Development of the kinetic model of platinum catalyzed ammonia oxidation in a microreactor

The ammonia oxidation reaction on supported polycrystalline platinum catalyst was investigated in an aluminum-based microreactor. An extensive set of reactions was included in the chemical reactor modeling to facilitate the construction of a kinetic model capable of satisfactory predictions for a wide range of conditions (NH3 partial pressure, 0.01-0.12 atm; O-2 partial pressure, 0.10-0.88 atm; temperature, 523-673 K; contact time, 0.3-0.7 ms). The elementary surface reactions used in developing the mechanism were chosen based on the literature data concerning ammonia oxidation on a Pt catalyst. Parameter estimates for the kinetic model were obtained using multi-response least squares regression analysis using the isothermal plug-flow reactor approximation. To evaluate the model, the behavior of a microstructured reactor was simulated by means of a complete Navier-Stokes model accounting for the reactions on the catalyst surface and the effect of temperature on the physico-chemical properties of the reacting mixture. In this way, the effect of the catalytic wall temperature non-uniformity and the effect of a boundary layer on the ammonia conversion and selectivity were examined. After further optimization of appropriate kinetic parameters, the calculated selectivities and product yields agree very well with the values actually measured in the microreactor. (C) 2002 Elsevier Science B.V. All rights reserved.

Dynamic Modeling and Interaction of Hybrid Natural Gas and Electricity Supply System in Microgrid

Natural gas (NG) network and electric network are becoming tightly integrated by microturbines in the microgrid. Interactions between these two networks are not well captured by the traditional microturbine (MT) models. To address this issue, two improved models for single-shaft MT and split-shaft MT are proposed in this paper. In addition, dynamic models of the hybrid natural gas and electricity system (HGES) are developed for the analysis of their interactions. Dynamic behaviors of natural gas in pipes are described by partial differential equations (PDEs), while the electric network is described by differential algebraic equations (DAEs). So the overall network is a typical two-time scale dynamic system. Numerical studies indicate that the two-time scale algorithm is faster and can capture the interactions between the two networks. The results also show the HGES with a single-shaft MT is a weakly coupled system in which disturbances in the two networks mainly influence the dc link voltage of the MT, while the split-shaft MT is a strongly coupled system where the impact of an event will affect both networks.

Deep Salience: Visual Salience Modeling via Deep Belief Propagation

Visual salience is an intriguing phenomenon observed in biological neural systems. Numerous attempts have been made to model visual salience mathematically using various feature contrasts, either locally or globally. However, these algorithmic models tend to ignore the problem’s biological solutions, in which visual salience appears to arise during the propagation of visual stimuli along the visual cortex. In this paper, inspired by the conjecture that salience arises from deep propagation along the visual cortex, we present a Deep Salience model where a multi-layer model based on successive Markov random fields (sMRF) is proposed to analyze the input image successively through its deep belief propagation. As a result, the foreground object can be automatically separated from the background in a fully unsupervised way. Experimental evaluation on the benchmark dataset validated that our Deep Salience model can consistently outperform eleven state-of-the-art salience models, yielding the higher rates in the precision-recall tests and attaining the best F-measure and mean-square error in the experiments.

Ecological niche modeling, cytogenetics and phylogeography of the genera Geomalacus and Letourneuxia (Gastropoda, Pulmonata) from the Iberian-Moroccan region

First described more that 150 years ago, the systematics of the genera Geomalacus and Letourneuxia (Arionidae, Gastropoda, Pulmonata) is still challenging. The taxonomic classification of arionid species is based on extremely labile characters such as body size or color that depends both on diet and environment, as well as age. Moreover, there is little information on the genetic diversity and population structure of the Iberian slugs that could provide extra clues to disentangle their problematic classification. The present work uses different analytical tools such as habitat suitability (Ecological Niche Modeling - ENM), cytogenetic analysis and phylogeography to establish the geographical distribution and evolutionary history of these pulmonate slugs. The potential distribution of the four Geomalacus species was modeled using ENM, which allowed the identification of new locations for G. malagensis, including a first report in Portugal. Also, it was predicted a much wider distribution for G. malagensis and G. oliveirae than previously known. Classical cytogenetic analyses were assayed with reproductive and a novel use of somatic tissues (mouth and tentacles) returning the number of chromosomes for the four Geomalacus species and L. numidica (n = 31, 2n = 62) and the respective karyotypes. G. malagensis and L. numidica present similar chromosome morphologies and karyotypic formulae, being more similar to each other than the Geomalacus among themselves. We further reconstructed the phylogeny of the genera Geomalacus and Letourneuxia using partial sequences of the mitochondrial cytochrome oxidase subunit I (COI) and the nuclear ribosomal small subunit (18S rRNA), and applied an independent evolutionary rate method, the indicator vectors correlation, to evaluate the existence of cryptic diversity within species. The five nominal species of Geomalacus and Letourneuxia comprise 14 well-supported cryptic lineages. Letourneuxia numidica was retrieved as a sister group of G. malagensis. G. oliveirae is paraphyletic with respect to G. anguiformis. According to our dating estimates, the most recent common ancestor of Geomalacus dates back to the Middle Miocene (end of the Serravallian stage). The major lineage splitting events within Geomalacus occurred during the dry periods of the Zanclean stage (5.3-3.6 million years) and some lineages were confined to more humid mountain areas of the Iberian Peninsula, which lead to a highly geographically structured mitochondrial genetic diversity. The major findings of this are the following: (1) provides updated species distribution maps for the Iberian Geomalacus expanding the known geographic distribution of the concerned species, (2) unravels the cryptic diversity within the genera Geomalacus and Letourneuxia, (3) Geomalacus oliveirae is paraphyletic with G. anguiformis and (4) Letourneuxia numidica is sister group of G. malagensis.

Biomechanical modeling and simulation of the spider crab (maja brachydactyla)

Uma linha de pesquisa e desenvolvimento na área da robótica, que tem recebido atenção crescente nos últimos anos, é o desenvolvimento de robôs biologicamente inspirados. A ideia é adquirir conhecimento de seres biológicos, cuja evolução ocorreu ao longo de milhões de anos, e aproveitar o conhecimento assim adquirido para implementar a locomoção pelos mesmos métodos (ou pelo menos usar a inspiração biológica) nas máquinas que se constroem. Acredita-se que desta forma é possível desenvolver máquinas com capacidades semelhantes às dos seres biológicos em termos de capacidade e eficiência energética de locomoção. Uma forma de compreender melhor o funcionamento destes sistemas, sem a necessidade de desenvolver protótipos dispendiosos e com longos tempos de desenvolvimento é usar modelos de simulação. Com base nestas ideias, o objectivo deste trabalho passa por efectuar um estudo da biomecânica da santola (Maja brachydactyla), uma espécie de caranguejo comestível pertencente à família Majidae de artrópodes decápodes, usando a biblioteca de ferramentas SimMechanics da aplicação Matlab / Simulink. Esta tese descreve a anatomia e locomoção da santola, a sua modelação biomecânica e a simulação do seu movimento no ambiente Matlab / SimMechanics e SolidWorks.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Modeling of in-situ crystallization processes in the Permian mafic layered intrusion of Mont Collon (Dent Blanche nappe, western Alps)

The Mont Collon mafic complex is one of the best preserved examples of the Early Permian magmatism in the Central Alps, related to the intra-continental collapse of the Variscan belt. It mostly consists (> 95 vol.%) of ol+hy-nonnative plagioclase-wehrlites, olivine- and cpx-gabbros with cumulitic structures, crosscut by acid dikes. Pegmatitic gabbros, troctolites and anorthosites outcrop locally. A well-preserved cumulative, sequence is exposed in the Dents de Bertol area (center of intrusion). PT-calculations indicate that this layered magma chamber emplaced at mid-crustal levels at about 0.5 GPa and 1100 degrees C. The Mont Collon cumulitic rocks record little magmatic differentiation, as illustrated by the restricted range of clinopyroxene mg-number (Mg#(cpx)=83-89). Whole-rock incompatible trace-element contents (e.g. Nb, Zr, Ba) vary largely and without correlation with major-element composition. These features are characteristic of an in-situ crystallization process with variable amounts of interstitial liquid L trapped between the cumulus mineral phases. LA-ICPMS measurements show that trace-element distribution in the latter is homogeneous, pointing to subsolidus re-equilibration between crystals and interstitial melts. A quantitative modeling based on Langmuir's in-situ crystallization equation successfully duplicated the REE concentrations in cumulitic minerals of all rock facies of the intrusion. The calculated amounts of interstitial liquid L vary between 0 and 35% for degrees of differentiation F of 0 to 20%, relative to the least evolved facies of the intrusion. L values are well correlated with the modal proportions of interstitial amphibole and whole-rock incompatible trace-element concentrations (e.g. Zr, Nb) of the tested samples. However, the in-situ crystallization model reaches its limitations with rock containing high modal content of REE-bearing minerals (i.e. zircon), such as pegmatitic gabbros. Dikes of anorthositic composition, locally crosscutting the layered lithologies, evidence that the Mont Collon rocks evolved in open system with mixing of intercumulus liquids of different origins and possibly contrasting compositions. The proposed model is not able to resolve these complex open systems, but migrating liquids could be partly responsible for the observed dispersion of points in some correlation diagrams. Absence of significant differentiation with recurrent lithologies in the cumulitic pile of Dents de Bertol points to an efficiently convective magma chamber, with possible periodic replenishment, (c) 2005 Elsevier B.V. All rights reserved.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Partial characterization of the cloned dihydrofolate reductase gene of Saccharomyces cerevisiae

The cloned dihydrofolate reductase gene of Saccharomyces cerevisiae (DFR 1) is expressed in Escherichia coli. Bacterial strain JF1754 transformed with plasmids containing DFR 1 is at least 5X more resistant to inhibition by the folate antagonist trimethoprim. Expression of yeast DFR 1 in E. coli suggests it is likely that the gene lacks intervening sequences. The 1.8 kbp DNA fragment encoding yeast dhfr activity probably has its own promotor, as the gene is expressed in both orientations in E. coli. Expression of the yeast dhfr gene cloned into M13 viral vectors allowed positive selection of DFR 1 - M13 bacterial transfectants in medium supplemented with trimethoprim. A series of nested deletions generated by nuclease Bal 31 digestion and by restriction endonuclease cleavage of plasmids containing DFR 1 physically mapped the gene to a 930 bp region between the Pst 1 and Sal 1 cut sites. This is consistent with the 21,000 molecular weight attributed to yeast dhfr in previous reports. From preliminary DNA sequence analysis of the dhfr DNA fragment the 3' terminus of DFR 1 was assigned to a position 27 nucleotides from the Eco Rl cut site on the Bam Hi - Eco Rl DNA segment. Several putative yeast transcription termination consensus sequences were identified 3' to the opal stop codon. DFR 1 is expressed in yeast and it confers resistance to the antifolate methotrexate when the gene is present in 2 - 10 copies per cell. Plasmid-dependent resistance to methotrexate is also observed in a rad 6 background although the effect is somewhat less than that conferred to wild-type or rad 18 cells. Integration of DFR 1 into the yeast genome showed an intermediate sensitivity to folate antagonists. This may suggest a gene dosage effect. No change in petite induction in these yeast strains was observed in transformed cells containing yeast dhfr plasmids. The sensitivity of rad 6 , rad 18 and wild-type cell populations to trimethoprim were unaffected by the presence of DFR 1 in transformants. Moreover, trimethoprim did not induce petites in any strain tested, which normally results if dhfr is inhibited by other antifolates such as methotrexate. This may suggest that the dhfr enzyme is not the only possible target of trimethoprim in yeast. rad 6 mutants showed a very low level of spontaneous petite formation. Methotrexate failed to induce respiratory deficient mutants in this strain which suggested that rad 6 might be an obligate grande. However, ethidium bromide induced petites to a level approximately 50% of that exhibited by wild-type and rad 18 strains.

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Does friendship give us non-derivative partial reasons ?

Une des façons d’approcher la question de l’existence de raisons partiales non-dérivatives d’une quelconque sorte consiste à expliquer ce que sont les raisons partiales et ensuite à chercher à savoir s’il y a des raisons de cette sorte. Si de telles raisons existent, alors il est au moins possible qu’il y ait des raisons partiales d’amitié. C’est cette approche que j’adopterai ici, et elle produit des résultats intéressants. Le premier a trait à la structure des raisons partiales. C’est au moins une condition nécessaire pour qu’une raison soit partiale qu’elle aie une composante relationnelle explicite. Cette composante, techniquement parlant, est un relatum dans la relation d’être une raison qui elle-même est une relation entre la personne à qui la raison s’applique et la personne concernée par l’action pour laquelle il y a une raison. La deuxième conclusion de ce texte est que cette composante relationnelle est aussi requise dans de nombreuses sortes de raisons admises comme impartiales. Afin d’éviter de banaliser la distinction entre raisons partiales et impartiales nous devons appliquer une condition suffisante additionnelle. Finalement, bien qu’il pourrait s’avérer possible de distinguer les raisons impartiales ayant une composante relationnelle des raisons partiales, cette approche suggère que la question de savoir si l’éthique est partiale ou impartiale devra se régler au niveau de l’éthique normative, ou à tout le moins, qu’elle ne pourra se régler au niveau du discours sur la nature des raisons d’agir.

Contexte de genre, autonomie des femmes et utilisation des services de santé maternelle en milieu rural africain : analyse par modèles d’équations structurelles

La vie des femmes du continent africain et de leurs enfants continue d’être mise en danger lors de chaque accouchement car les risques de décès maternels et infantiles sont encore très élevés. Il est estimé chaque année à environ le quart du million le nombre de décès maternel et de près de quatre millions celui des enfants de moins de cinq ans. La comparaison de la situation sanitaire avec d’autres contextes permet de mieux cerner l’ampleur du problème : en Afrique sub-Saharienne, le risque de décès lié à la grossesse est de l’ordre de 1 pour 31, alors qu’il n’est que de 1 pour 4300 dans les pays industrialisés. Cette situation est évitable et, le plus souvent, résulte de la sous ou non-utilisation des services de santé maternelle, du manque de structures adéquates de soins ou de personnel de santé qualifié. Notre thèse cherche à comprendre la manière dont les inégalités de genre au sein du ménage et dans la communauté renforcent les inégalités quant à l’utilisation des services de santé maternelle, ainsi qu’aux relations empiriques qui lient les différents recours aux soins. Concrètement, elle vise à 1) proposer une mesure des normes de genre favorables à la violence contre les femmes et à analyser son influence sur leur prise de décision au sein du ménage, 2) analyser simultanément l’influence de ces normes et de l’autonomie des femmes sur le recours aux soins prénatals et à l’accouchement assisté et finalement, 3) cerner l’influence des soins prénatals sur le recours à l’accouchement assisté. Chacun de ces objectifs se heurte à un problème méthodologique substantiel, soit de mesure ou de biais de sélection, auxquels l’approche par modèles d’équations structurelles que nous avons adoptée permet de remédier. Les résultats de nos analyses, présentés sous forme d’articles scientifiques, s’appuient sur les données issues des Enquêtes Démographiques et de Santé (EDS) du Ghana, du Kenya, de l’Ouganda et de la Tanzanie et concernent les femmes vivant en milieu rural. Notre premier article propose une mesure des normes de genre et, plus exactement, celles liées à la violence contre les femmes en recourant à l’approche des variables latentes. Les cinq questions des EDS relatives à l’attitude des femmes sur la légitimation de la violence ont permis de saisir cette mesure au niveau contextuel. Les résultats suggèrent d’une part que cette mesure a de bons critères de validité puisque l’Alpha de Cronbach varie de 0.85 pour le Kenya à 0.94 pour le Ghana; les chi-deux sont non significatifs partout; le RMSEA est en dessous de 0.05; le CFI supérieur à 0.96 et les saturations sont pour la plupart supérieures à 0.7 dans tous les pays. D’autre part, à l’aide du modèle d’équations structurelles multiniveaux, nous avons trouvé qu’au-delà de leur propre attitude envers la violence contre les femmes, celles qui vivent dans un milieu où les normes de genres sont plus favorables à la violence ont plus de chances d’être de faible autonomie ou sans autonomie (comparativement à forte autonomie) dans l’ensemble des pays étudiés. Le second article documente l’influence des inégalités de genre, cernées au niveau contextuel par les normes favorables à la violence contre les femmes et au niveau individuel par l’autonomie de prise de décision au sein du ménage, sur la survenue des soins prénatals au cours du premier trimestre et sur les recours à au moins 4 consultations prénatales et à l’accouchement assisté. En utilisant également les modèles d’équations structurelles multiniveaux sur les mêmes données du premier article, nous constatons que chacune de ces variables dépendantes est fortement influencée par la grappe dans laquelle la femme vit. En d’autres mots, son lieu de résidence détermine le comportement de santé maternelle que l’on adopte. De même, en contrôlant pour les autres variables explicatives, nos résultats montrent que les femmes qui vivent dans un milieu où les normes de genre liées à la violence contre les femmes sont élevées ont, en moyenne, une plus grande chance de ne pas accoucher auprès d’un personnel qualifié au Ghana et en Ouganda, de ne pas débuter leurs soins prénatals dans le premier trimestre dans les mêmes pays, et de ne pas recourir à au moins quatre consultations prénatales en Tanzanie. Par contre, cette variable contextuelle n’influence pas significativement le recours aux soins de santé maternelle au Kenya. Enfin, les résultats montrent que les normes de genre favorables à la violence contre les femmes sont plus déterminantes pour comprendre le recours aux soins de santé maternelle dans les pays étudiés que l’autonomie de prise de décision de la femme. Dans le cadre du troisième et dernier article empirique de la thèse, nous nous sommes intéressés à l’importance des soins prénatals dans le processus de recours à l’accouchement assisté et à la place du contenu des soins reçus avant l’accouchement dans cette relation. Cet article met en exergue l’existence de biais d’endogénéité au Kenya et en Tanzanie, où sans sa prise en compte, l’effet des soins prénatals sur le recours à l’accouchement auprès d’un personnel qualifié serait fortement biaisé. De plus, il ressort qu’à l’exception du Ghana et dans une moindre mesure de la Tanzanie, cet effet est totalement médiatisé par le contenu des soins prénatals que les femmes reçoivent. L’article met ainsi en relief le rôle des prestataires de soins qui pour atteindre plus efficacement les populations doivent agir en tant que leaders au sein de leur communauté.

Non invasive classification system of scoliosis curve types using least-squares support vector machines

Objective To determine scoliosis curve types using non invasive surface acquisition, without prior knowledge from X-ray data. Methods Classification of scoliosis deformities according to curve type is used in the clinical management of scoliotic patients. In this work, we propose a robust system that can determine the scoliosis curve type from non invasive acquisition of the 3D back surface of the patients. The 3D image of the surface of the trunk is divided into patches and local geometric descriptors characterizing the back surface are computed from each patch and constitute the features. We reduce the dimensionality by using principal component analysis and retain 53 components using an overlap criterion combined with the total variance in the observed variables. In this work, a multi-class classifier is built with least-squares support vector machines (LS-SVM). The original LS-SVM formulation was modified by weighting the positive and negative samples differently and a new kernel was designed in order to achieve a robust classifier. The proposed system is validated using data from 165 patients with different scoliosis curve types. The results of our non invasive classification were compared with those obtained by an expert using X-ray images. Results The average rate of successful classification was computed using a leave-one-out cross-validation procedure. The overall accuracy of the system was 95%. As for the correct classification rates per class, we obtained 96%, 84% and 97% for the thoracic, double major and lumbar/thoracolumbar curve types, respectively. Conclusion This study shows that it is possible to find a relationship between the internal deformity and the back surface deformity in scoliosis with machine learning methods. The proposed system uses non invasive surface acquisition, which is safe for the patient as it involves no radiation. Also, the design of a specific kernel improved classification performance.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.