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- SOMMAIRE/SUMMARY 1996 - TOME 323 - SERIE I - N° 5
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An example of a non adequate numeral system Un exemple d'un système numérique non adéquat Karim NOUR.......... Page(s) .......... 439
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- (voir tome 323, série I, 1996, p. 521 see Tome 323, Series I, 1996, p. 521).
- .......... Page(s) .......... 535
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- (voir tome 323, série I, 1996, p. 439 see Tome 323, Series I, 1996, p. 439).
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- CONTENTS 1996 - TOME 323 - SERIES I - No. 5
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- .......... Page(s) .......... 439
- A numeral system is defined by three closed-terms: a normal -term d for Zero, a -term S for Successor, and a -term for Zero Test, such that the -term (S d) are normalizable and have different normal forms. A numeral system is said adequate if and only if it has a -term-term for Predecessor. This Note gives a simple example of a non adequate numeral system.
- .......... Page(s) .......... 443
- .......... Page(s) .......... 443
- We give two explicit upper bounds for the values whenever is a primitive and odd Dirichlet character.
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- Let J be the Fourier expansion at infinity of the modular invariant j. Since it is known that, if q is a complex number with then q and J(q) cannot both be algebraic. We prove here, by modular tools as in [1], an approximation measure of J(q) when q is algebraic, an approximation measure of q when J(q) is algebraic and the corresponding transcendence measures.
- .......... Page(s) .......... 453
- .......... Page(s) .......... 453
- Let X be a two dimensional finite simplicial complex. We give a condition on X so that the fundamental group of X has property (T). This condition is satisfied by Euclidean Tits buildings.
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- Let G be a connected semisimple Lie group and H be the fixed point group for some involution of G. Assume G/H is split. In this case we compute some generalized coefficients of the spherical principal series of G in term of the B-matrix introduced by E. van den Ban. We use the wave front set to give a formula for the B-matrix corresponding to the longest element of the Weyl group.
- .......... Page(s) .......... 463
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- We study the propagation of an initial disturbance of an equilibrium state for the scalar conservation law
- We give a necessary and sufficient condition on for the following propagation property: if support of is compact then the support of is also compact for , for some . The proofs are based on the study of suitable associated Riemann problems.
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- Using the concept of strictly singular operators, we give a characterization of the essential spectrum on L-spaces. By means of the obtained results, we analyse the essential spectrum of the one-dimensional transport operator for wide classes of boundary and collision operators.
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- We introduce Zeta and Eta functions for continuous spectrum of differential operators. Our goal is to extend the classification results obtained for discrete spectrum problems. The existence of meromorphic extension is proved for a large class of differential operators on, asymptotically equal Then, we give applications for asymptotically flat manifolds and for indices computations.
- Aggregation problems in consumer theory and exterior differential calculus, Pierre-André CHIAPPORI and Ivar EKELAND (see Tome 323, Series I, 1996, p. 565).
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- In this Note, we use the notion of integrated semi-group to establish some results of existence and uniqueness of solutions of a retarded functional differential equation in infinite dimensional spaces. This work extends previous results on retarded differential equations in finite dimensional spaces ([1] to [4]).
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- We construct an extension of norms from a closed subspace of a Banach space to the whole space that preserves various types of rotundity possessed by the subspace norms.
- .......... Page(s) .......... 491
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- One knows that the notion of Harder-Narasimhan's canonical polygon allows one to write the stacks classifying Drinfeld's shtukas of rank at least 2 as inductive limits of open substacks of finite type. When there is no level structure, we present here a smooth modular compactification of each such open substack, generalizing Drinfeld's construction for rank 2.
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- Let F be a field of characteristic not 2 and be an anisotropic quadratic form over F of dimension 8 with trivial discriminant. We give a characterization of the quadratic forms such that becomes isotropic over the function field F () of the projective quadric defined by the equation . We deduce some consequences on the isotropy of quadratic form of dimension 7. For quadratic forms of dimension 6, this allows us to solve most of the cases not considered by Hoffmann [4] and to recover the known results on the isotropy of quadratic form of dimension 5 or 6. The proofs of the results announced in this Note will appear in [8], [9] and [10].
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- We prove the existence of a class of holomorphic vector bundles on some non-algebraic surfaces, especially on tori and primary Kodaira surfaces. This entails the existence of non-empty moduli spaces of stable bundles over non-Kähler surfaces which admit compactifications as constructed in [4].
- .......... Page(s) .......... 507
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- In this Note, we compute explicitly the asymptotics, as, of the capacity in of a condenser made of two identical domains, with boundary separated by a distance . So we answer a question raised by Polya and Szegö. This problem had also been considered by Kirchoff in the case of circular domains, and n = 2.
- .......... Page(s) .......... 511
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- To every convergence, there corresponds its topology , A convergence is topologically maximal in a class of convergences and if no convergence , is strictly finer than For pretopologies, paratopologies and pseudotopologies a characterization of maximality is given. The relationship with accessibility types of Whyburn and Siwiec and different classes of quotient maps is shown. Various topological properties are extended to convergences and characterized with the aid of different kinds of covering-maps.
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- We study via the chaotic calculus the independence of multiple stochastic integrals In (fn), Im (gm) with respect to martingales, that satisfy a deterministic structure equation. It is shown that if the integrals are independent and if a contraction denoted as does not vanish on a.e., then the stochastic measure associated to is Gaussian on A. In the Poisson case, , are independent if and only if vanishes a.e.
- We study, here, the behaviour of sums of a linear process associated to a sequence of i.i.d., zero mean random variables with values in B and such that and are linear bounded operators from B to B. We give a strong law and a weak law of large numbers for the sequence and an exponential rate of convergence if satisfies the Crmer conditions. Moreover, we obtain two compact laws of the iterated logarithm, one under the condition and an other under a weaker condition on the sequence but assuming that there exists such that .
- .......... Page(s) .......... 525
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- This Note studies the semi-parametric estimation of the model. The proposed method does not make use of the minoration of the density of the exogenous variable . The function is estimated over a variable compact set.
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- The method suggested in this Note shows that in order to make the Cox partial likelihood strictly concave with maximum it is sufficient to increase the number of the effective random observations with an appropriate finite set of preliminary non random functions called "starting observations" which are used exactly as random elements. Furthermore the "starting observations" ensure the existence of maximizators for any sieve consisting of a sequence of finite dimensional subspaces in the space of real bounded measurable functions on [0, 1]. In this way the penalty functional as in Zucker and Karr [5] or the histogram sieve as in Murphy and Sen [3] is not necessary.
- Laws of large numbers and compact law of the iterated logarithm for linear processes with values in a Banach space of type 2, Florence MERLEVEDE (see Tome 323, Series I, 1996, p. 521).
- .......... Page(s) .......... 535
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- In this Note, we study the application of the mixed finite elements method (MFE) for the simulation of the simplified hydrodynamic and energy transport models. The two main points are, firstly the use of "quasi-entropic" variables which gives a symmetric definite positive problem, and secondly the coupled computation of the equations, which requires a generalization of the MFE method for vector valued problems. We obtain a first validation of our method with some results on a ballistic diode n+ - n - n+.
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- In this Note, we're interested in the numerical approximation of scalar one-dimensionnal conservation laws with a non-linear, arbitrary stiff reaction term. We introduce a new scheme, built in order to respect original PDE's right steady-states and for which we give a convergence result for particular fluxes. Then we show a possible extension of this algorithm to more general problems.
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- We exhibit a quadratic functional for the harmonic Maxwell equations in exterior domain. The functional reaches its unique minimum in the space of out-going and/or in-going solution at the out-going solutions with absorbing boundary condition. It gives a "natural" Hilbertian framework to this problem. It is possible to compute explicitly all the terms of the functional to obtain a mixed integral system. Simple algorithms solve the system.
- .......... Page(s) .......... 553
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- The original motivation of this work was to give a co-inductive definition of reduction between infinite terms. We define a special reduction relation, so called semi-standard reduction, which is used to prove the main properties of reduction between infinite terms. For instance, though this reduction is not Church Rosser, a normal form, if it exists, is uniquely determined. This notion of semi-standard reduction is interesting even for finite terms and allows for a simple proof of the standardisation theorem.
- An example of a non adequate numeral system. Karim NOUR (see Tome 323, Series I, 1996, p. 439).
- .......... Page(s) .......... 565
- .......... Page(s) .......... 565
- We investigate under which conditions a smooth function is the demand function of a collectivity. Two particular versions of this problem have attracted specific attention in the literature: the characterization of household demand and that of aggregate market demand (as stemming from the addition of a large number of individual demand functions). Using Cartan's exterior differential calculus, we reconsider two open problems, and show they can be solved for analytical functions.
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- Informatique théorique
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- (voir tome 323, série I, 1996, p. 439)
- Problèmes mathématiques de la mécanique
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- Economie mathématique
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
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- .......... Page(s) .......... V-IX
- Logique
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- Théorie des nombres
- Théorie des groupes
- Equations aux dérivées partielles
- Analyse fonctionnelle
- Géométrie algébrique
- Géométrie analytique
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- Géométrie différentielle
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- Topologie
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- Probabilités
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- Statistique
- Analyse numérique
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