kees Lankester served as moderator. The outcome was an Aide Memoire which served to guide the participants in the run-up to the 2007 meeting of the International Whaling Commission (IWC), held in Anchorage, Alaska, in June. One point of agreement was that a second consultation should be held in the months following the Anchorage meeting, involving some but not necessarily all of the participants in the first, but concentrating this time on scientific issues – especially those encountered in the Scientific Committee of the IWC –with particular attention to informing a wider public about those scientific activities in relation to the problems confronting the IWC and the views of scientists about them. This document is the report of that Conversation, referred to as Paciano II. The moderator was Dr Giuseppe Notarbartolo di Sciara and the Report was written by Kieran Mulvaney in consultation with all participants, and with reference to an Aide Memoire prepared by the Rapporteur, Dr Russell Leaper. The sponsor and organisers have agreed with the general sentiment expressed by participants in Paciano II that further such conversations should be held at roughly yearly intervals and they will try to satisfy that desire. Although these future gatherings would be concerned with the living ocean they would not necessarily be restricted in future to consideration of whales and whaling. Discussions are on-going for selection of a theme which is of both scientific interest and practical concern for conservation of marine life and management of the uses of ocean space. (Document has 18 pages)

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In 2006 the UK-based charity, Global Ocean, with local support from the Third Millennium Foundation, convened a Conversation among specialists about the problems facing the conservation of whales. Called "A consultation on whaling", this gathering was held in the ancient village of Paciano, in Umbria near the border with Tuscany, 15 – 17 October 2006. There were 15 participants from 11 countries. Dr Kees Lankester served as moderator. The outcome was an Aide Memoire which served to guide the participants in the run-up to the 2007 meeting of the International Whaling Commission (IWC), held in Anchorage, Alaska, in June. One point of agreement was that a second consultation should be held in the months following the Anchorage meeting, involving some but not necessarily all of the participants in the first, but concentrating this time on scientific issues – especially those encountered in the Scientific Committee of the IWC –with particular attention to informing a wider public about those scientific activities in relation to the problems confronting the IWC and the views of scientists about them. This document is the report of that Conversation, referred to as Paciano II. The moderator was Dr Giuseppe Notarbartolo di Sciara and the Report was written by Kieran Mulvaney in consultation with all participants, and with reference to an Aide Memoire prepared by the Rapporteur, Dr Russell Leaper. The sponsor and organisers have agreed with the general sentiment expressed by participants in Paciano II that further such conversations should be held at roughly yearly intervals and they will try to satisfy that desire. Although these future gatherings would be concerned with the living ocean they would not necessarily be restricted in future to consideration of whales and whaling. Discussions are on-going for selection of a theme which is of both scientific interest and practical concern for conservation of marine life and management of the uses of ocean space. (19 page document)

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Ground-water is not widely used in Baker County, but the presence of a high equipotential area in the artesian system beneath the County made it necessary that the resource be understood insofar as this high affected the ground-water resources of Nassau and Duval counties which were being intensively studied and mapped. The method and rates of movement of ground-water from one point to another in the artesian aquifer are understood more fully by use of the data in this report. (PDF contains 30 pages)

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In this thesis I apply paleomagnetic techniques to paleoseismological problems. I investigate the use of secular-variation magnetostratigraphy to date prehistoric earthquakes; I identify liquefaction remanent magnetization (LRM), and I quantify coseismic deformation within a fault zone by measuring the rotation of paleomagnetic vectors.

In Chapter 2 I construct a secular-variation reference curve for southern California. For this curve I measure three new well-constrained paleomagnetic directions: two from the Pallett Creek paleoseismological site at A.D. 1397-1480 and A.D. 1465-1495, and one from Panum Crater at A.D. 1325-1365. To these three directions I add the best nine data points from the Sternberg secular-variation curve, five data points from Champion, and one point from the A.D. 1480 eruption of Mt. St. Helens. I derive the error due to the non-dipole field that is added to these data by the geographical correction to southern California. Combining these yields a secular variation curve for southern California covering the period A.D. 670 to 1910, with the best coverage in the range A.D. 1064 to 1505.

In Chapter 3 I apply this curve to a problem in southern California. Two paleoseismological sites in the Salton trough of southern California have sediments deposited by prehistoric Lake Cahuilla. At the Salt Creek site I sampled sediments from three different lakes, and at the Indio site I sampled sediments from four different lakes. Based upon the coinciding paleomagnetic directions I correlate the oldest lake sampled at Salt Creek with the oldest lake sampled at Indio. Furthermore, the penultimate lake at Indio does not appear to be present at Salt Creek. Using the secular variation curve I can assign the lakes at Salt Creek to broad age ranges of A.D. 800 to 1100, A.D. 1100 to 1300, and A.D. 1300 to 1500. This example demonstrates the large uncertainties in the secular variation curve and the need to construct curves from a limited geographical area.

Chapter 4 demonstrates that seismically induced liquefaction can cause resetting of detrital remanent magnetization and acquisition of a liquefaction remanent magnetization (LRM). I sampled three different liquefaction features, a sandbody formed in the Elsinore fault zone, diapirs from sediments of Mono Lake, and a sandblow in these same sediments. In every case the liquefaction features showed stable magnetization despite substantial physical disruption. In addition, in the case of the sandblow and the sandbody, the intensity of the natural remanent magnetization increased by up to an order of magnitude.

In Chapter 5 I apply paleomagnetics to measuring the tectonic rotations in a 52 meter long transect across the San Andreas fault zone at the Pallett Creek paleoseismological site. This site has presented a significant problem because the brittle long-term average slip-rate across the fault is significantly less than the slip-rate from other nearby sites. I find sections adjacent to the fault with tectonic rotations of up to 30°. If interpreted as block rotations, the non-brittle offset was 14.0+2.8, -2.1 meters in the last three earthquakes and 8.5+1.0, -0.9 meters in the last two. Combined with the brittle offset in these events, the last three events all had about 6 meters of total fault offset, even though the intervals between them were markedly different.

In Appendix 1 I present a detailed description of my standard sampling and demagnetization procedure.

In Appendix 2 I present a detailed discussion of the study at Panum Crater that yielded the well-constrained paleomagnetic direction for use in developing secular variation curve in Chapter 2. In addition, from sampling two distinctly different clast types in a block-and-ash flow deposit from Panum Crater, I find that this flow had a complex emplacement and cooling history. Angular, glassy "lithic" blocks were emplaced at temperatures above 600° C. Some of these had cooled nearly completely, whereas others had cooled only to 450° C, when settling in the flow rotated the blocks slightly. The partially cooled blocks then finished cooling without further settling. Highly vesicular, breadcrusted pumiceous clasts had not yet cooled to 600° C at the time of these rotations, because they show a stable, well clustered, unidirectional magnetic vector.

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[ES]El South Pointing Chariot es un antiguo mecanismo de origen chino usado en sus inicios como instrumento de orientación, siendo su principal característica la existencia de un punto que siempre tiene velocidad angular absoluta nula. Tomando sus fundamentos como base, es posible realizar sistemas de guiado en direcciones estacionarias con múltiples aplicaciones en la actualidad, pudiendo usarse, por ejemplo, como sistema estabilizador. Para ello, debe realizarse su análisis cinemático, para comprender su funcionamiento, y comprobar que los resultados son correctos, pudiéndose hacer esto mediante un prototipo. La realización del prototipo engloba su diseño y posterior fabricación.

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The process of prophage integration by phage λ and the function and structure of the chromosomal elements required for λ integration have been studied with the use of λ deletion mutants. Since attφ, the substrate of the integration enzymes, is not essential for λ growth, and since attφ resides in a portion of the λ chromosome which is not necessary for vegetative growth, viable λ deletion mutants were isolated and examined to dissect the structure of attφ.

Deletion mutants were selected from wild type populations by treating the phage under conditions where phage are inactivated at a rate dependent on the DNA content of the particles. A number of deletion mutants were obtained in this way, and many of these mutants proved to have defects in integration. These defects were defined by analyzing the properties of Int-promoted recombination in these att mutants.

The types of mutants found and their properties indicated that attφ has three components: a cross-over point which is bordered on either side by recognition elements whose sequence is specifically required for normal integration. The interactions of the recognition elements in Int-promoted recombination between att mutants was examined and proved to be quite complex. In general, however, it appears that the λ integration system can function with a diverse array of mutant att sites.

The structure of attφ was examined by comparing the genetic properties of various att mutants with their location in the λ chromosome. To map these mutants, the techniques of heteroduplex DNA formation and electron microscopy were employed. It was found that integration cross-overs occur at only one point in attφ and that the recognition sequences that direct the integration enzymes to their site of action are quite small, less than 2000 nucleotides each. Furthermore, no base pair homology was detected between attφ and its bacterial analog, attB. This result clearly demonstrates that λ integration can occur between chromosomes which have little, if any, homology. In this respect, λ integration is unique as a system of recombination since most forms of generalized recombination require extensive base pair homology.

An additional study on the genetic and physical distances in the left arm of the λ genome was described. Here, a large number of conditional lethal nonsense mutants were isolated and mapped, and a genetic map of the entire left arm, comprising a total of 18 genes, was constructed. Four of these genes were discovered in this study. A series of λdg transducing phages was mapped by heteroduplex electron microscopy and the relationship between physical and genetic distances in the left arm was determined. The results indicate that recombination frequency in the left arm is an accurate reflection of physical distances, and moreover, there do not appear to be any undiscovered genes in this segment of the genome.

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A espécie Sotalia guianensis apresenta um variado repertório de assobios que estão ligados a interação social e a diferentes contextos de comportamento. As variações intraespecíficas nas estruturas dos assobios podem indicar diferenças entre populações dessa espécie. O presente estudo caracterizou e comparou o repertório dos assobios de Sotalia guianensis, em três baías do estado do Rio de Janeiro: Baía de Guanabara (BG), Baía de Sepetiba (BS) e Baía da Ilha Grande (BI), utilizando um sistema de gravação com limite superior de frequência de 48 kHz e através da aplicação das análises quantitativas e qualitativas dos parâmetros acústicos. As gravações dos assobios foram realizadas com embarcações de 5,5 e 7m e sistema de gravação composto por um hidrofone High Tech, modelo HTI-96-MIN, e um gravador digital modelo PMD 671 Marantz, com limite superior de frequência de 48 kHz. As análises dos espectrogramas foram realizadas com os softwares Adobe Audition 1.5 e Raven 1.3. Os assobios foram classificados em seis categorias de forma de contorno e 11 parâmetros acústicos foram medidos para cada assobio. Para comparar os parâmetros acústicos de mesma forma de contorno entre as três baías, foram aplicados a análise descritiva e testes estatísticos de comparação de média. Um total de 1800 assobios foi selecionado e 61,38% (N=1105) dos assobios apresentaram forma de contorno ascendente. Assobios com zero ou um ponto de inflexão foram mais frequentes (N=1476), correspondendo a 82%. A amplitude de frequência encontrada variou de 1,03 a 46,87 kHz, maior alcance registrado para essa espécie no Brasil. A média de duração dos assobios da BG foi menor do que as médias encontradas na BS e na BI. Os resultados de todas as comparações realizadas demonstraram que os parâmetros de frequência (FI, FF, FMAX e F3/4) foram os que mais apresentaram diferenças significativas entre as três áreas. A variação encontrada nos assobios de S. guianensis entre as três áreas estudadas pode também estar ligada aos tipos de assobios mais comuns em cada área, representados pelos assobios ascendentes, que apesar de apresentarem a mesma forma de contorno, possuem diferenças em seus parâmetros acústicos, possivelmente ligados a informações individuais. A utilização de um sistema de gravação com limite superior de 48 kHz possibilitou a análise de muitos assobios. Com isso, foi possível verificar a importância do limite de frequência aplicado para caracterizar o repertório acústico dessa espécie, juntamente com as análises qualitativas das formas de contorno e as análises quantitativas dos parâmetros acústicos dos assobios. A aplicação dessa metodologia foi eficaz na comparação intraespecífica dos assobios, e futuramente, estudos mais detalhados da classificação dos assobios, poderá acrescentar informações relevantes sobre a variação desse tipo de emissão sonora no repertório acústico S. guianensis

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Atualmente no cenário mundial a qualidade da água tem gerado muitas preocupações, pois milhares de produtos sintéticos são produzidos para facilitar muitas práticas industriais, domésticas e pessoais e com isso diversas substâncias químicas utilizadas para esses fins são introduzidas no meio ambiente. Os parabenos são substâncias químicas utilizadas pelas indústrias farmacêuticas, de alimentos e cosméticos e que cuja função é a conservação, sendo que há muitos questionamentos em relação a sua segurança, pois alguns relatórios têm mostrado que a exposição a esses parabenos pode modular ou perturbar o sistema endócrino e com isso gerar consequências prejudiciais à saúde humana e aos ambientes aquáticos. Esse estudo teve como objetivo avaliar a presença dos Parabenos Metilparabeno e Propilparabeno no ambiente aquático e os seus potenciais estrogênicos e a toxicidade aguda. A metodologia se desenvolveu a partir do ensaio in vitro YES para a determinação da atividade estrogênica, ensaios de toxicidade aguda em Daphnia similis e em Aliivibrio fischeri e a quantificação dos parabenos na água do Rio Maracanã-RJ através da cromatografia líquida acoplada ao espectrômetro de massa. Os resultados obtidos para a CE50 dos MP e PP, a partir do ensaio in vitro YES, foi de 18,91 mgL-1 e 7 mgL-1 e a magnitude da resposta foi de 10-5 e 10-4 menos potente que 17ß-estradiol para o MP e o PP, respectivamente. A partir do ensaio de toxicidade aguda, os valores de CE50 obtidos em Daphnia similis, foi de 29,42 mgL-1 e 9,94 mgL-1e em Aliivibrio fischeri foi de 3,047 mgL-1 e 1,946 mgL-1, respectivamente, com isso observou-se que o PP é mais tóxicos em todos os organismos testados, sendo mais tóxicos para um e menos para outros. A água do Rio Maracanã não foi tóxica para a Daphnia similis em nenhum dos dois pontos, já para o Aliivibrio fischeri foi tóxica em apenas um ponto. As concentrações encontradas de MP e PP foram maiores no ponto onde, de acordo com os parâmetros físico-químicos, a qualidade da água não está dentro dos padrões exigidos pela legislação, sendo quantificados na ordem de ngL-1, contudo é válido ressaltar que os DEs não são encontrados no meio ambiente separados, eles interagem entre si e provocam efeitos aditivos ou sinérgicos, sendo muito difícil de prever qual o efeito, por isso é importante o conhecimento do potencial estrogênico das substâncias simples, pois em um estudo com uma matriz ambiental, pode-se observar se houve algum efeito aditivo ou sinérgico de outras substâncias.

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An high-resolution prestack imaging technique of seismic data is developed in this thesis. By using this technique, the reflected coefficients of sheet sands can be gained in order to understand and identify thin oil reservoirs. One-way wave equation based migration methods can more accurately model seismic wave propagation effect such as multi-arrivals and obtain almost correct reflected energy in the presence of complex inhomogeneous media, and therefore, achieve more superiorities in imaging complex structure. So it is a good choice to apply the proposed high-resolution imaging to the presatck depth migration gathers. But one of the main shorting of one-way wave equation based migration methods is the low computational efficiency, thus the improvement on computational efficiency is first carried out. The method to improve the computational efficiency of prestack depth migration is first presented in this thesis, that is frequency-dependent varying-step depth exploration scheme plus a table-driven, one-point wavefield interpolation technology for wave equation based migration methods; The frequency-dependent varying-step depth exploration scheme reduces the computational cost of wavefield depth extrapolation, and the a table-driven, one-point wavefield interpolation technology reconstructs the extrapolated wavefield with an equal, desired vertical step with high computational efficiency. The proposed varying-step depth extrapolation plus one-point interpolation scheme results in 2/3 reduction in computational cost when compared to the equal-step depth extrapolation of wavefield, but gives the almost same imaging. The frequency-dependent varying-step depth exploration scheme is presented in theory by using the optimum split-step Fourier. But the proposed scheme can also be used by other wave equation based migration methods of the frequency domain. The proposed method is demonstrated by using impulse response, 2-D Marmousi dataset, 3-D salt dataset and the 3-D field dataset. A method of high-resolution prestack imaging is presented in the 2nd part of this thesis. The seismic interference method to solve the relative reflected coefficients is presented. The high-resolution imaging is obtained by introducing a sparseness- constrained least-square inversion into the reflected coefficient imaging. Gaussian regularization is first imposed and a smoothed solution is obtained by solving equation derived from the least-square inversion. Then the Cauchy regularization is introducing to the least-square inversion , the sparse solution of relative reflected coefficients can be obtained, that is high-resolution solution. The proposed scheme can be used together with other prestack imaging if the higher resolution is needed in a target zone. The seismic interference method in theory and the solution to sparseness-constrained least-square inversion are presented. The proposed method is demonstrated by synthetic examples and filed data.

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Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.

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The phototherapy effects in the skin are related to biomodulation, usually to accelerate wound healing. However, there is no direct proof of the interrelation between the effects of low-level laser therapy (LLLT) and light-emitting diode (LED) in neuropeptide secretion, these substances being prematurely involved in the neurogenic inflammation phase of wound healing. This study therefore focused on investigating LLLT and LED in Calcitonin gene-related peptide (CGRP) and substance P (SP) secretion in healthy rat skin. Forty rats were randomly distributed into five groups with eight rats each: Control Group, Blue LED Group (470 nm, 350 mW power), Red LED Group (660 nm, 350 mW power), Red Laser Group (660 nm, 100 mW power), and Infrared Laser Group (808 nm, 100 mW power) (DMCA (R) Equipamentos Ltda., So Carlos, So Paulo, Brazil). the skin of the animals in the experimental groups was irradiated using the punctual contact technique, with a total energy of 40 J, single dose, standardized at one point in the dorsal region. After 14 min of irradiation, the skin samples were collected for CGRP and SP quantification using western blot analysis. SP was released in Infrared Laser Group (p = 0.01); there was no difference in the CGRP secretion among groups. Infrared (808 nm) LLLT enhances neuropeptide SP secretion in healthy rat skin.

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Ashmore, P. Brayshay, B.A Edwards, K.J Gilbertson, D. Grattan, J. Kent, M. Pratt, K. Weaver, R. 'Allochthonous and autochthonous mire deposits, slope instability and palaeoenvironmental investigations in the Borve Valley, Barra, Outer Hebrides, Scotland' The Holocene 2000 10, 1 pp.97-108

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In this paper we discuss a new type of query in Spatial Databases, called Trip Planning Query (TPQ). Given a set of points P in space, where each point belongs to a category, and given two points s and e, TPQ asks for the best trip that starts at s, passes through exactly one point from each category, and ends at e. An example of a TPQ is when a user wants to visit a set of different places and at the same time minimize the total travelling cost, e.g. what is the shortest travelling plan for me to visit an automobile shop, a CVS pharmacy outlet, and a Best Buy shop along my trip from A to B? The trip planning query is an extension of the well-known TSP problem and therefore is NP-hard. The difficulty of this query lies in the existence of multiple choices for each category. In this paper, we first study fast approximation algorithms for the trip planning query in a metric space, assuming that the data set fits in main memory, and give the theory analysis of their approximation bounds. Then, the trip planning query is examined for data sets that do not fit in main memory and must be stored on disk. For the disk-resident data, we consider two cases. In one case, we assume that the points are located in Euclidean space and indexed with an Rtree. In the other case, we consider the problem of points that lie on the edges of a spatial network (e.g. road network) and the distance between two points is defined using the shortest distance over the network. Finally, we give an experimental evaluation of the proposed algorithms using synthetic data sets generated on real road networks.