Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Unfolded singularities of analytic differential equations

La thèse est composée d’un chapitre de préliminaires et de deux articles sur le sujet du déploiement de singularités d’équations différentielles ordinaires analytiques dans le plan complexe. L’article Analytic classification of families of linear differential systems unfolding a resonant irregular singularity traite le problème de l’équivalence analytique de familles paramétriques de systèmes linéaires en dimension 2 qui déploient une singularité résonante générique de rang de Poincaré 1 dont la matrice principale est composée d’un seul bloc de Jordan. La question: quand deux telles familles sontelles équivalentes au moyen d’un changement analytique de coordonnées au voisinage d’une singularité? est complètement résolue et l’espace des modules des classes d’équivalence analytiques est décrit en termes d’un ensemble d’invariants formels et d’un invariant analytique, obtenu à partir de la trace de la monodromie. Des déploiements universels sont donnés pour toutes ces singularités. Dans l’article Confluence of singularities of non-linear differential equations via Borel–Laplace transformations on cherche des solutions bornées de systèmes paramétriques des équations non-linéaires de la variété centre de dimension 1 d’une singularité col-noeud déployée dans une famille de champs vectoriels complexes. En général, un système d’ÉDO analytiques avec une singularité double possède une unique solution formelle divergente au voisinage de la singularité, à laquelle on peut associer des vraies solutions sur certains secteurs dans le plan complexe en utilisant les transformations de Borel–Laplace. L’article montre comment généraliser cette méthode et déployer les solutions sectorielles. On construit des solutions de systèmes paramétriques, avec deux singularités régulières déployant une singularité irrégulière double, qui sont bornées sur des domaines «spirals» attachés aux deux points singuliers, et qui, à la limite, convergent vers une paire de solutions sectorielles couvrant un voisinage de la singularité confluente. La méthode apporte une description unifiée pour toutes les valeurs du paramètre.

Characterization of the unfolding of a weak focus and modulus of analytic classification

La thèse présente une description géométrique d’un germe de famille générique déployant un champ de vecteurs réel analytique avec un foyer faible à l’origine et son complexifié : le feuilletage holomorphe singulier associé. On montre que deux germes de telles familles sont orbitalement analytiquement équivalents si et seulement si les germes de familles de difféomorphismes déployant la complexification de leurs fonctions de retour de Poincaré sont conjuguées par une conjugaison analytique réelle. Le “caractère réel” de la famille correspond à sa Z2-équivariance dans R^4, et cela s’exprime comme l’invariance du plan réel sous le flot du système laquelle, à son tour, entraîne que l’expansion asymptotique de la fonction de Poincaré est réelle quand le paramètre est réel. Le pullback du plan réel après éclatement par la projection monoidal standard intersecte le feuilletage en une bande de Möbius réelle. La technique d’éclatement des singularités permet aussi de donner une réponse à la question de la “réalisation” d’un germe de famille déployant un germe de difféomorphisme avec un point fixe de multiplicateur égal à −1 et de codimension un comme application de semi-monodromie d’une famille générique déployant un foyer faible d’ordre un. Afin d’étudier l’espace des orbites de l’application de Poincaré, nous utilisons le point de vue de Glutsyuk, puisque la dynamique est linéarisable auprès des points singuliers : pour les valeurs réels du paramètre, notre démarche, classique, utilise une méthode géométrique, soit un changement de coordonée (coordonée “déroulante”) dans lequel la dynamique devient beaucoup plus simple. Mais le prix à payer est que la géométrie locale du plan complexe ambiante devient une surface de Riemann, sur laquelle deux notions de translation sont définies. Après avoir pris le quotient par le relèvement de la dynamique nous obtenons l’espace des orbites, ce qui s’avère être l’union de trois tores complexes plus les points singuliers (l’espace résultant est non-Hausdorff). Les translations, le caractère réel de l’application de Poincaré et le fait que cette application est un carré relient les différentes composantes du “module de Glutsyuk”. Cette propriété implique donc le fait qu’une seule composante de l’invariant Glutsyuk est indépendante.

Propagation of nonstationary curved and stretched premixed flames with multistep reaction mechanisms

The propagation speed of a thin premixed flame disturbed by an unsteady fluid flow of a larger scale is considered. The flame may also have a general shape but the reaction zone is assumed to be thin compared to the flame thickness. Unlike in preceding publications, the presented asymptotic analysis is performed for a general multistep reaction mechanism and, at the same time, the flame front is curved by the fluid flow. The resulting equations define the propagation speed of disturbed flames in terms of the properties of undisturbed planar flames and the flame stretch. Special attention is paid to the near-equidiffusion limit. In this case, the flame propagation speed is shown to depend on the effective Zeldovich number Z(f) , and the flame stretch. Unlike the conventional Zeldovich number, the effective Zeldovich number is not necessarily linked directly to the activation energies of the reactions. Several examples of determining the effective Zeldovich number for reduced combustion mechanisms are given while, for realistic reactions, the effective Zeldovich number is determined from experiments. Another feature of the present approach is represented by the relatively simple asymptotic technique based on the adaptive generalized curvilinear system of coordinates attached to the flame (i.e., intrinsic disturbed flame equations [IDFE]).

Towards the clonal propagation of coconut

Past studies from our laboratory have shown that whole immature, or mature sliced, zygotic embryos are a very good starting explant for coconut somatic embryogenesis. The highest rate of somatic embryogenesis was obtained when certain polyamines were added into the culture medium as well as activated charcoal (AC) to absorb unwanted phenolics. These past studies also showed that the development and maturation of the somatic embryos produced could be improved by the addition of abscisic acid (ABA), alone or with one of several osmotically active agents, into the culture medium. In the present study this well characterised somatic embryogenic system for zygotic tissues is being modified and applied to somatic tissues. This recent approach should be a better method for the rapid production of clonal, true-to-type coconut palms. The present research approach is focused on young leaf section explants which have been found to be very responsive to callus production. Young leaf sections produced optimum callus when cultured on media containing 2,4-D (150 μM) and the amount produced could be increased by soaking the sections in sterile water (15 to 60 minutes) or ascorbic acid (15 to 30 minutes) prior to culturing. Further improvement in callus production, as well as a reduction in the time taken for callogenesis was obtained when casein hydrolysate and/or certain polyamines were added to the callus induction medium. The development of the somatic embryos was improved by using ABA and polyethylene glycol (PEG) in the maturation medium. Despite these initial successes in improving coconut somatic embryogenesis, further studies are now being considered to shorten the time to achieve somatic embryogenesis, to better germinate somatic embryos and to improve the rate of somatic seedling conversion into plantlets.

Influence of leaf retention on cutting propagation of Lavandula dentata L.

Vegetative propagation of lavender offers several advantages over sexual propagation, among them crop homogeneity and yield of higher quality essential oil. However, Lavandula species have been propagated mostly by seeds and are said to be recalcitrant to rooting when propagated by cuttings. During cutting propagation, one of the important variables that influence the rooting capacity of cuttings is the leaf retention. The objective of this work was to evaluate the influence of leaf retention on rooting of L. dentata cuttings. Apical cuttings of L. dentata of 10 cm in length, keeping approximately 1/3, 1/2 or 2/3 of their leaves were planted in commercial substrate Plantmax HT® under intermittent mist. After two months, averages of root number, length of the longest root, root fresh and dry weights, and the survival percentage were evaluated. Root length and fresh weight were statistically greater with 2/3 of leaf retention and when fewer leaves were kept on the cuttings, lower means of root dry weight was observed. Under the conditions applied in this study, greater leaf retention was better for rooting of L. dentata cuttings.

Chemical sterilization in in vitro propagation of Arundina bambusifolia Lindl. and Epidendrum ibaguense Kunth

There is a great demand for simpler and less costly laboratory techniques and for more accessible procedures for orchid breeders who do not have the necessary theoretical basis to use the traditional seed and clone production methods of orchids in vitro. The aim of this study was to assess the use of sodium hypochlorite (NaClO) as a decontaminant in the process of inoculating adult orchid explants of Arundina bambusifolia and Epidendrum ibaguenses. Solutions of NaClO (1.200, 2.400, 3.600, 4.800 and 6.000 mg L-1 - equivalent to 50, 100, 150, 200 and 250 mL L-1 of commercial bleach - CB) were sprayed on the explants (1.0 mL) and the culture medium (GB5), in the presence or absence of activated charcoal (2 g L-1). The explants used were nodal segments of field-grown adult plants. The procedures for inoculating the explants were conducted outside the laminar flow chamber (LFC), except for the control treatment (autoclaved medium and explant inoculation inside the LFC). The best results for fresh weight yield, height and number of shoots were obtained using NaClO in solution at 1.200 mg L-1 (equivalent to 50 mL L-1 commercial bleach) with activated charcoal in the culture medium. Fresh weight figures were 1.10 g/jar for Arundina bambusifolia and 0.16 g/jar for Epidendrum ibaguenses. Spraying the NaClO solutions controls the contamination of the culture medium already inoculated with the explants.

Propagation of waves generated by a pressure disturbance moving in a channel

This paper studies the effect of ship speed and water depth on the propagation of ship generated waves. The ship is represented by a moving pressure distribution function at the free surface that is able to reproduce most of the phenomena involved in wave propagation. Results are obtained for a ship sailing along a coastal stretch made of a sloping bottom and a constant depth region. The results show that in the sloping bottom the crests of waves are bent along the slope and in the constant depth the standard Kelvin wave patterns can be found for the subcritical regime. In the critical regime the wave system is characterized by significant diverging waves and for a supercritical regime, the transverse waves disappear. © 2015 Taylor & Francis Group, London.

Credit markets and the propagation of monetary policy shocks

This paper analyzes the propagation of monetary policy shocks through the creation of credit in an economy. Models of the monetary transmission mechanism typically feature responses which last for a few quarters contrary to what the empirical evidence suggests. To propagate the impact of monetary shocks over time, these models introduce adjustment costs by which agents find it optimal to change their decisions slowly. This paper presents another explanation that does not rely on any sort of adjustment costs or stickiness. In our economy, agents own assets and make occupational choices. Banks intermediate between agents demanding and supplying assets. Our interpretation is based on the way banks create credit and how the monetary authority affects the process of financial intermediation through its monetary policy. As the central bank lowers the interest rate by buying government bonds in exchange for reserves, high productive entrepreneurs are able to borrow more resources from low productivity agents. We show that this movement of capital among agents sets in motion a response of the economy that resembles an expansionary phase of the cycle.

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Sources and propagation of international cycles: Common shocks or transmission?

This paper studies the generation and transmission of international cycles in a multi-country model with production and consumption interdependencies. Two sources of disturbance are considered and three channels of propagation are compared. In the short run the contemporaneous correlation of disturbances determines the main features of the transmission. In the medium run production interdependencies account for the transmission of technology shocks and consumption interdependencies account for the transmission of government shocks. Technology disturbances, which are mildly correlated across countries, are more successful than government expenditure disturbances in reproducing actual data. The model also accounts for the low cross country consumption correlations observed in the data.

Deciding analytically or trusting your intuition? The advantadges and disadvantadges of analytic and intuitive thought

Recent research has highlighted the notion that people can make judgmentsand choices by means of two systems that are labeled here tacit(or intuitive) and deliberate (or analytic). Whereas most decisionstypically involve both systems, this chapter examines the conditions underwhich each system is liable to be more effective. This aims to illuminatethe age-old issue of whether and when people should trust intuition or analysis. To do this, a framework is presented to understand how thetacit and deliberate systems work in tandem. Distinctions are also madebetween the types of information typically used by both systems as wellas the characteristics of environments that facilitate or hinder accuratelearning by the tacit system. Next, several experiments that havecontrasted intuitive and analytic modes on the same tasks are reviewed.Together, the theoretical framework and experimental evidence leads tospecifying the trade-off that characterizes their relative effectiveness.Tacit system responses can be subject to biases. In making deliberate systemresponses, however, people might not be aware of the correct rule to dealwith the task they are facing and/or make errors in executing it. Whethertacit or deliberate responses are more valid in particular circumstancesrequires assessing this trade-off. In this, the probability of making errorsin deliberate thought is postulated to be a function of the analytical complexityof the task as perceived by the person. Thus the trade-off is one of bias (inimplicit responses) versus analytical complexity (when tasks are handled indeliberate mode). Finally, it is noted that whereas much attention has beenpaid in the past to helping people make decisions in deliberate mode, effortsshould also be directed toward improving ability to make decisions intacit mode since the effectiveness of decisions clearly depends on both. Thistherefore represents an important frontier for research.

A numerical characterization of hypersurface singularities

In this note we give a numerical characterization of hypersurface singularities in terms of the normalized Hilbert-Samuel coefficients, and we interpret this result from the point of view of rigid polynomials.

Simulations in evolution. II. Relative fitness and the propagation of mutants.

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms which propel biological evolution. Our previous article presented a histogram model [1] consisting in populations of individuals whose number changed under the influence of variation and/or fitness, the total population remaining constant. Individuals are classified into bins, and the content of each bin is calculated generation after generation by an Excel spreadsheet. Here, we apply the histogram model to a stable population with fitness F(1)=1.00 in which one or two fitter mutants emerge. In a first scenario, a single mutant emerged in the population whose fitness was greater than 1.00. The simulations ended when the original population was reduced to a single individual. The histogram model was validated by excellent agreement between its predictions and those of a classical continuous function (Eqn. 1) which predicts the number of generations needed for a favorable mutation to spread throughout a population. But in contrast to Eqn. 1, our histogram model is adaptable to more complex scenarios, as demonstrated here. In the second and third scenarios, the original population was present at time zero together with two mutants which differed from the original population by two higher and distinct fitness values. In the fourth scenario, the large original population was present at time zero together with one fitter mutant. After a number of generations, when the mutant offspring had multiplied, a second mutant was introduced whose fitness was even greater. The histogram model also allows Shannon entropy (SE) to be monitored continuously as the information content of the total population decreases or increases. The results of these simulations illustrate, in a graphically didactic manner, the influence of natural selection, operating through relative fitness, in the emergence and dominance of a fitter mutant.