Role of G protein coupled inwardly rectifier K+ channels (GIRK) on the neurobiology depression

353 págs.

Population dynamics of the skipjack tuna (Katsuwonus pelamis) of the Eastern Pacific Ocean

ENGLISH: Catches of skipjack tuna supporting major fisheries in parts of the western, central and eastern Pacific Ocean have increased in recent years; thus, it is important to examine the dynamics of the fishery to determine man's effect on the abundance of the stocks. A general linear hypothesis model was developed to standardize fishing effort to a single vessel size and gear type. Standardized effort was then used to compute an index of abundance which accounts for seasonal variability in the fishing area. The indices of abundance were highly variable from year to year in both the northern and southern areas of the fishery but indicated a generally higher abundance in the south. Data from 438 fish tagged and recovered in the eastern Pacific Ocean were used to compute growth curves. A least-squares technique was used to estimate the parameters of the von Bertalanffy growth function. Two estimates of the parameters were made by analyzing the same data in different ways. For the first set of estimates, K= 0.819 on an annual instantaneous basis and L= 729 mm; for the second, K = 0.431 and L=881. These compared well with estimates derived using the Chapman-Richards growth function, which includes the von Bertalanffy function as a special case. It was concluded that the latter function provided an adequate empirical fit to the skipjack data since the more complicated function did not significantly improve the fit. Tagging data from three cruises involving 8852 releases and 1777 returns were used to compute mortality rates during the time the fish were in the fishery. Two models were used in the analyses. The best estimates of the catchability coefficient (q) in the north and south were 8.4 X 10- 4 and 5.0 X 10- 5 respectively. The other loss rate (X), which included losses due to emigration, natural mortality and mortality due to carrying a tag, was 0.14 on an annual instantaneous basis for both areas. To detect the possible effect of fishing on abundance and total yield, the relation between abundance and effort and between total catch and effort was examined. It was found that at levels of intensity observed in the fishery, fishing does not appear to have had any measurable effect on the stocks. It was concluded therefore that the total catch could probably be increased by substantially increasing total effort beyond the present level, and that the fluctuations in abundance are fishery-independent. The estimates of growth, mortality and fishing effort were used to compute yield-per-recruitment isopleths for skipjack in both the northern and southern areas. For a size at first entry of about 425 mm, the yield per recruitment was calculated at 3 pounds in the north and 1.5 pounds in the south. In both areas it would be possible to increase the yield per recruitment by increasing fishing effort. It was not possible to assess potential production of the skipjack stocks fished in the eastern Pacific, except to note that the fishery had not affected their abundance and that they were certainly under-exploited. It was concluded that the northern and southern stocks could support increased harvests, especially the latter. SPANISH: Las capturas de atún barrilete que sostienen las pesquerías principales de la parte occidental, central y oriental del Océano Pacífico han aumentado en los últimos años; así que es importante examinar la dinámica de la pesquería para determinar el efecto que pueda tener sobre la abundancia de los stocks. Se desarrolló un modelo hipotético, lineal para standardizar el esfuerzo de pesca a un solo tamaño de barco y tipo de arte. Luego se usó el esfuerzo standardizado para computar un índice de la abundancia que pueda dar razón de la variabilidad estacional en el área de pesca. Los índices de la abundancia variaron mucho de un año a otro tanto en el área septentrional como en el área meridional de la pesquería, pero indicaron una abundancia generalmente superior en el sur. Se emplearon los datos de 438 peces marcados y recuperados en el Océano Pacífico oriental para computar las curvas de crecimiento. Una técnica de mínimos cuadrados fue usada para estimar los parámetros de la función de crecimiento de van Bertalanffy. Se hicieron dos estimativos de los parámetros mediante el análisis de los mismos datos, de diferente manera. Para el primer juego de estimativos, K=0.819 sobre una base anual instantánea y L∞=729 mm; para el segundo, K=0.431 y L∞=881. Estos se correlacionaron bien con los estimativos obtenidos usando la función de crecimiento de Chapman-Richards, que incluye la de von Bertalanffy como un caso especial. Se decidió que la última función proveía un ajuste empírico, adecuado a los datos del barrilete, ya que la función más complicada no mejoró significativamente el ajuste. Los datos de marcación de tres cruceros incluyendo 8852 liberaciones y 1777 retornos, fueron usados para computar las tasas de mortalidad durante el tiempo en que los peces estuvieron en la pesquería. Se usaron dos modelos en los análisis. Los mejores estimativos del coeficiente de capturabilidad (q) en el norte y en el sur fueron 8.4 X 10-4 y 5.0 X 10-5 , respectivamente. La otra tasa de pérdida (X), la cual incluyó pérdidas debidas a la emigración, mortalidad natural y mortalidad debida a llevar una marca, fue 0.14 sobre una base anual instantánea para las dos áreas. Con el fin de descubrir el efecto que posiblemente pueda tener la pesca sobre la abundancia y el rendimiento total, se examinó la relación entre la abundancia y el esfuerzo y entre la captura total y el esfuerzo. Se encontró que a los niveles de la intensidad observada en la pesquería, la pesca no parece haber tenido ningún efecto perceptible en los stocks. Por lo tanto se decidió que mediante un aumento substancial del esfuerzo total, más allá del nivel actual, la captura total probablemente podría aumentarse, y que las fluctuaciones de la abundancia son independientes de la pesquería. Los estimativos del crecimiento, mortalidad y esfuerzo de pesca fueron usados para computar las isopletas del rendimiento por recluta del barrilete, tanto en las áreas del norte como del sur. Para una talla de primera entrada de unos 425 mm, el rendimiento por recluta fue calculado en 3 libras en el norte y 1.5 libras en el sur. En ambas áreas sería posible aumentar el rendimiento por recluta mediante un aumento del esfuerzo de pesca. No fue posible determinar la producción potencial de los stocks del barrilete pescado en el Pacífico oriental, excepto para observar que la pesquería no ha afectado su abundancia y que ciertamente se encuentran subexplotados. Se concluyó que los stocks norte y sur pueden soportar un aumento en el rendimiento, especialmente este último. (PDF contains 274 pages.)

Splitting the fast and slow motions in molecular dynamics simulations based on the change of cold potential well bottom

Abstract. The atomic motion is coupled by the fast and slow components due to the high frequency vibration of atoms and the low frequency deformation of atomic lattice, respectively. A two-step approximate method was presented to determine the atomic slow motion. The first step is based on the change of the location of the cold potential well bottom and the second step is based on the average of the appropriate slow velocities of the surrounding atoms. The simple tensions of one-dimensional atoms and two-dimensional atoms were performed with the full molecular dynamics simulations. The conjugate gradient method was employed to determine the corresponding location of cold potential well bottom. Results show that our two-step approximate method is appropriate to determine the atomic slow motion under the low strain rate loading. This splitting method may be helpful to develop more efficient molecular modeling methods and simulations pertinent to realistic loading conditions of materials.

The influence of some environmental variables on the apparent abundance of skipjack tuna, Katsuwonus pelamis, in the Eastern Pacific Ocean

ENGLISH: The abundance of skipjack larvae in the central and western Pacific approximately doubled for every 1°C increase in sea-surface temperature (SST) from 23°C to a maximum of about 29°C, and then usually decreased with further increases in SST. Skipjack larvae are scarce in the eastern Pacific Ocean (EPO), so most skipjack recruits and adults in this area are believed to have originated in the central and, possibly, the western Pacific. The catch per unit of effort (CPUE), in short tons per day's fishing, and the catch rate, in number of fish per day's fishing, are estimates of apparent abundance in a fishery. The logarithm of the annual CPUE for skipjack for international baitboats in the EPO for the 1934-1960 period was positively correlated with SST in the spawning area in the central Pacific 18 months earlier (r2 0.31), during the July-June period when most of the recruits in each cohort were presumed to have been spawned. Adequate data for other environmental variables were not available for testing with the baitboat data. The other environmental variables available and selected for testing for correlation with estimates of skipjack abundance for purse seiners for the 1961-1984 period and the reasons for their selection are as follows. 1)Wind-mixing index (WMI). The degree of mixing in the upper layers of the ocean is proportional to the cube of the wind speed, called WMI. The degree of mixing in the spawning areas of the central and the western Pacific may affect the concentration of organisms that skipjack larvae feed upon, thereby influencing their survival, and ultimately determining cohort strength and the number of recruits to the eastern Pacific fishery. 2) SST in the fishing areas at the time of fishing (SST). The CPUE for yellowfin tuna has been shown to be inversely related to SST in the fishing areas, and there are indications that skipjack CPUE is lower during EI Nino events when SST is higher than normal. 3) North-south SST gradient across the thermal front off the Gulf of Guayaquil. This is a measure of the degree of upwelling and nutrient enrichment of the upper waters south of the front and ultimately of the production of food for tunas. 4) Speed of the North Equatorial Countercurrent (NECC). Young skipjack may migrate from the central Pacific to the EPO in the eastward flowing NECC; if so, the number of recruits might be affected by variations in the speed of the current. The logarithm of the annual catch rate of skipjack recruits by international purse seiners in the EPO for the 1961-1984 period was positively correlated with SST in the spawning area of the central Pacific 18 months earlier (r2 = 0.21),and inversely correlated with WMI in the spawning area 18 months earlier (r2 0.46). The logarithm of CPUE for purse seiners in the area off the Gulf of Guayaquil was not correlated with SST in the spawning area 18 months earlier, but was inversely correlated with WMI in the spawning area 18 months earlier (r2 = 0.19), and inversely correlated with the north-south SST gradient in the fishing area at the time of fishing (r2 0.32). Neither of these estimates of apparent abundance from purse seiners were correlated with SST in the fishing areas, or with the speed of the NECC at earlier times. SPANISH: La abundancia de larvas de barrilete en el Pacífico central y occidental se multiplicó por dos, aproximadamente, por cada aumento de 1°Cen la temperatura de la superficie del mar (TSM) entre 23°C y un máximo de unos 29°C, y luego generalmente disminuyó con más aumentos en la TSM. Las larvas de barrilete son escasas en el Océano Pacífico oriental (OPO), y por lo tanto se cree que la mayoría de los reclutas y adultos en esta zona surgieron del Pacífico central, y posiblemente también del Pacífico occidental. La captura por unidad de esfuerzo (CPUE), en toneladas cortas por día de pesca, y la tasa de captura, en número de peces por día de pesca, son estimaciones de la abundancia aparente en una pesquería. El logaritmo de la CPUE anual de barrilete lograda por barcos de carnada en el OPO en el período 1934-1960 se correlacionó positivamente con la TSM en la zona de desove en el Pacífico central de 18 meses antes (r2 = 0.31), durante el período de junio-julio en el cual se cree que nació la mayoría de los reclutas en cada cohorte. No se dispuso de datos suficientes sobre otras variables ambientales para comprobarlos con los datos de los barcos de carnada. Las demás variables ambientales disponibles y seleccionadas para someterlas a pruebas de correlación con las estimaciones de la abundancia del barrilete de barcos cerqueros en el período 1961-1984, y las razones por su selección, son las siguientes: 1) Indice de mezcla por el viento (IMV). El grado de mezcla en las capas superiores del océano es proporcional al cubo de la velocidad del viento, llamado IMV. Es posible que el grado de mezcla en las zonas de desove del Pacífico central y occidental afecte la concentración de los organismos que alimentan a las larvas del barrilete, afectando así la supervivencia de éstas, y finalmente determinando el tamaño de las cohortes y el número de reclutas a la pesquería del OPO. 2) TSM en la zona de pesca al realizarse la pesca (TSM). Se ha mostrado que la relación de la CPUE del atún aleta amarilla a la TSM en la zona de pesca es inversa, y existen indicaciones que la CPUE de barrilete es inferior durante eventos del Niño, cuando las TSM son superiores a lo normal. 3) Gradiente norte-sur de las TSM a través del frente térmico frente al Golfo de Guayaquil. Esto es una medida del grado de afloramiento y enriquecimiento nutritivo del nivel superior de las aguas al sur de dicho frente, y finalmente de la producción de alimento para los atunes. 4) La velocidad de la Contracorriente Ecuatorial del Norte (CCEN). Es posible que los bariletes juveniles migren del Pacífico central al Pacífico oriental en la CCEN, que fluye hacia el este; de ser así, es posible que la cantidad de reclutas se vea afectada por variaciones en la velocidad de la corriente. El logaritmo de la tasa anual de captura de reclutas de barrilete por cerqueros de varias banderas en el OPO en el período 1961-1964 estuvo correlacionado de forma positiva con las TSM en la zona de desove del Pacífico central de 18meses antes (r2 0.21),y de forma inversa con el IMV de la zona de desove de 18 meses antes (r2 0.46). El logaritmo de la CPUE de los cerqueros en la zona frente al Golfo de Guayaquil no estuvo correlacionado con las TSM en la zona de desove de 18 meses antes, pero sí estuvo correlacionado de forma inversa con el IMV en la zona de desove de 18 meses antes (r2 0.19),y con el gradiente norte-sur de las TSM en la zona de pesca al realizarse la pesca (r2 0.32). Ninguna de estas estimaciones de abundancia aparente provenientes de barcos cerqueros estuvo correlacionada con las TSM en las zonas de pesca o con la velocidad de la CCEN en épocas anteriores. (PDF contains 140 pages.)

The influence of diets and body manipulations on the growth of African prawn Macrobrachium vollenhovenii (Herklots)

Live African prawns Macrobrachium vollenhovenii were collected from Asejire reservoir (Nigeria) by trapping. After acclimatization, the prawns were differently amputated: some had their eye-stalks cut; some had their chelae cut; some had both eyestalks and chelae cut while some were intact which served as the control. Each set was placed under different levels of crude protein viz 15%; 20%; and 25%. Weekly weight changes were monitored. Results obtained were subjected to statistical analysis including analysis of variance (ANOVA). The results showed that prawns fed with 20% crude protein had the best growth rate. Specimens with the eyestalk and chelae removed also showed superior growth when compared with the others. Specimens that had their eyestalks removed were able to feed for 18 hours in the day while those with intact body fed for 6 hours during the same period. The amputation of the chelate appendages reduced considerably the cannibalistic urge in the prawns. This enabled a high number of prawns to be grown in the experimental tanks

An investigation of the effect of replacing fish meal with soyabean meal, groundnut cake and blood meal at varied proportion on growth and food utilization of the Clarias anguillaris fingerlings fed in outdoor hapas

Fingerlings of Clarias anguillaris obtained from a homogenous source through induce breeding and each with a mean weight of 2.8g were stocked in ten hapas each measuring 1.0x1.0m in outdoor concrete tank and were fed for eight (8) weeks. Results shows that the best growth rate was recorded among fingerlings fed fish meal as the only protein source (TD5) while DT2 containing soya bean, groundnut cake (40%), blood meal as the protein sources came next. The growth rate of fingerlings fed DT2 (40 % groundnut cake, 10% soyabean meal and 10% blood meal) was higher than those fed DT4 containing 10% fish meal but lower than those fed DT5 which has fish meal as its sole source of protein (53.0%). Analysis of various growth parameters like SGR, FCR and PER. shows that DT5 was the overall best diet but there was no significant statistical difference in weight gained by fish fed the five diets (P <0.05)

A Mechanical Model For The Quantification Of The Effect Of Laser Quenching On Ctod In Steels

The technology of laser quenching is widely used to improve the surface properties of steels in surface engineering. Generally, laser quenching of steels can lead to two important results. One is the generation of residual stress in the surface layer. In general, the residual stress varies from the surface to the interior along the quenched track depth direction, and the residual stress variation is termed as residual stress gradient effect in this work. The other is the change of mechanical properties of the surface layer, such as the increases of the micro-hardness, resulting from the changes of the microstructure of the surface layer. In this work, a mechanical model of a laser-quenched specimen with a crack in the middle of the quenched layer is developed to quantify the effect of residual stress gradient and the average micro-hardness over the crack length on crack tip opening displacement (CTOD). It is assumed that the crack in the middle of the quenched layer is created after laser quenching, and the crack can be a pre-crack or a defect due to some reasons, such as a void, cavity or a micro-crack. Based on the elastic-plastic fracture mechanics theory and using the relationship between the micro-hardness and yield strength, a concise analytical solution, which can be used to quantify the effect of residual stress gradient and the average micro-hardness over the crack length resulting from laser quenching on CTOD, is obtained. The concise analytical solution obtained in this work, cannot only be used as a means to predict the crack driving force in terms of the CTOD, but also serve as a baseline for further experimental investigation of the effect after laser-quenching treatment on fracture toughness in terms of the critical CTOD of a specimen, accounting for the laser-quenching effect. A numerical example presented in this work shows that the CTOD of the quenched can be significantly decreased in comparison with that of the unquenched. (C) 2008 Elsevier B.V. All rights reserved.

Performance analysis of bit error rate for free space optical communication with tip-tilt compensation based on gamma-gamma distribution

In this paper, the gamma-gamma probability distribution is used to model turbulent channels. The bit error rate (BER) performance of free space optical (FSO) communication systems employing on-off keying (OOK) or subcarrier binary phase-shift keying (BPSK) modulation format is derived. A tip-tilt adaptive optics system is also incorporated with a FSO system using the above modulation formats. The tip-tilt compensation can alleviate effects of atmospheric turbulence and thereby improve the BER performance. The improvement is different for different turbulence strengths and modulation formats. In addition, the BER performance of communication systems employing subcarrier BPSK modulation is much better than that of compatible systems employing OOK modulation with or without tip-tilt compensation.

THE FORMATION MECHANISM OF THE VITRIFIED SLAG IN A PLASMA ARC REACTOR FOR HAZARDOUS WASTE TREATMENT

Various hazardous wastes with additives have been vitrified to investigate the formation mechanism of the glassy slag by a 30 kW DC plasma-arc reactor developed by the Institute of Mechanics, Chinese Academy of Sciences. The average temperature in the reaction area is controlled at 1500°C. The chemical compositions of three sorts of fly ashes are analyzed by XRF (X-Ray Fluorescence). Fly ashes with vitrifying additives can be vitrified to form glassy slag, which show that the ratio of the whole oxygen ions to the whole network former ions in glass (R) is appropriate in the range of 2~3 to form durable vitrified slag. In this experiment, the arc power is controlled below 5 kW to inhibit waste evaporation. To enhance the effects of heat transfer to wastes, ferrous powder has been added into the graphite crucible, which aggregates as ingot below the molten silicate after vitrification. The slag fails to form glass if the quenching rate is less than 1 K/min. Therefore, the slag will break into small chips due to the sharp quenching rate, which is more than 100 K/sec.

The cast net fishery, Kainji Lake, Nigeria 1970-1997

This study was carried out to establish trends in the cast net fishery of Kainji Lake, Nigeria. The cast net fishery was second in importance to the gillnet fishery in the early years after impoundment of the lake and still continues to be an important component of the fishery. Some of the economically important species such as Citharinus spp, Tilapia spp, Labeo spp, Alestes spp and Synodontis spp are exploited by cast nets. The study has not revealed any drastic perturbation in the species diversity, catch composition, and any real ecosystem overfishing. On the other hand, both the catfish, Auchenoglanis spp and the predator Hydrocynus spp appear to have increased in the catch in recent years. Never-the-less there is a decline in the mean weight of the major exploited fish species due to the capture of under sized fishes without allowing them to grow to 'legally' marketable sizes. The use of small meshed cast net and also fishing in the shallow waters of the lake can give rise to this situation. Thus, there are signs of growth overfishing in the fish stocks. It must also be acknowledged that the situation is complicated by the fact that in a multi-gear fishery as on Kainji Lake, the cast net fishery could not be managed in isolation without due regard to the other competing gears. The catch per unit of effort (CPUE) has declined in the cast net fishery possibly due to the increase in effort by the major fishing gears over the years. The ongoing extension campaigns by the KLFPP appears to be having the desired effect, as there was reduction in the number of the major fishing gears on the Lake in 1997. It can be anticipated that if this trend continues, the CPUE will recover in the long run. Yields observed from the mesh selectivity study revealed that for major species in the cast net fishery, both by number and weight, were maximal at 2.5 inch mesh, which contrasts with the fact that current minimum allowable mesh in the Fisheries Edict for the Lake is 2.0 inch. The adoption of 2.5 inch as the minimum allowable mesh in the cast net fishery is recommended to be included in future revision of existing regulations. It is also recommended that for this control to have a desired effect, the casting of the net from the shore should be prohibited so as to reduce the incidence of juvenile mortality in the nursery areas. (PDF contains 28 pages)

Studies of molecular bonding, interactions and decomposition reactions on the (001) surface of ruthenium

The interactions of N₂, formic acid and acetone on the Ru(001) surface are studied using thermal desorption mass spectrometry (TDMS), electron energy loss spectroscopy (EELS), and computer modeling.

Low energy electron diffraction (LEED), EELS and TDMS were used to study chemisorption of N₂ on Ru(001). Adsorption at 75 K produces two desorption states. Adsorption at 95 K fills only the higher energy desorption state and produces a (√3 x √3)R30° LEED pattern. EEL spectra indicate both desorption states are populated by N₂ molecules bonded "on-top" of Ru atoms.

Monte Carlo simulation results are presented on Ru(001) using a kinetic lattice gas model with precursor mediated adsorption, desorption and migration. The model gives good agreement with experimental data. The island growth rate was computed using the same model and is well fit by R(t)^m - R(t₀)^m = At, with m approximately 8. The island size was determined from the width of the superlattice diffraction feature.

The techniques, algorithms and computer programs used for simulations are documented. Coordinate schemes for indexing sites on a 2-D hexagonal lattice, programs for simulation of adsorption and desorption, techniques for analysis of ordering, and computer graphics routines are discussed.

The adsorption of formic acid on Ru(001) has been studied by EELS and TDMS. Large exposures produce a molecular multilayer species. A monodentate formate, bidentate formate, and a hydroxyl species are stable intermediates in formic acid decomposition. The monodentate formate species is converted to the bidentate species by heating. Formic acid decomposition products are CO₂, CO, H₂, H₂O and oxygen adatoms. The ratio of desorbed CO with respect to CO₂ increases both with slower heating rates and with lower coverages.

The existence of two different forms of adsorbed acetone, side-on, bonded through the oxygen and acyl carbon, and end-on, bonded through the oxygen, have been verified by EELS. On Pt(111), only the end-on species is observed. On dean Ru(001) and p(2 x 2)O precovered Ru(001), both forms coexist. The side-on species is dominant on clean Ru(001), while O stabilizes the end-on form. The end-on form desorbs molecularly. Bonding geometry stability is explained by surface Lewis acidity and by comparison to organometallic coordination complexes.

ZnSe nanowires grown on the crystal surface by femtosecond laser ablation in air

Uniform ZnSe nanowires are observed on the ablation crater on ZnSe crystal surface irradiated by femtosecond lasers in air, while other parts of the sample surface are not polluted. The nanowire growth rate is about 5 mu m/s, it is higher than that fabricated by chemical vapor deposition method by a factor of 10(4). The nanowire length and diameter can be controlled by varying laser pulse energy and pulse number. The formation mechanism is studied and found to be self-catalyzed vapor-liquid-solid process. (c) 2006 American Institute of Physics.

Inter-stage line ratio of He- and Li-like Ti emissions for the electron temperature measurement

Under coronal conditions, the steady state rate-equations are used to calculate the inter-stage line ratios between Li-like Is(2)2p(P-2(3/2))-> 1s(2)2s -> ((2) S-1/2) and He-like 1s2p (P-1(1))-> 1s(2) (S-1(0)) transitions for Ti in the electronic temperature ranges from 0.1 keV to 20 keV. The results show that the. temperature sensitivities are higher at the electronic temperature less than 5000 eV and the temperature sensitivities will decrease with the increase of electronic temperature.

The theory of long distance electron transfer reactions

The rate of electron transport between distant sites was studied. The rate depends crucially on the chemical details of the donor, acceptor, and surrounding medium. These reactions involve electron tunneling through the intervening medium and are, therefore, profoundly influenced by the geometry and energetics of the intervening molecules. The dependence of rate on distance was considered for several rigid donor-acceptor "linkers" of experimental importance. Interpretation of existing experiments and predictions for new experiments were made.

The electronic and nuclear motion in molecules is correlated. A Born-Oppenheimer separation is usually employed in quantum chemistry to separate this motion. Long distance electron transfer rate calculations require the total donor wave function when the electron is very far from its binding nuclei. The Born-Oppenheimer wave functions at large electronic distance are shown to be qualitatively wrong. A model which correctly treats the coupling was proposed. The distance and energy dependence of the electron transfer rate was determined for such a model.

Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.