Comptes Rendus de l'Académie des Sciences - Series I - Mathematics最新文献

Let S be a complex analytic manifold and C⊂S a reduced complete intersection. We construct a complex $\text{Ω}{}_{\mathrm{S}}{}^{\mathrm{•}}\text{(}\text{log}\text{C)}$ of sheaves of the so-called multi-logarithmic differential forms on S with respect to C and define a residue map $\text{res}\text{:Ω}{}_{\mathrm{S}}{}^{\mathrm{•}}\text{(}\text{log}\text{C)→ω}{}_{\mathrm{C}}{}^{\mathrm{•}}$ from this complex onto the Barlet complex ω_C^• of regular meromorphic differential forms on C. The residue map is proved to be a natural morphism between the two complexes; it follows then that sections of the complex ω_C^• may be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the map res can be given explicitly in terms of a certain integration current.

In this work we prove a kind of Arnold–Liouville theorem for n-forms ω in dimension 2n, whose local model is $\text{ω=∑}{}_{\mathrm{j=1}}{}^{\mathrm{n}}\text{d}\text{y}{}_{\mathrm{j}}\text{∧}\text{d}\text{x}{}_1\text{∧⋯∧}\text{d}\text{̂}\text{x}{}_{\mathrm{j}}\text{∧⋯∧}\text{d}\text{x}{}_{\mathrm{n}}$. Some global aspects of these forms are studied as well.

Given a smooth variety, X and a map g:X→Δ such that g⁻¹(0) is a normal crossing variety X₀=X₁∪_ZX₂, we consider stable maps F₀:C₀→X₀ which appear as the central fibre of a family of maps Splitting such a stable map up into F₁:C₁→X₁ and F₂:C₂→X₂, we derive conditions on the 0-cycle C_i∩Z_i in the Chow group A⁰(F⁻¹_i(Z)). These conditions provide an elementary geometric justification for the work of Li and Ruan in [4] and of Gathmann in [2].

In this paper the existence of solution for a new elastohydrodynamic model for journal bearing devices is proved. The lubricant pressure and the concentration are governed by Reynolds equation combined with Elrod–Adams model for cavitation, while the bearing displacement follows a Koiter model for shells. A regularization procedure is proposed to overcome the Heaviside concentration–pressure relation. A fixed point theorem leads to the solution of the regularized problem. The introduction of prolongation and restriction operators copes with the additional difficulty of elastic and hydrodynamic subproblems posed on different domains. The estimates for the regularized problem allow to pass to the limit and state the existence result.

In this Note, we give the exact asymptotic mean integrated squared error and the mean squared error for the kernel estimator of the hazard rate from truncated and censored data. Martingale techniques and combinatory calculus are used to obtain these results. A probability bound and the optimal bandwidth choice are also given.

In this Note, we describe many examples of two-dimensional random variables {B_T,T} obtained from the position of a Brownian motion $\text{(B}{}_{\mathrm{t}}\text{;}\text{t⩾0)}$ at a stopping time T such that T and B_T are independent. For such pairs, the law of T determines that of B_T and vice versa; we study the constraints on these laws induced by the independence assumption.

We prove existence and uniform a priori estimates for Euclidean Gibbs states of quantum lattice systems with unbounded spins. These results substantially extend all previous existence results. Detailed proofs are contained in [3].

We generalize the results on the explicit form of Hamilton's equations in local coordinates near a group orbit of Roberts, Wulff and Lamb to local momentum maps with cocycles. We use these equations to study the dynamics near relative equilibria.

Consider the ring of germs of analytic functions at the origin of $\text{C}{}^2$. Let I be an ideal of this ring, and let us denote by $\text{I}$, the integral closure of this ideal. J. Lipman and B. Teissier proved that the following formula: $\text{I}{}^{\mathrm{n+1}}\text{=}\text{I}\text{·I}{}^{\mathrm{n}}$, holds for every integer n. In this paper, we discuss, under certain condition over I, of a similar formula for the fractional powers of I.

Let (M^m,g) and (Nⁿ,h) (m⩾2) be two compact Riemannian manifolds without boundary. When Riem_N⩽0, we show the global existence of a weak solution of the heat equation for p-harmonic maps (p>1) and the convergence of this solution at infinity to a regular weakly p-harmonic map; so generalizing the result of Eells–Sampson for harmonic maps to the case that p>1.