867 resultados para curve fitting


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A presente Dissertação de Mestrado tem como objetivo o estudo do problema de inversão sísmica baseada em refletores planos para arranjo fonte-comum (FC) e ponto-médiocomum (PMC). O modelo direto é descrito por camadas homogêneas, isotrópicas com interfaces plano-horizontais. O problema é relacionado ao empilhamento NMO baseado na otimização da função semblance, para seções PMC corrigidas de sobretempo normal (NMO). O estudo foi baseado em dois princípios. O primeiro princípio adotado foi de combinar dois grupos de métodos de inversão: um Método Global e um Método Local. O segundo princípio adotado foi o de cascata, segundo a teoria Wichert-Herglotz-Bateman, que estabelece que para conhecer uma camada inferior tem-se que conhecer primeiro a camada superior (dissecação). A aplicação do estudo é voltada à simulação sísmica de Bacia Sedimentar do Solimões e de Bacia Marinha para se obter uma distribuição local 1D de velocidades e espessuras para a subsuperfície em horizontes alvo. Sendo assim, limitamos a inversão entre 4 e 11 refletores, uma vez que na prática a indústria limita uma interpretação realizada apenas em número equivalente de 3 a 4 refletores principais. Ressalta-se que este modelo é aplicável como condição inicial ao imageamento de seções sísmicas em regiões geologicamente complexas com variação horizontal suave de velocidades. Os dados sintéticos foram gerados a partir dos modelos relacionados a informações geológicas, o que corresponde a uma forte informação a priori no modelo de inversão. Para a construção dos modelos relacionados aos projetos da Rede Risco Exploratório (FINEP) e de formação de recursos humanos da ANP em andamento, analisamos os seguintes assuntos relevantes: (1) Geologia de bacias sedimentares terrestre dos Solimões e ma rinha (estratigráfica, estrutural, tectônica e petrolífera); (2) Física da resolução vertical e horizontal; e (3) Discretização temporal-espacial no cubo de multi-cobertura. O processo de inversão é dependente do efeito da discretização tempo-espacial do campo de ondas, dos parâmetros físicos do levantamento sísmico, e da posterior reamostragem no cubo de cobertura múltipla. O modelo direto empregado corresponde ao caso do operador do empilhamento NMO (1D), considerando uma topografia de observação plana. O critério básico tomado como referência para a inversão e o ajuste de curvas é a norma 2 (quadrática). A inversão usando o presente modelo simples é computacionalmente atrativa por ser rápida, e conveniente por permitir que vários outros recursos possam ser incluídos com interpretação física lógica; por exemplo, a Zona de Fresnel Projetada (ZFP), cálculo direto da divergência esférica, inversão Dix, inversão linear por reparametrização, informações a priori, regularização. A ZFP mostra ser um conceito út il para estabelecer a abertura da janela espacial da inversão na seção tempo-distância, e representa a influência dos dados na resolução horizontal. A estimativa da ZFP indica uma abertura mínima com base num modelo adotado, e atualizável. A divergência esférica é uma função suave, e tem base física para ser usada na definição da matriz ponderação dos dados em métodos de inversão tomográfica. A necessidade de robustez na inversão pode ser analisada em seções sísmicas (FC, PMC) submetida a filtragens (freqüências de cantos: 5;15;75;85; banda-passante trapezoidal), onde se pode identificar, comparar e interpretar as informações contidas. A partir das seções, concluímos que os dados são contaminados com pontos isolados, o que propõe métodos na classe dos considerados robustos, tendo-se como referência a norma 2 (quadrados- mínimos) de ajuste de curvas. Os algoritmos foram desenvolvidos na linguagem de programação FORTRAN 90/95, usando o programa MATLAB para apresentação de resultados, e o sistema CWP/SU para modelagem sísmica sintética, marcação de eventos e apresentação de resultados.

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Zusammenfassung: Thema dieser Arbeit ist der Einfluss von elektrischen Feldern auf die Viskosität nematischer Flüssigkristalle sowie isotroper Polymerlösungen.Für zwei thermotrope nematische Flüssigkristalle, 4-(trans-4'-n-Pentylcyclohexyl)-benzonitril (PCH-5) und 4-n-Pentyl-4'-cyanobiphenyl (5CB), wurde die Viskosität mit elektrorheologischen Messungen in Abhängigkeit von Feldstärke und Scherrate bestimmt. Alle Messwerte kommen bei Auftragung gegen E?/? auf einer Masterkurve zu liegen. Die Anpassung dieser Daten mit einer auf der Theorie von Ericksen und Leslie basierenden Gleichung liefert gleichzeitig die Scherviskositäten ? und ? sowie die Rotationsviskosität ? in guter Übereinstimmung mit Literaturwerten. Elektrorheologische Messungen stellen somit eine Methode zur Bestimmung dieser Viskositätskoeffizienten für Nematen dar, wenn diese eine ausreichend große positive dielektrische Anisotropie aufweisen. Bei den isotropen Polymerlösungen ließ sich der elektrorheologische Effekt des Systems Decalin/Polystyrol im Bereich der Entmischungstemperatur klären. Während im Ein-Phasen-Gebiet nur eine geringe Viskositätsänderung im E-Feld aufgrund elektrohydrodynamischer Strömungen zu beobachten ist, tritt unterhalb der Entmischungstemperatur ein deutlicher, aber nicht reproduzierbarer ER-Effekt auf. Dieser ist auf einen Einfluss des E-Felds auf die Zwei-Phasen-Morphologie zurückzuführen.Für das System Diethylbenzol/Isopentylcellulose wurde ein negativer elektrorheologischer Effekt auf die Dissoziation von assoziierten Polymermolekülen zurückgeführt. Die Dissoziation erfolgt aufgrund der Wirkung des elektrischen Feldes auf freie Ladungen.

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Die Röntgenabsorptionsspektroskopie (Extended X-ray absorption fine structure (EXAFS) spectroscopy) ist eine wichtige Methode zur Speziation von Schwermetallen in einem weiten Bereich von umweltrelevanten Systemen. Um Strukturparameter wie Koordinationszahl, Atomabstand und Debye-Waller Faktoren für die nächsten Nachbarn eines absorbierenden Atoms zu bestimmen, ist es für experimentelle EXAFS-Spektren üblich, unter Verwendung von Modellstrukturen einen „Least-Squares-Fit“ durchzuführen. Oft können verschiedene Modellstrukturen mit völlig unterschiedlicher chemischer Bedeutung die experimentellen EXAFS-Daten gleich gut beschreiben. Als gute Alternative zum konventionellen Kurven-Fit bietet sich das modifizierte Tikhonov-Regularisationsverfahren an. Ergänzend zur Tikhonov-Standardvariationsmethode enthält der in dieser Arbeit vorgestellte Algorithmus zwei weitere Schritte, nämlich die Anwendung des „Method of Separating Functionals“ und ein Iterationsverfahren mit Filtration im realen Raum. Um das modifizierte Tikhonov-Regularisationsverfahren zu testen und zu bestätigen wurden sowohl simulierte als auch experimentell gemessene EXAFS-Spektren einer kristallinen U(VI)-Verbindung mit bekannter Struktur, nämlich Soddyit (UO2)2SiO4 x 2H2O, untersucht. Die Leistungsfähigkeit dieser neuen Methode zur Auswertung von EXAFS-Spektren wird durch ihre Anwendung auf die Analyse von Proben mit unbekannter Struktur gezeigt, wie sie bei der Sorption von U(VI) bzw. von Pu(III)/Pu(IV) an Kaolinit auftreten. Ziel der Dissertation war es, die immer noch nicht voll ausgeschöpften Möglichkeiten des modifizierten Tikhonov-Regularisationsverfahrens für die Auswertung von EXAFS-Spektren aufzuzeigen. Die Ergebnisse lassen sich in zwei Kategorien einteilen. Die erste beinhaltet die Entwicklung des Tikhonov-Regularisationsverfahrens für die Analyse von EXAFS-Spektren von Mehrkomponentensystemen, insbesondere die Wahl bestimmter Regularisationsparameter und den Einfluss von Mehrfachstreuung, experimentell bedingtem Rauschen, etc. auf die Strukturparameter. Der zweite Teil beinhaltet die Speziation von sorbiertem U(VI) und Pu(III)/Pu(IV) an Kaolinit, basierend auf experimentellen EXAFS-Spektren, die mit Hilfe des modifizierten Tikhonov-Regularisationsverfahren ausgewertet und mit Hilfe konventioneller EXAFS-Analyse durch „Least-Squares-Fit“ bestätigt wurden.

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In natural history studies of chronic disease, it is of interest to understand the evolution of key variables that measure aspects of disease progression. This is particularly true for immunological variables in persons infected with the Human Immunodeficiency Virus (HIV). The natural timescale for such studies is time since infection. However, most data available for analysis arise from prevalent cohorts, where the date of infection is unknown for most or all individuals. As a result, standard curve fitting algorithms are not immediately applicable. Here we propose two methods to circumvent this difficulty. The first uses repeated measurement data to provide information not only on the level of the variable of interest, but also on its rate of change, while the second uses an estimate of the expected time since infection. Both methods are based on the principal curves algorithm of Hastie and Stuetzle, and are applied to data from a prevalent cohort of HIV-infected homosexual men, giving estimates of the average pattern of CD4+ lymphocyte decline. These methods are applicable to natural history studies using data from prevalent cohorts where the time of disease origin is uncertain, provided certain ancillary information is available from external sources.

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The goal of this research is to provide a framework for vibro-acoustical analysis and design of a multiple-layer constrained damping structure. The existing research on damping and viscoelastic damping mechanism is limited to the following four mainstream approaches: modeling techniques of damping treatments/materials; control through the electrical-mechanical effect using the piezoelectric layer; optimization by adjusting the parameters of the structure to meet the design requirements; and identification of the damping material’s properties through the response of the structure. This research proposes a systematic design methodology for the multiple-layer constrained damping beam giving consideration to vibro-acoustics. A modeling technique to study the vibro-acoustics of multiple-layered viscoelastic laminated beams using the Biot damping model is presented using a hybrid numerical model. The boundary element method (BEM) is used to model the acoustical cavity whereas the Finite Element Method (FEM) is the basis for vibration analysis of the multiple-layered beam structure. Through the proposed procedure, the analysis can easily be extended to other complex geometry with arbitrary boundary conditions. The nonlinear behavior of viscoelastic damping materials is represented by the Biot damping model taking into account the effects of frequency, temperature and different damping materials for individual layers. A curve-fitting procedure used to obtain the Biot constants for different damping materials for each temperature is explained. The results from structural vibration analysis for selected beams agree with published closed-form results and results for the radiated noise for a sample beam structure obtained using a commercial BEM software is compared with the acoustical results of the same beam with using the Biot damping model. The extension of the Biot damping model is demonstrated to study MDOF (Multiple Degrees of Freedom) dynamics equations of a discrete system in order to introduce different types of viscoelastic damping materials. The mechanical properties of viscoelastic damping materials such as shear modulus and loss factor change with respect to different ambient temperatures and frequencies. The application of multiple-layer treatment increases the damping characteristic of the structure significantly and thus helps to attenuate the vibration and noise for a broad range of frequency and temperature. The main contributions of this dissertation include the following three major tasks: 1) Study of the viscoelastic damping mechanism and the dynamics equation of a multilayer damped system incorporating the Biot damping model. 2) Building the Finite Element Method (FEM) model of the multiple-layer constrained viscoelastic damping beam and conducting the vibration analysis. 3) Extending the vibration problem to the Boundary Element Method (BEM) based acoustical problem and comparing the results with commercial simulation software.

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Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a noninvasive technique for quantitative assessment of the integrity of blood-brain barrier and blood-spinal cord barrier (BSCB) in the presence of central nervous system pathologies. However, the results of DCE-MRI show substantial variability. The high variability can be caused by a number of factors including inaccurate T1 estimation, insufficient temporal resolution and poor contrast-to-noise ratio. My thesis work is to develop improved methods to reduce the variability of DCE-MRI results. To obtain fast and accurate T1 map, the Look-Locker acquisition technique was implemented with a novel and truly centric k-space segmentation scheme. In addition, an original multi-step curve fitting procedure was developed to increase the accuracy of T1 estimation. A view sharing acquisition method was implemented to increase temporal resolution, and a novel normalization method was introduced to reduce image artifacts. Finally, a new clustering algorithm was developed to reduce apparent noise in the DCE-MRI data. The performance of these proposed methods was verified by simulations and phantom studies. As part of this work, the proposed techniques were applied to an in vivo DCE-MRI study of experimental spinal cord injury (SCI). These methods have shown robust results and allow quantitative assessment of regions with very low vascular permeability. In conclusion, applications of the improved DCE-MRI acquisition and analysis methods developed in this thesis work can improve the accuracy of the DCE-MRI results.

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Sediments at the southern summit of Hydrate Ridge display two distinct modes of gas hydrate occurrence. The dominant mode is associated with active venting of gas exsolved from the accretionary prism and leads to high concentrations (15%-40% of pore space) of gas hydrate in seafloor or near-surface sediments at and around the topographic summit of southern Hydrate Ridge. These near-surface gas hydrates are mainly composed of previously buried microbial methane but also contain a significant (10%-15%) component of thermogenic hydrocarbons and are overprinted with microbial methane currently being generated in shallow sediments. Focused migration pathways with high gas saturation (>65%) abutting the base of gas hydrate stability create phase equilibrium conditions that permit the flow of a gas phase through the gas hydrate stability zone. Gas seepage at the summit supports rapid growth of gas hydrates and vigorous anaerobic methane oxidation. The other mode of gas hydrate occurs in slope basins and on the saddle north of the southern summit and consists of lower average concentrations (0.5%-5%) at greater depths (30-200 meters below seafloor [mbsf]) resulting from the buildup of in situ-generated dissolved microbial methane that reaches saturation levels with respect to gas hydrate stability at 30-50 mbsf. Net rates of sulfate reduction in the slope basin and ridge saddle sites estimated from curve fitting of concentration gradients are 2-4 mmol/m**3/yr, and integrated net rates are 20-50 mmol/m**2/yr. Modeled microbial methane production rates are initially 1.5 mmol/m**3/yr in sediments just beneath the sulfate reduction zone but rapidly decrease to rates of <0.1 mmol/m**3/yr at depths >100 mbsf. Integrated net rates of methane production in sediments away from the southern summit of Hydrate Ridge are 25-80 mmol/m**2/yr. Anaerobic methane oxidation is minor or absent in cored sediments away from the summit of southern Hydrate Ridge. Ethane-enriched Structure I gas hydrate solids are buried more rapidly than ethane-depleted dissolved gas in the pore water because of advection from compaction. With subsidence beneath the gas hydrate stability zone, the ethane (mainly of low-temperature thermogenic origin) is released back to the dissolved gas-free gas phases and produces a discontinuous decrease in the C1/C2 vs. depth trend. These ethane fractionation effects may be useful to recognize and estimate levels of gas hydrate occurrence in marine sediments.

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Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero “local mean,” and a final nonoscillatory mode. With this device, we obtain a set of “mean trends,” each of which represents a “mean” in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of “indicial response function” is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.

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The distribution of optimal local alignment scores of random sequences plays a vital role in evaluating the statistical significance of sequence alignments. These scores can be well described by an extreme-value distribution. The distribution’s parameters depend upon the scoring system employed and the random letter frequencies; in general they cannot be derived analytically, but must be estimated by curve fitting. For obtaining accurate parameter estimates, a form of the recently described ‘island’ method has several advantages. We describe this method in detail, and use it to investigate the functional dependence of these parameters on finite-length edge effects.

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Changes in the secondary structure of some dozen different proteins upon lyophilization of their aqueous solutions have been investigated by means of Fourier-transform infrared spectroscopy in the amide III band region. Dehydration markedly (but reversibly) alters the secondary structure of all the proteins studied, as revealed by both the quantitative analysis of the second derivative spectra and the Gaussian curve fitting of the original infrared spectra. Lyophilization substantially increases the beta-sheet content and lowers the alpha-helix content of all proteins. In all but one case, proteins become more ordered upon lyophilization.

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Propõe-se método novo e completo para análise de acetona em ar exalado envolvendo coleta com pré-concentração em água, derivatização química e determinação eletroquímica assistida por novo algoritmo de processamento de sinais. Na literatura recente a acetona expirada vem sendo avaliada como biomarcador para monitoramento não invasivo de quadros clínicos como diabetes e insuficiência cardíaca, daí a importância da proposta. Entre as aminas que reagem com acetona para formar iminas eletroativas, estudadas por polarografia em meados do século passado, a glicina apresentou melhor conjunto de características para a definição do método de determinação por voltametria de onda quadrada sem a necessidade de remoção de oxigênio (25 Hz, amplitude de 20 mV, incremento de 5 mV, eletrodo de gota de mercúrio). O meio reacional, composto de glicina (2 mol·L-1) em meio NaOH (1 mol·L-1), serviu também de eletrólito e o pico de redução da imina em -1,57 V vs. Ag|AgCl constituiu o sinal analítico. Para tratamento dos sinais, foi desenvolvido e avaliado um algoritmo inovador baseado em interpolação de linha base por ajuste de curvas de Bézier e ajuste de gaussiana ao pico. Essa combinação permitiu reconhecimento e quantificação de picos relativamente baixos e largos sobre linha com curvatura acentuada e ruído, situação em que métodos convencionais falham e curvas do tipo spline se mostraram menos apropriadas. A implementação do algoritmo (disponível em http://github.com/batistagl/chemapps) foi realizada utilizando programa open source de álgebra matricial integrado diretamente com software de controle do potenciostato. Para demonstrar a generalidade da extensão dos recursos nativos do equipamento mediante integração com programação externa em linguagem Octave (open source), implementou-se a técnica da cronocoulometria tridimensional, com visualização de resultados já tratados em projeções de malha de perspectiva 3D sob qualquer ângulo. A determinação eletroquímica de acetona em fase aquosa, assistida pelo algoritmo baseado em curvas de Bézier, é rápida e automática, tem limite de detecção de 3,5·10-6 mol·L-1 (0,2 mg·L-1) e faixa linear que atende aos requisitos da análise em ar exalado. O acetaldeído, comumente presente em ar exalado, em especial, após consumo de bebidas alcoólicas, dá origem a pico voltamétrico em -1,40 V, contornando interferência que prejudica vários outros métodos publicados na literatura e abrindo possibilidade de determinação simultânea. Resultados obtidos com amostras reais são concordantes com os obtidos por método espectrofotométrico, em uso rotineiro desde o seu aperfeiçoamento na dissertação de mestrado do autor desta tese. Em relação à dissertação, também se otimizou a geometria do dispositivo de coleta, de modo a concentrar a acetona num volume menor de água gelada e prover maior conforto ao paciente. O método completo apresentado, englobando o dispositivo de amostragem aperfeiçoado e o novo e efetivo algoritmo para tratamento automático de sinais voltamétricos, está pronto para ser aplicado. Evolução para um analisador portátil depende de melhorias no limite de detecção e facilidade de obtenção eletrodos sólidos (impressos) com filme de mercúrio, vez que eletrodos de bismuto ou diamante dopado com boro, entre outros, não apresentaram resposta.

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La scoliose idiopathique de l’adolescent (SIA) est une déformation tridimensionnelle (3D) de la colonne vertébrale. Pour la plupart des patients atteints de SIA, aucun traitement chirurgical n’est nécessaire. Lorsque la déformation devient sévère, un traitement chirurgical visant à réduire la déformation est recommandé. Pour déterminer la sévérité de la SIA, l’imagerie la plus utilisée est une radiographie postéroantérieure (PA) ou antéro-postérieure (AP) du rachis. Plusieurs indices sont disponibles à partir de cette modalité d’imagerie afin de quantifier la déformation de la SIA, dont l’angle de Cobb. La conduite thérapeutique est généralement basée sur cet indice. Cependant, les indices disponibles à cette modalité d’imagerie sont de nature bidimensionnelle (2D). Celles-ci ne décrivent donc pas entièrement la déformation dans la SIA dû à sa nature tridimensionnelle (3D). Conséquemment, les classifications basées sur les indices 2D souffrent des mêmes limitations. Dans le but décrire la SIA en 3D, la torsion géométrique a été étudiée et proposée par Poncet et al. Celle-ci mesure la tendance d’une courbe tridimensionnelle à changer de direction. Cependant, la méthode proposée est susceptible aux erreurs de reconstructions 3D et elle est calculée localement au niveau vertébral. L’objectif de cette étude est d’évaluer une nouvelle méthode d’estimation de la torsion géométrique par l’approximation de longueurs d’arcs locaux et par paramétrisation de courbes dans la SIA. Une première étude visera à étudier la sensibilité de la nouvelle méthode présentée face aux erreurs de reconstructions 3D du rachis. Par la suite, deux études cliniques vont présenter la iv torsion géométrique comme indice global et viseront à démontrer l’existence de sous-groupes non-identifiés dans les classifications actuelles et que ceux-ci ont une pertinence clinique. La première étude a évalué la robustesse de la nouvelle méthode d’estimation de la torsion géométrique chez un groupe de patient atteint de la SIA. Elle a démontré que la nouvelle technique est robuste face aux erreurs de reconstructions 3D du rachis. La deuxième étude a évalué la torsion géométrique utilisant cette nouvelle méthode dans une cohorte de patient avec des déformations de type Lenke 1. Elle a démontré qu’il existe deux sous-groupes, une avec des valeurs de torsion élevées et l’autre avec des valeurs basses. Ces deux sous-groupes possèdent des différences statistiquement significatives, notamment au niveau du rachis lombaire avec le groupe de torsion élevée ayant des valeurs d’orientation des plans de déformation maximales (PMC) en thoraco-lombaire (TLL) plus élevées. La dernière étude a évalué les résultats chirurgicaux de patients ayant une déformation Lenke 1 sous-classifiées selon les valeurs de torsion préalablement. Cette étude a pu démontrer des différences au niveau du PMC au niveau thoraco-lombaire avec des valeurs plus élevées en postopératoire chez les patients ayant une haute torsion. Ces études présentent une nouvelle méthode d’estimation de la torsion géométrique et présentent cet indice quantitativement. Elles ont démontré l’existence de sous-groupes 3D basés sur cet indice ayant une pertinence clinique dans la SIA, qui n’étaient pas identifiés auparavant. Ce projet contribue dans la tendance actuelle vers le développement d’indices 3D et de classifications 3D pour la scoliose idiopathique de l’adolescent.

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We have developed a statistical gap-filling method adapted to the specific coverage and properties of observed fugacity of surface ocean CO2 (fCO2). We have used this method to interpolate the Surface Ocean CO2 Atlas (SOCAT) v2 database on a 2.5°×2.5° global grid (south of 70°N) for 1985-2011 at monthly resolution. The method combines a spatial interpolation based on a 'radius of influence' to determine nearby similar fCO2 values with temporal harmonic and cubic spline curve-fitting, and also fits long term trends and seasonal cycles. Interannual variability is established using deviations of observations from the fitted trends and seasonal cycles. An uncertainty is computed for all interpolated values based on the spatial and temporal range of the interpolation. Tests of the method using model data show that it performs as well as or better than previous regional interpolation methods, but in addition it provides a near-global and interannual coverage.

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The paper describes a procedure for accurately and speedily calibrating tanks used for the chemical processing of nuclear materials. The procedure features the use of (1) precalibrated vessels certified to deliver known volumes of liquid, (2) calibrated linear measuring devices, and (3) a digital computer for manipulating data and producing printed calibration information. Calibration records of the standards are traceable to primary standards. Logic is incorporated in the computer program to accomplish curve fitting and perform the tests to accept or to reject the calibration, based on statistical, empirical, and report requirements. This logic is believed to be unique.

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Slag composition determines the physical and chemical properties as well as the application performance of molten oxide mixtures. Therefore, it is necessary to establish a routine instrumental technique to produce accurate and precise analytical results for better process and production control. In the present paper, a multi-component analysis technique of powdered metallurgical slag samples by X-ray Fluorescence Spectrometer (XRFS) has been demonstrated. This technique provides rapid and accurate results, with minimum sample preparation. It eliminates the requirement for a fused disc, using briquetted samples protected by a layer of Borax(R). While the use of theoretical alpha coefficients has allowed accurate calibrations to be made using fewer standard samples, the application of pseudo-Voight function to curve fitting makes it possible to resolve overlapped peaks in X-ray spectra that cannot be physically separated. The analytical results of both certified reference materials and industrial slag samples measured using the present technique are comparable to those of the same samples obtained by conventional fused disc measurements.