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The study of the setQ ofWightman's functionals begun in ref. [5] is continued in this paper. Haag-Ruelle asymptotic construction [1, 2] is formulated for the case when all the pureWightman's functionals contained in the decomposition of the given functional $$\bar w \in Q$$ generate the same set of asymptotic states. As an example we consider a theory with the degenerate vacuum and prove that it is physically equivalent to a theory with the single vacuum. For this case we show that the transition to the theory with the degenerate vacuum is equivalent to introducing of a charged spurion in the theory with the single vacuum. The mathematically correct creation and destruction operators for this spurion are given.

In a previous paper we have shown that, using the differential equations of the trajectories of Jacobi constant J in the restricted problem, we could demonstrate the existence of periodic solutions of the first and the second kind, symmetric and asymmetric, and quasi-periodic solutions of the second kind, for sufficiently small eccentricities, in the neighbourhood of one of the primaries. Some of the intermediate equations have to be corrected, but the conclusions remain unchanged. Those conclusions are now compared to the known existence demonstrations. Finally we show that Uno's demonstration of non-existence of asymmetric periodic solutions of the second kind does not apply to the cases we are studying., Sergysels Roland, Sergysels-Lamy Anne. Solutions périodiques et quasi-périodiques du problème restreint (II). In: Bulletin de la Classe des sciences, tome 60, 1974. pp. 436-443.

Copyright © International Union of Crystallography; After a brief review of the crystallographic Fourier transform problem, this paper compares three methods for its computer implementation with reference to core-storage capacity and computation time: the classic method, the simple Fast Fourier Transform algorithms and a new method. The first method needs, especially for a macromolecular three-dimensional structure, too many operations and therefore too long a computation time and poor accuracy. The remarkable FFT algorithm, on the other hand, leads to large savings in computation time with a better accuracy, but using no crystallographic symmetry wastes too much storage capacity. The third method, using FFT but taking into account Friedel's law by means of a simple in situ process, approximately halves the storage capacity as well as the computation time.

Melting point curves of DNA are used to calculate average GC content. Four methods of Tm determination are described and are used in the case of all DNA samples studied. The results presented confirme that thermal denaturation curves are asymetrical, and this limits the use of "normal probability paper" and "regression lines" methods. Best reproductibility is obtained by a study of the function (see article) followed by a linear interpolation of the median. This approach yields at the same time interesting information about bacterial DNA. The graphic determination of Tm appears to be the method for choice for routine analysis.

This paper describes a model which makes allowance for unequal follow up times in estimating the risk as a function of risk factors. It is the exponential model with a hazard which is also an exponential function of risk factors. Computing methods and an extension of the model are given.

This paper deals with the kinetic inhibition of six cephalosporinases (cephalosporin amido-beta-lactamhydrolase, EC 3.5.2.8) by carbenicillin. In previous cases, the inhibition has appeared usually to be competitive and slowly reversible. This makes it possible to measure the two terms of the ratio Ki=k5/k4;k4 and k5 being respectively the velocity constants of formation and destruction of the enzyme-inhibitor complex. A program was prepared which made it possible to obtain these constants from only one experiment. With ampicillin and cloxacillin, we verified that the reaction is faster, and that only Ki can be measured. These facts suggest that special precautions should be taken in order to obtain signigicant values for the constants governing inhibition.

Il punto di partenza di questo lavoro e l'interpretazione delle topologie di Grothendieck nel linguaggio dei sistemi relazionali (cfr. [5]); cio permette uno studio aritmetico di tali topologie. Attraverso nuove tecniche, qui introdotte, si ottengono risultati non privi di interesse, tra i quali una caratterizzazione degli spazi topologici noetheriani, ed ulteriori strutture topologiche di tipo locale (siti tangenti), per le quali vengono dimostrate numerose proprieta. Vengono, infine, date alcune applicazioni alla teoria degli schemi, utilizzando il funtore inviluppo affine. The starting point of this paper is the interpretation of Grothendieck's topologies in the language of relational systems (cfr. [5]); this permits an arithmetical study of these topologies. By applying new techniques introduced here, we have achieved interesting results. These include a new characterization of Noetherian topological spaces, and further topological structures of local type (tangent sites) for which we have shown numerous properties. Finally, we have used the affine-envelope functor to illustrate some applications to the theory of schemes.

In a recent paper (Hairer-Wanner [1]) we have given a theory with which it is easy to calculate the order conditions for Nystrom methods. Here we show how it is possible to solve this system of non-linear algebraic equations. Moreover we present all methods of orders fors=2, 3, 4 (s?1 indicates the number of function evaluations per step); methods with one parameter of orders fors=5, 6 and some special methods of orders?1 fors=8, 9. Dans un recent article (Hairer-Wanner [1]) nous avons donne une theorie a l'aide de laquelle on peut facilement calculer les conditions d'ordre pour une methode de Nystrom. Ici nous montrons comment on peut resoudre ce systeme d'equations non-lineaires. Nous donnons de plus toutes les methodes d'ordres pours=2, 3, 4 (ous?1 indique le nombre d'evaluations de la fonction a chaque pas); des methodes avec un parametre d'ordres pours=5, 6 et des methodes particulieres d'ordres?1 pours=8, 9.

The purpose of this paper is to present an automatic method of signal analysis. To help physicians in their diagnostics, this method is implemented on a minicomputer in order to detect non-stationary points in electroencephalograms. The signal is modelled with an autoregressive filter. The parameters of this filter are adapted at each step. Identification gives the best model in the sense of a cost function representing the mean square error of noise, which is estimated during the optimisation time-window. The cost function is expressed by a quadratic formula. This allows the use of a fast algorithm, the 'conjugate gradient method'. An original statistical test is developed to detect non-stationary points in the signal. The performance of this method is tested with artificial data to determine the sensitivity of method parameters. Detection using real data is presented.

The testing of heterozygosity for PKU by mean of an oral load of phenylalanine is a widely used method. In this paper, the need of a genetic counselling for two adults, with family story of PKU, lead us to reinvestigate criteria of heterozygote recognition. With all variables of the phenylalanine tolerance test, overlapping and mis classification occured. Probability density functions plotting, as proposed by GOLD, illustrated well the genetic risk of a patient. However, in practice, the heterozygote likelihood ratio determination seemed to be the best way to avoid possibly erroneous categoric statement by correcting the ratio for the a priori probability of heterozygosity.

Cet article est une application très simple de recherches développées par Tallis et Scheinberg. Il rappelle l’expression de la variance d’échantillonnage de l’estimation de coefficients de corrélation (génétique, génotypique, due à l’environnement, hénotypique) obtenus en analyse de variance-covariance. Il particularise au cas d’un test clonal et montre que l’on commet une erreur parfois importante en jugeant la signification des corrélations génotypique et phénotypique uniquement à l’aide des caractéristiques du dispositif : nombre de clones, nombre d’individus par clone., This paper gives a very simple application of research developed by Tallis and Scheinberg. It recalls the expression of the sampling variance of correlation coefficient estimation (genetic, genotypic, environmental and phenotypic) calculated from analyses of variance and covariance. It mentions in detail the case of a clonal test and shows that a serious error may occur when the significance level of the genotypic and phenotypic correlations is appreciated by means of clonal test characteristics only : number of clones, size of each clone.

The frequency distribution of Wuchereria bancrofti microfilariae counts in capillary blood, at a community level, is shown to differ significantly from the log-normal distribution, commonly used (and recommended by WHO). A much better fit is obtained with a truncated negative-binomial distribution, the k exponent of which is estimated to 0.3. This value does not seem to be affected by the endemic level, by microfilaricide mass-treatments or by the blood sample volume. This result has immediate practical interests: 1) it facilitates a posteriori comparisons between surveys in which different volumes of blood were examined; 2) at a given density it allows calculation the change in sensitivity (detection rate) as a function of a change in the volume of blood examined, thus allowing better a priori planning of surveys. The paper provides the formulae required to calculate k, or, given k, to calculate the expected numbers in the various density classes. It also provides nomograms (fig. 4ab) giving estimates of the true mean M and of the detection rate TD, given any one of the three following observations, made on observed positives: the median Dmf. 50, the mean m, or the percentage Pl having only 1 mf. The effect of changing the volume of blood on the rate of detection can then be read easily from the nomogram. These results, likely to apply to other important parasitic diseases, should instigate more elaborated statistical research in this direction.

In this paper, the theory of fuzzy sets and fuzzy logic is approached as a diagnostic aid for practitioners and biologists. A few theoretical considerations are followed by two practical applications. The first is a modification of the WHO-Fredrickson classification of hyperlipoproteinemias, with the introduction of secondary or minor types corresponding to everyday medical practice. The other is an attempt at classifying the four most prevalent anemias encountered in internal medicine. Recent studies have shown that the various parameters should be grouped on a hierarchical basis.

A lot of biological systems can be modeled by mathematical relations. Furthermore, existence of regulations and optimizations lead to optimal control systems. In this paper we want to describe with simple examples some difficulties and advantages of such systemic approaches.

Pascal Engel: Intensional Logic and the Fregean Heritage in Semantics. Although Frege's logic and «semantics» inspired most later developments, neither Carnap nor Church, who used fregean ideas to build their systems, were faithful to these. The fregean heritage has been distorted in two ways: intensional logic obliterates the distinction between concepts and objects, and Frege recommends an extensional · treatment of logic. This paper tries to restate the fregean doctrine of functions by using combinatory logic, and defends the «neo-fregean» point of view of a logical semantics based on Tarski's theory of truth and Davidson's programme for the semantics of natural language., Engel Pascal. La logique intensionnelle et l'héritage de Frege en sémantique. In: Histoire Épistémologie Langage, tome 5, fascicule 2, 1983. La sémantique logique : Problèmes d'histoire et de méthode, sous la direction de Frédéric Nef. pp. 95-116.

Pierre-Yves Raccah: Presupposition and Intension. ln this paper, I argue for the adequacy of formal approaches to the description of meaning, even in cases of expressions conveying conventionaI implicature. By formal approaches, I mean frameworks intended to account for sentence meaning, and meeting the conditions of compositionnality, autonomy towards knowledge and beliefs about the world, and modularity. I first show that presupposition, instead of being considered as a relation between a sentence (or an utterance) and another sentence (or, at best, a proposition), should rather be seen as a relation between a sentence and a meaning. Besides avoiding the presupposition-entailment paradox, this position is shown to allow a compositionnal treatment of presupposition, using, for instance, Karttunen and Peters' tools. 1 then give the bases of a «representation al semantics», that aims at freeing semantic description from both speakers» intentions and truth conditions. 1 conclude with a couple of examples of semantic analyses for sentences containing intensional verbs such as «savoir» or «espérer», and show how these analyses fulfill the task they were ascribed. Some questions are left open as to the generalization of this treatment to other intensional cases, and as to the exact shape meaning representations should have., Raccah Pierre-Yves. Présupposition et intension. In: Histoire Épistémologie Langage, tome 5, fascicule 2, 1983. La sémantique logique : Problèmes d'histoire et de méthode, sous la direction de Frédéric Nef. pp. 153-162.

Oblique plane osteotomy allows correction of associated angular and rotational deformity by a single bony section and also allows modification of the existing angle at the cervico-diaphyseal level in the femur. Exact assessment of the direction of the osteotomy and of extent of rotation are essential to success. This paper proposes a simple method by use of a table and performance is facilitated by the of Kirschner wires.

JACQUES BRUNSCHWIG: Remarks on the Stoic Theory ofNames The Stoics' «invention» of the name as a grammatical category is linked to the general characteristics of Stoic logic, ontology and gnoseology. It is within this framework that the grammar of names (in particular, the fact of their declension and possible construction with the article) and, subsequently, the semantic definitions of the name and the common noun are examined. The paper goes on to analyse the truth-conditions of simple propositions in order to throw light on the peculiarities of the case where the subject is a name. In conclusion, an attempt is made to relate the logic of names and the physics of the individual by showing that the study of the construction of the name with the article is strictly similar to physical or grammatical analysis., Brunschwig Jacques. Remarques sur la théorie stoïcienne du nom propre. In: Histoire Épistémologie Langage, tome 6, fascicule 1, 1984. Logique et grammaire, sous la direction de Suzanne Bachelard . pp. 3-19.

This paper proves that in any boolean graph, the determination of the stable states reduces to the classical determination of the stable sets of the underlying pure graph. For this purpose use is made of exclusive graphs : that is boolean graph in which all the vertices are NOR. To be more specific : it is proved that a coloured exclusive graph is stable if and only if the starting points of its red arrows (that is the arrows of value 1) constitute a stable set of the extended graph obtained in equipping all red arrows with a starting point (original or new)., Decaestecker Christine. Sur les coloriages stables des graphes booliens exclusifs . In: Bulletin de la Classe des sciences, tome 71, 1985. pp. 297-300.

This paper deals with predictable representation and time changed processes. Let $(M^i)_{i\geq 0}$ be a sequence of independent local martingales. Suppose that each $M^i$ has the property of predictable representation with respect to its natural filtration. Suppose also that $(A^i)_{i\geq 1}$ is a sequence of continuous, increasing, $(\mathscr{F}^{M^0}_t)$ adapted processes. We study sufficient conditions in order that $M = M^0 + \sum M^i_{A^i}$ be a local martingale and $M$ have the property of predictable representation with respect to the filtration $(\mathscr{F}^{M^0}_t) \vee (\mathscr{F}^{M^1_{A^1}}_t \vee (\mathscr{F}^{M^2_{A^2}}_t \vee \cdots$. Such problems arise in the modeling of a security market with continuous trading [1].

Les auteurs effectuent une revue critique des méthodes statistiques et géostatistiques employées pour l’étude de la variabilité spatiale multiparamétrique des propriétés hydrodynamiques du sol. L’illustration et la discussion des méthodes fait référence, chaque fois que cela est possible, aux résultats obtenus en science du sol. Deux approches différentes mais complémentaires sont analysées. La première repose sur des techniques descriptives (analyse en composantes principales, analyse des covariogrammes, analyse des proximités spatiales, analyse krigeante, mise en facteur d’échelle), qui sont examinées suivant leurs aptitudes à faciliter la synthèse et la compréhension des covariations spatiales. La seconde vise à l’interpolation spatiale d’un paramètre en utilisant des échantillons d’observations d’autres paramètres. Les méthodes utilisées (régression, cokrigeage) sont comparées en fonction de la qualité des interpolations., This review focuses attention on statistical and geostatistical methods which are used to study the multivariate spatial variability of the hydrodynamical properties of soil. Whenever possible the discussion of the methods is illustrated by examples found in soil science papers. Two different, but complementary approaches are analysed. The first concerns descriptive procedures (principal component analysis, covariogram analysis, spatial proximity analysis, kriging analysis, scaling factor analysis) which are examined for their ability to synthesize and explain spatial covariations. The second sets out the purpose of spatial interpolation of one parameter from samples of others. The methods usually employed (regression, cokriging) are compared on the basis of their precision.

1 This paper presents a physiological model for the analysis of the "running curve" (i.e. the relationship between running time and power output) (Table I and Fig. 1). This model is derived from the basic hyperbolic model (Eq. 2: Fig. 2 a) modified in order to take into account the slow adjustment of oxygen utilization and of glycolysis at the onset of exercise (Eq. 7) and the progressive reduction of average aerobic power sustained with increasing running time for races lasting longer than 7 min (Eq. 10; Fig. 2 b, 2 d). 2 This model provides a satisfactory smoothing of the running curve from 200 m to marathon. Average errors (in absolute value) between actual and estimated power output are 0.9 +/- 0.2% (+/- SE) and 1.3 +/- 0.4% for male and female world records respectively (Table II). The basic hyperbolic model (Ptc = A/tc + B) provides a satisfactory smoothing of the running curve on comparatively narrow ranges of events (Table III). 3 Estimations of anaerobic energy stores and of VO2 max made for male and female from world records (1,219 J.kg-1 and 76.4 ml.kg-1.min-1; 1,118 J.kg-1 and 67.8 ml.kg-1.min-1 respectively) are in reasonable agreement with expected values in elite runners (Table IV). 4 The model allows the computation of an objective measure of endurance, i.e. the so-called "ability to sustain a high percentage of VO2 max for a long period of time".(ABSTRACT TRUNCATED AT 250 WORDS)

It has long been known that roots of an equation (or a system of equations), can be obtained by first writing the system in the form xn+1 = F(xn), then deriving the recurrence system xn+1 — F(xn) ; these roots are the fixed points of the iteration, i.e. the values x0 such that x0 = F(x0). However, an iterative process may converge to or diverge from a fixed point x0, depending on the slope of F(x) at this point. Many efficient methods have been derived to promote (or accelerate) the convergence of this type of iterative process. The method described here as "directed iteration" aims to render attractive any chosen type of fixed point from a large domain of initial points. The present paper describes one-variable systems ; a subsequent paper will deal with n-variable systems. In short, we substitute for the original recurrence : [FORMULA] in which A is a positive or a negative number depending on whether the slope of F(x) at the fixed point chosen is itself positive or negative. Convergence is fastest when the value of A equals this slope ; for higher absolute values of A, convergence persists, although it is increasingly slow. More generally, one can write : [FORMULA] in which A is a caricature of the Jacobian matrix of F(x0) and I is the unitary matrix. For n-variable systems, however, it is more convenient to adopt a form closer to the Newton-Raphson recurrence : [FORMULA] in which H(xn) = F(xn) — xn and J is a caricature of the Jacobian matrix of H(x0). Our algorithm is included (as well as the Newton-Raphson and the Whit-taker algorithms) in a more general formulation given by Isaacson and Keller (1966) ; however, its usefulness in the context described here does not seem to have been considered before. As pointed out to us by C. Mira, a method developped by Giraud (1969) for two variable systems also uses ad hoc matrices which modify the attractiveness of fixed points. In the search for steady state values of systems of non-linear ordinary differential equations, directed iteration often permits convergence to a chosen steady state (or type of steady state) from a wide range of initial guesses where classical iterations fail to converge or converge from a small interval around the steady state., Ari Richard d', Richelle Jean, Thomas René. Itération dirigée vers un point fixe ou un type de point fixe donné. In: Bulletin de la Classe des sciences, tome 73, 1987. pp. 62-83.

On se propose de calculer des estimateurs non biaisés de la régression linéaire dans le cas où les variables (x) et (y) de la régression, sont entachées d’erreurs. Dans une première partie, on présente les bases théoriques de la réduction du biais des estimateurs. Ces bases permettent d’aboutir à la construction d’estimateurs sans biais à l’ordre 1. De plus, on décrit la méthodologie permettant de quantifier rigoureusement l’ensemble des sources d’erreur à prendre en compte successivement pour les variables (x) et (y). Dans une seconde partie, ces résultats théoriques sont appliqués à deux instruments de mesure nécessitant un étalonnage préliminaire, un gamma densimètre à transmission (étalonné en laboratoire) et une sonde à neutrons (étalonnée in situ). Les résultats numériques montrent que les erreurs de mesure sont négligeables pour les variables (x) (taux de comptage) et (y) (masse volumique sèche) dans le cas du gamma densimètre à transmission (≤ 0,4 p. 100). Dans le cas de la sonde à neutrons, il en est de même pour la variable (x) (taux de comptage), mais les erreurs deviennent non négligeables (9 à 16 p. 100) pour la variable (y) (teneur en eau volumique). Lorsque les erreurs de mesure restent faibles (cas du gamma densimètre à transmission), il y a peu de différences entre les estimateurs de la droite d’étalonnage avec ou sans prise en compte des erreurs de mesure. Par contre, les différences deviennent plus sensibles lorsque les erreurs deviennent plus importantes (cas de l’humidimètre à neutrons), notamment en ce qui concerne la précision de l’estimation de valeurs prédites à partir de l’étalonnage., This paper proposes unbiased estimators of linear regression when the variables (x, y) present measurement errors. In the first part, theoretical calculations are described to obtain first-order unbiased estimators, and an error analysis is developed to take into account all the error components involved in each variable (x or y). In the second part, these theoretical results were applied to the calibration of a gamma-ray attenuation probe (laboratory calibration) and a neutron probe (field calibration). Numerical results showed that the measurement errors were negligible in the case of the gamma-ray attenuation equipement (≤ 0.4 %), but were greater (9 to 16 %) for the neutron probe, particularly for variable (y). When the measurement errors are small (gamma-ray attenuation probe), there is no difference between the parameters of the calibration estimated according to the classical approach or the proposed model. But when the measurement errors are greater (neutron probe), the differences between these two calibrations become higher especially for the precision of new predicted values.

The importance of mathematical modeling in dialysis arose recently as a consequence of the achievement of individualized treatment therapies. Two distinct models were used in our center, namely the urea kinetic model (UK) and the direct dialysis quantification (ddq), for the estimation of the urea distribution volume (V) and the urea generation rate (G). It turned out that, for the same patient, they provided us with different results. The basic hypotheses on which the two models rely are poorly described in the literature. The aim of this paper is an attempt to fill this gap and to show that the discrepancy observed between the two models is not surprising at all. The study also shows that from a theoretical viewpoint, ddq is more appropriate than UK for the estimation of V and G. The question of the intrinsic quality of ddq is not discussed here.

On présente un programme permettant l’ajustement de données expérimentales aux modèles non-linéaires : Y= a * X1α * X2β +b ou Y= a * X1α + b particulièrement utile dans le domaine des estimations de biomasse forestière (Y = biomasse totale d’un arbre ; Xl = diamètre à 1,30 m ; X2 = hauteur totale). Le calcul intègre à la fois : - la recherche des valeurs optimales des exposants α et β; - la possibilité de pondérer les résidus de la régression par une fonction puissance de la variable explicative X1 α * X2 β ou X1 α; selon le cas ; - le calcul des intervalles de confiance (à 95 p. 100) des valeurs estimées ; - le calcul de l’erreur commise en appliquant ce modèle à l’estimation de ΣY pour une population. L'intérêt pratique du programme réside dans sa souplesse d’utilisation (abondance du conversationnel, nombreux choix possibles, résultats partiels en ligne pour aides aux décisions) et son autonomie de fonctionnement sur micro-ordinateur compatible PC., The paper presents a computer program destined to fit experimental data through the nonlinear models : Y= a * X1α * X2β +b ou Y= a * X1α + b. This kind of model is particularly interesting for forestry biomass estimations (where Y = dry weight ; X1 = diameter ; X2 = height of the tree). The program takes into account : - the research of optimal values for both exponents α and β ; - the possibility to weight the residuals of the regression with a power function of the explanatory data X1 α * X2 β ou X1 α as the case may be ; - the calculation of the confidence bounds (level 95 p. 100) for estimated values ; - the calculation of the error when a such an equation is used to predict an estimation of the total biomass (ΣY) of a population. The practical interest of the program stands in its flexibility (conversational program with possibilities of choice and a partial presentation of the important intermediate results on the screen - helping to choose the best option) and in the fact that it is a self sufficient program for the PC.