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1.
Waste Manag ; 29(1): 360-7, 2009 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-18799299

RESUMEN

An investigation was carried out to establish the physical, mechanical and chemical characteristics of a non-standard (unprocessed) pulverised fuel ash (PFA) and waste tyres from a former landfill site at the Power Station Hill near Church Village, South Wales, United Kingdom. Investigations are on-going to establish the suitability of the fly ash and/or tyres in road construction (embankment and pavement) and also in concrete to be used in the construction of the proposed highway. This paper reports on concrete-based construction where concrete blends (using various levels of PFA as partial replacement for Portland cement (PC), and shredded waste tyres (chips 15-20mm) as aggregate replacement) were subjected to unconfined compressive strength tests to establish performance, hence, optimising mix designs. Strength development up to 180 days for the concrete made with PC-PFA blends as binders (PC-PFA concrete), with and without aggregate replacement with tyre chips, is reported. The binary PC-PFA concrete does not have good early strength but tends to improve at longer curing periods. The low early strength observed means that PC-PFA concrete cannot be used for structures, hence, only as low to medium strength applications such as blinding, low-strength foundations, crash barriers, noise reduction barriers, cycle paths, footpaths and material for pipe bedding.


Asunto(s)
Carbono , Conservación de los Recursos Naturales/métodos , Materiales de Construcción , Material Particulado , Goma , Residuos , Ceniza del Carbón , Microscopía Electrónica de Rastreo , Eliminación de Residuos/métodos
2.
J Phys Condens Matter ; 30(31): 315901, 2018 Aug 08.
Artículo en Inglés | MEDLINE | ID: mdl-29916821

RESUMEN

A two-phase Hessian approach to DFT slab relaxation of slabs has been implemented and tested. It addresses weaknesses in the modified Broyden and Pfrommer BFGS algorithms specific to relaxing slabs. Complete Hessian and then inverse Hessian matrices with no strain/stress components are first constructed at high force signal-to-noise ratios with no accompanying relaxation. In a second phase the static inverse Hessian is used to relax the slab down to a low force tolerance.

3.
Endocrinology ; 97(4): 1008-13, 1975 Oct.
Artículo en Inglés | MEDLINE | ID: mdl-1193000

RESUMEN

Rabbit hearts perfused by the Langendorff technique were studied. The addition of ovine prolactin (NIH-P-S-10) to the perfusate in a concentration of 50 ng/ml produced rapid increases in both the amplitude and rate of contraction in 33 adult male hearts studied in winter. Prepubertal male animals showed no response, and only 1 out of 12 adult females responded. Pretreatment for 10 days with 2.5 mg/day testosterone propionate led to minimal inotropic but not chronotropic responses in 2 out of 4 prepubertal males and 2 out of 4 adult females to prolactin. Clear responses to prolactin were seen in 5 adult males pretreated with reserpine. Propanolol consistently reversed both the inotropic and chronotropic actions of prolactin. The original experiments were performed in January and February. When tested in May, adult males failed to respond to prolactin and this situation, persisted until October when responsiveness again appeared. The same prolactin preparation and procedures were used throughout indicating that the changes must have been due to seasonal variations in the cardiac responsiveness to the hormone.


Asunto(s)
Frecuencia Cardíaca/efectos de los fármacos , Contracción Miocárdica/efectos de los fármacos , Prolactina/farmacología , Animales , Interacciones Farmacológicas , Femenino , Masculino , Propranolol/farmacología , Conejos , Reserpina/farmacología , Estaciones del Año , Factores Sexuales , Maduración Sexual , Testosterona/farmacología
4.
Neuropharmacology ; 43(4): 467-75, 2002 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-12367593

RESUMEN

In both human and rat tissues, complex patterns of transcripts are derived from the genes that encode the gamma-aminobutyric acid (GABA)(A) receptor epsilon subunit. An epsilon subunit transcript (approximately 3.6 kb) is expressed at relatively high levels in regions of the human brain and heart, but is not detected in most other major tissues. The encoded human epsilon subunit (epsilon (h)) confers distinctive properties to receptors into which it assembles. A distinct transcript of the gene (6.2 kb) is expressed abundantly in a variety of human tissues. This alternative transcript (ET2) appears to originate from within the epsilon subunit gene. It is possible that this transcript encodes a truncated subunit (epsilon (hS)), containing all of the transmembrane and intracellular domains. However, a combination of biochemical and electrophysiological analyses does not support this hypothesis. A distinct transcript of the epsilon subunit gene, encoding a large extracellular pro/glx domain, is expressed abundantly in rat and mouse brain. Functional analyses also failed to provide evidence for incorporation of this subunit (epsilon (rL)) into recombinant receptors. However, a shorter rat epsilon subunit (epsilon (r)), which lacks the pro/glx domain, conferred epsilon (h)-like properties to recombinant receptors, providing evidence for a functional rat epsilon subunit. In common with its human orthologue, incorporation of the epsilon (r) subunit into recombinant GABA(A) receptors confers several distinctive properties, including a reduced modulation by the anesthetic propofol and the appearance of spontaneous current.


Asunto(s)
Receptores de N-Metil-D-Aspartato/genética , Animales , Western Blotting , Membrana Celular/química , Membrana Celular/metabolismo , Clonación Molecular , ADN Complementario/genética , Electrofisiología , Regulación de la Expresión Génica/genética , Humanos , Potenciales de la Membrana/fisiología , Técnicas de Placa-Clamp , Ratas , Receptores de N-Metil-D-Aspartato/metabolismo , Proteínas Recombinantes/biosíntesis , Proteínas Recombinantes/genética , Especificidad de la Especie , Transfección
5.
Neuropharmacology ; 39(4): 611-20, 2000 Feb 14.
Artículo en Inglés | MEDLINE | ID: mdl-10728882

RESUMEN

Cell lines are commonly used for studying recombinant heterooligomeric ion channels with defined subunit composition. Such studies often ignore the contribution of endogenous proteins in the assembly of mature channels. We examined whether an endogenous subunit was required for the functional expression of gamma-aminobutyric acid type A (GABA(A)) receptors in WSS-1 cells, HEK293 cells stably expressing recombinant alpha1 and gamma2 subunits. Our pharmacological and RT-PCR analyses of GABA(A) receptors and their mRNAs in WSS-1 cells confirm the presence of alpha1 and gamma2 subunits and suggest the existence of an endogenous beta3 subunit. Whole-cell GABA-evoked currents recorded from untransfected WSS-1 cells were blocked by bicuculline methiodide and enhanced by anesthetics and anticonvulsants including the subunit-selective compounds diazepam and loreclezole. These data suggest that, in addition to the gamma2 subunit, WSS-1 cell receptors also contain beta2/3 subunits. RT-PCR revealed that WSS-1 cells and parental HEK293 cells contain beta3 mRNA. We examined the contribution of the beta3 subunit in the function of receptors formed by expression of alpha1 and gamma2S subunits. Untransfected HEK293 cells were unresponsive to GABA. Cells transfected with alpha1 and gamma2S cDNAs displayed small diazepam and loreclezole responsive GABA-activated currents. By contrast, the expression of alpha1 and gamma2S cDNAs in the neuroblastoma NB41A3 cell line, that lacks beta subunit mRNAs, failed to produce functional receptors. These data reaffirm that alpha1 and gamma2S subunits alone do not form functional GABA(A) receptors and that receptors of WSS-1 cells contain alpha1, beta3 and gamma2S subunits.


Asunto(s)
Receptores de GABA-A/metabolismo , Animales , Línea Celular , Diazepam/farmacología , Moduladores del GABA/farmacología , Humanos , Ratones , Técnicas de Placa-Clamp , ARN Mensajero/metabolismo , Receptores de GABA-A/efectos de los fármacos , Receptores de GABA-A/fisiología , Proteínas Recombinantes/metabolismo , Reacción en Cadena de la Polimerasa de Transcriptasa Inversa , Transfección , Triazoles/farmacología
6.
Neuropharmacology ; 44(2): 214-23, 2003 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-12623220

RESUMEN

The identification of a second 5-HT(3) (5-HT(3B)) subunit provides an explanation for 5-HT(3) receptor heterogeneity. We investigated whether introduction of recombinant 5-HT(3B) subunits would alter the functional properties of mouse neuroblastoma 5-HT(3) receptors. RT-PCR analysis revealed that NB41A3 cells contain mRNAs encoding 5-HT(3A) and 5-HT(3B) subunits. 5-HT increased intracellular Ca(2+) concentration ([Ca(2+)](i)) and caused the concentration-dependent activation of inward currents recorded at -60 mV. Both actions of 5-HT were antagonized by ondansetron. The 5-HT concentration-response relationship of NB41A3 cells was indistinguishable from that of the related NG108-15 cell line. The selective 5-HT(3)-receptor agonist mCPBG also elevated [Ca(2+)](i) and activated inward currents. 2-M-5HT was less efficacious than 5-HT as an activator of 5-HT(3) receptors in NB41A3 cells and did not significantly increase [Ca(2+)](i). The 5-HT induced increase in [Ca(2+)](i) did not involve caffeine- or thapsigargin-sensitive intracellular Ca(2+) stores. The introduction of the 5-HT(3B) subunit by transient transfection of NB41A3 cells caused 5-HT to become less potent as an activator of 5-HT(3) receptors and altered the kinetics of 5-HT activated currents so that they resembled currents mediated by 5-HT(3AB) receptors. The 5-HT(3B) subunit also abolished the 5-HT induced [Ca(2+)](i) increase seen in untransfected NB41A3 cells. These data are consistent with the hypothesis that NB41A3 cells predominantly express homomeric 5-HT(3A) receptors that become heteromeric 5-HT(3AB) receptors upon introduction of the recombinant 5-HT(3B) subunit.


Asunto(s)
Subunidades de Proteína/metabolismo , Receptores de Serotonina/metabolismo , Receptores de Serotonina/fisiología , Proteínas Recombinantes de Fusión/fisiología , Serotonina/análogos & derivados , Serotonina/farmacología , Animales , Biguanidas/farmacología , Calcio/metabolismo , Diferenciación Celular/efectos de los fármacos , Diferenciación Celular/fisiología , Línea Celular/clasificación , Relación Dosis-Respuesta a Droga , Interacciones Farmacológicas , Fluorescencia , Expresión Génica , Proteínas Fluorescentes Verdes , Proteínas Luminiscentes/metabolismo , Ratones , Datos de Secuencia Molecular , Neuroblastoma/clasificación , Ondansetrón/farmacología , Técnicas de Placa-Clamp , ARN Mensajero/análisis , Ratas , Receptores de Serotonina/química , Receptores de Serotonina/genética , Receptores de Serotonina 5-HT3 , Proteínas Recombinantes/química , Proteínas Recombinantes/metabolismo , Reacción en Cadena de la Polimerasa de Transcriptasa Inversa , Antagonistas de la Serotonina/farmacología , Agonistas de Receptores de Serotonina/farmacología , Transfección
7.
Br J Pharmacol ; 120(5): 899-909, 1997 Mar.
Artículo en Inglés | MEDLINE | ID: mdl-9138697

RESUMEN

1. Radioligand binding and patch-clamp techniques were used to study the actions of gamma-aminobutyric acid (GABA) and the general anaesthetics propofol (2,6-diisopropylphenol), pentobarbitone and 5 alpha-pregnan-3 alpha-ol-20-one on rat alpha 1 and beta 3 GABAA receptor subunits, expressed either alone or in combination. 2. Membranes from HEK293 cells after transfection with alpha 1 cDNA did not bind significant levels of [35S]-tert-butyl bicyclophosphorothionate ([35S]-TBPS) (< 0.03 pmol mg-1 protein). GABA (100 microM) applied to whole-cells transfected with alpha 1 cDNA and clamped at -60 mV, also failed to activate discernible currents. 3. The membranes of cells expressing beta 3 cDNAs bound [35S]-TBPS (approximately 1 pmol mg-1 protein). However, the binding was not influenced by GABA (10 nM-100 microM). Neither GABA (100 microM) nor picrotoxin (10 microM) affected currents recorded from cells expressing beta 3 cDNA, suggesting that beta 3 subunits do not form functional GABAA receptors or spontaneously active ion channels. 4. GABA (10 nM-100 microM) modulated [35S]-TBPS binding to the membranes of cells transfected with both alpha 1 and beta 3 cDNAs. GABA (0.1 microM-1 mM) also dose-dependently activated inward currents with an EC50 of 9 microM recorded from cells transfected with alpha 1 and beta 3 cDNAs, clamped at -60 mV. 5. Propofol (10 nM-100 microM), pentobarbitone (10 nM-100 microM) and 5 alpha-pregnan-3 alpha-ol-20-one (1 nM-30 microM) modulated [35S]-TBPS binding to the membranes of cells expressing either alpha 1 beta 3 or beta 3 receptors. Propofol (100 microM), pentobarbitone (1 mM) and 5 alpha-pregnan-3 alpha-ol-20-one (10 microM) also activated currents recorded from cells expressing alpha 1 beta 3 receptors. 6. Propofol (1 microM-1 mM) and pentobarbitone (1 mM) both activated currents recorded from cells expressing beta 3 homomers. In contrast, application of 5 alpha-pregnan-3 alpha-ol-20-one (10 microM) failed to activate detectable currents. 7. Propofol (100 microM)-activated currents recorded from cells expressing either alpha 1 beta 3 or beta 3 receptors reversed at the Cl- equilibrium potential and were inhibited to 34 +/- 13% and 39 +/- 10% of control, respectively, by picrotoxin (10 microM). 5 alpha-Pregnan-3 alpha-ol-20-one (100 nM) enhanced propofol (100 microM)-evoked currents mediated by alpha 1 beta 3 receptors to 1101 +/- 299% of control. In contrast, even at high concentration 5 alpha-pregnan-3 alpha-ol-20-one (10 microM) caused only a modest facilitation (to 128 +/- 12% of control) of propofol (100 microM)-evoked currents mediated by beta 3 homomers. 8. Propofol (3-100 microM) activated alpha 1 beta 3 and beta 3 receptors in a concentration-dependent manner. For both receptor combinations, higher concentrations of propofol (300 microM and 1 mM) caused a decline in current amplitude. This inhibition of receptor function reversed rapidly during washout resulting in a "surge' current on cessation of propofol (300 microM and 1 mM) application. Surge currents were also evident following pentobarbitone (1 mM) application to cells expressing either receptor combination. By contrast, this phenomenon was not apparent following applications of 5 alpha-pregnan-3 alpha-ol-20-one (10 microM) to cells expressing alpha 1 beta 3 receptors. 9. These observations demonstrate that rat beta 3 subunits form homomeric receptors that are not spontaneously active, are insensitive to GABA and can be activated by some general anaesthetics. Taken together, these data also suggest similar sites on GABAA receptors for propofol and barbiturates, and a separate site for the anaesthetic steroids.


Asunto(s)
Anestésicos Generales/farmacología , Pentobarbital/farmacología , Pregnanolona/farmacología , Propofol/farmacología , Receptores de GABA-A/efectos de los fármacos , Animales , Compuestos Bicíclicos Heterocíclicos con Puentes/metabolismo , Línea Celular Transformada , Humanos , Ensayo de Unión Radioligante , Ratas , Receptores de GABA-A/química , Receptores de GABA-A/clasificación , Proteínas Recombinantes/química , Proteínas Recombinantes/clasificación , Proteínas Recombinantes/efectos de los fármacos , Radioisótopos de Azufre , Ácido gamma-Aminobutírico/farmacología
8.
Plant Cell Rep ; 17(3): 206-210, 1998 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-30736501

RESUMEN

Comparisons were made between the efficiency of barley plant regeneration from anther culture (AC) and isolated microspore culture (IMC) for the European winter cultivar `Igri' and the spring F1 Australian breeder's hybrid Amagi Nijo×WI2585. In both cases, IMC produced a higher number of green regenerant plantlets per anther than AC. For `Igri' there was a 100- to 200-fold improvement and for Amagi Nijo×WI2585 there was a five- to ninefold improvement of IMC over AC. To improve the consistency and reliability of the IMC method, we investigated several parameters, including maltose concentration, subculture protocol, microspore plating density and colony plating density. Subculturing during the liquid culture phase produced no significant improvement in the number of microspores developing into colonies. The optimal concentration of maltose in the liquid induction medium was found to be 90 g l-1. Both microspore plating density and colony plating density were found to influence plant regeneration. Microspores produced the highest numbers of colonies when plated at densities greater than 5×104 ml-1, and colonies produced optimal numbers of green plantlets when plated at 12.5-25 colonies/cm2.

9.
Man Ther ; 5(3): 158-64, 2000 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-11034886

RESUMEN

Flexion and extension movements or positions have been advocated in the treatment of various forms of low back dysfunction due to the potential pain relieving effects attributed to displacements of the intervertebral disc (IVD). Objective in vivo determination of the segmental behaviour of the disc to contrasting positions has until recently been difficult. Magnetic resonance imaging (MRI) was used in this study to evaluate the influence of sagittal plane positions on lumbar IVD height and nucleus displacement in a small asymptomatic population.T2-weighted sagittal plane images from L1 to S1 were obtained from 10 subjects (mean age: 30+/-5 years) positioned supine in lumbar flexion, followed by extension. Changes in disc height and localization of nucleus position (determined by peak MRI signal intensity) between the two positions were calculated. Discs were classified for degenerative changes using a semi-quantitative grading scale. The mean range of lumbar sagittal movement achieved in the MRI was 44 degrees (range: 22-77 degrees ). Between flexion and extension, a significant increase in measured anterior disc height of 1.1 mm (P<0.0001) and anterior displacement of the nucleus of 6.7% (P<0.0001) was observed. Despite the anterior displacement of the nucleus in extension observed in the pooled analysis, 30% of discs did not follow this trend. Nucleus degeneration was observed in at least one disc in nine subjects and in 26% of all discs examined. Lumbar spine position was found to be associated with small measured changes in anterior disc height and nucleus position, however, this response was variable within and between individuals. The theoretical concept of a stereotypical effect of spinal position on the lumbar IVD is challenged by these initial data. Since the health of the disc is often unknown in clinical practice, manual therapy treatment for lumbar spine pain should be based on the symptomatic response to movement and position rather than biomechanical theory.


Asunto(s)
Interpretación de Imagen Asistida por Computador/métodos , Desplazamiento del Disco Intervertebral/diagnóstico , Dolor de la Región Lumbar/diagnóstico , Vértebras Lumbares/patología , Imagen por Resonancia Magnética/métodos , Adulto , Análisis de Varianza , Femenino , Humanos , Imagen por Resonancia Magnética/instrumentación , Masculino , Rango del Movimiento Articular , Reproducibilidad de los Resultados
10.
Acta Cytol ; 27(3): 334-6, 1983.
Artículo en Inglés | MEDLINE | ID: mdl-6575551

RESUMEN

A 17-year-old active sportsman presented three weeks after a football injury with pain in the right hip and back. Osteomyelitis was the initial clinical diagnosis. A full blood count and erythrocyte sedimentation rate were normal. Fine needle aspiration of the anterior inferior iliac spine showed the presence of numerous blasts. This case represents an unusual presentation and method of diagnosis of acute leukemia.


Asunto(s)
Leucemia Linfoide/patología , Adolescente , Biopsia con Aguja , Citodiagnóstico/métodos , Humanos , Íleon/diagnóstico por imagen , Leucemia Linfoide/diagnóstico , Masculino , Radiografía
11.
Int J Artif Organs ; 13(12): 837-45, 1990 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-2289837

RESUMEN

A mathematical model is developed which relates the time needed to perform immunoadsorption with Sepharose-Protein A to the column dimensions and choice of whether to use one or two columns. Measurements of parameters needed to apply the model, including the reaction rate constant and adsorption capacity, are reported. It is concluded that one large column can remove immunoglobulins more quickly than two smaller columns containing the same total volume of Sepharose-Protein A, but with the penalty of a greater loss of other plasma constituents. The model involves only simple computations, and can be applied to other immunoadsorbents if the dissociation constant of the complex formed by adsorption is lower than the final plasma concentration of the molecule adsorbed.


Asunto(s)
Inmunoglobulinas , Técnicas de Inmunoadsorción , Sefarosa , Proteína Estafilocócica A , Humanos , Modelos Teóricos , Factores de Tiempo
12.
Waste Manag ; 33(11): 2234-44, 2013 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-23978558

RESUMEN

The uptake in Europe of Energy from Waste (EfW) incinerator plants has increased rapidly in recent years. In the UK, 25 municipal waste incinerators with energy recovery are now in operation; however, their waste supply chains and business practices vary significantly. With over a hundred more plant developments being considered it is important to establish best business practices for ensuring efficient environmental and operational performance. By reviewing the 25 plants we identify four suitable case study plants to compare technologies (moving grate, fluidised bed and rotary kiln), plant economics and operations. Using data collected from annual reports and through interviews and site visits we provide recommendations for improving the supply chain for waste incinerators and highlight the current issues and challenges faced by the industry. We find that plants using moving grate have a high availability of 87-92%. However, compared to the fluidised bed and rotary kiln, quantities of bottom ash and emissions of hydrogen chloride and carbon monoxide are high. The uptake of integrated recycling practices, combined heat and power, and post incineration non-ferrous metal collections needs to be increased among EfW incinerators in the UK. We conclude that one of the major difficulties encountered by waste facilities is the appropriate selection of technology, capacity, site, waste suppliers and heat consumers. This study will be of particular value to EfW plant developers, government authorities and researchers working within the sector of waste management.


Asunto(s)
Incineración/normas , Incineración/instrumentación , Reino Unido
14.
Water Res ; 44(1): 320-30, 2010 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-19800651

RESUMEN

A combination of experimental methods was applied at a clogged, horizontal subsurface flow (HSSF) municipal wastewater tertiary treatment wetland (TW) in the UK, to quantify the extent of surface and subsurface clogging which had resulted in undesirable surface flow. The three dimensional hydraulic conductivity profile was determined, using a purpose made device which recreates the constant head permeameter test in-situ. The hydrodynamic pathways were investigated by performing dye tracing tests with Rhodamine WT and a novel multi-channel, data-logging, flow through Fluorimeter which allows synchronous measurements to be taken from a matrix of sampling points. Hydraulic conductivity varied in all planes, with the lowest measurement of 0.1md(-1) corresponding to the surface layer at the inlet, and the maximum measurement of 1550md(-1) located at a 0.4m depth at the outlet. According to dye tracing results, the region where the overland flow ceased received five times the average flow, which then vertically short-circuited below the rhizosphere. The tracer break-through curve obtained from the outlet showed that this preferential flow-path accounted for approximately 80% of the flow overall and arrived 8h before a distinctly separate secondary flow-path. The overall volumetric efficiency of the clogged system was 71% and the hydrology was simulated using a dual-path, dead-zone storage model. It is concluded that uneven inlet distribution, continuous surface loading and high rhizosphere resistance is responsible for the clog formation observed in this system. The average inlet hydraulic conductivity was 2md(-1), suggesting that current European design guidelines, which predict that the system will reach an equilibrium hydraulic conductivity of 86md(-1), do not adequately describe the hydrology of mature systems.


Asunto(s)
Eliminación de Residuos Líquidos/métodos , Movimientos del Agua , Humedales
18.
Nurs Times ; 64(30): 994-6, 1968 Jul 26.
Artículo en Inglés | MEDLINE | ID: mdl-5661831
19.
Appl Opt ; 31(28): 6021-6, 1992 Oct 01.
Artículo en Inglés | MEDLINE | ID: mdl-20733804

RESUMEN

A new type of lens is described that, when used as a secondary concentrator together with a primary Fresnel lens to illuminate a silicon solar cell, would tend to return escaping light to the cell and therefore enhance the light trapping caused primarily by internal reflection within the silicon. In the ideal case of a perfect mirror at the back surface of the cell, it is calculated that, with a lens with a refractive index of 1.5, the cell could be reduced in thickness by a factor of 3 and still absorb as much light. The thinner cell would permit higher concentration and efficiency. Uniformity of illumination would also be improved by the lens. There are no metallic reflectors used; instead the lens traps light by total internal reflection. Its geometry and properties are presented in terms of the refractive index of the lens material.

20.
Appl Opt ; 31(34): 7277-82, 1992 Dec 01.
Artículo en Inglés | MEDLINE | ID: mdl-20802594

RESUMEN

Ray-tracing computations for calculating the fraction of radiant energy (intercept factor I) transmitted by an optical system are often performed by using the Monte Carlo method, i.e., selection of sample rays at random. However, this is not economical regarding computing time since the error E in I is proportional to N(-(1/2)), where N is the number of rays traced. It is found that, in example computations, the selection of sample rays according to a regular grid gives better results. An equation for estimating E in this case is derived on a theoretical basis and agrees with the computations. This predicts E alpha N(-(3/4)) for systems where three ray coordinates are needed (e.g., with rotational symmetry) and E alpha N(-?) where four are required, which is the general case.

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