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R. Thomas conjectured, 20 years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of several stable states. Recently, E. Remy et al. stated and proved the conjecture for Boolean dynamical systems. Using a similar approach, we generalize the result to discrete dynamical systems, and by focusing on the asynchronous dynamics that R. Thomas used in the course of his analysis of genetic networks, we obtain a more general variant of R. Thomas’ conjecture. In this way, we get a necessary condition for genetic networks to lead to differentiation. 相似文献
3.
This Note deals with the sensitivity analysis of a newtonian incompressible fluid driven by the Navier–Stokes equations with respect to the dynamic of the fluid domain boundary. The structure of the gradient with respect to the velocity of the domain for a given cost function is established. This result is obtained using new shape derivation tools for Eulerian functionals and the Min–Max derivation principle. To cite this article: R. Dziri et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
4.
We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under renormalization group transformations. The model is used as a playground to investigate various features of field theory at finite temperature. For example we verify that, as expected from general arguments, the cancellation of ultraviolet divergences takes place at finite temperature without the need for introducing counterterms beyond those of zero temperature. As well known, the discrete chiral symmetry of the (1+1)-dimensional model is spontaneously broken at zero temperature and restored, in leading order, at some temperature Tc; we find that the 1/N approximation breaks down for temperatures below Tc: as the temperature increases, the fluctuations become eventually too large to be treated as corrections, and a Landau pole invalidates the calculation of the effective potential in the vicinity of its minimum. Beyond Tc, the 1/N expansion becomes again regular: it predicts that in leading order the system behaves as a free gas of massless fermions and that, at the next-to-leading order, it remains weakly interacting. In the limit of large temperature, the pressure coincides with that given by perturbation theory with a coupling constant defined at a scale of the order of the temperature, as expected from asymptotic freedom. 相似文献
5.
We study the vibration of an elastic thin shell which is pre-constrained by a large displacement with a small deformation. In this first Note we prove the solutions exist and we investigate both the interior regularity and the boundary regularity which is known to be important in the shape differentiation of hyperbolic equations. To cite this article: J. Cagnol, J.-P. Zolésio, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 161–166 相似文献
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An alternative definition of entropy for non-commutative systems, equivalent to the one by A. Connes, H. Narnhofer, and W. Thirring, is given. It is based on the concepts of conditional entropy, and stationary couplings with classical systems. It allows to prove that any quantum dynamical system with singular spectrum has zero entropy. 相似文献
8.
István E. MarkóJean-Christophe Vanherck Ali AtesBernard Tinant Jean-Paul Declercq 《Tetrahedron letters》2003,44(16):3333-3336
Upon treatment with tBuOK/H2O, a variety of ω-halo-β-keto-ketals undergo smooth cyclisation, affording in excellent yields mono-protected [n,m] spiro bicyclic diketones. This transformation is highly stereoselective producing, in all cases, the diastereoisomerically pure spiro derivatives. 相似文献
9.
We present a linear rational pseudospectral (collocation) method with preassigned poles for solving boundary value problems. It consists in attaching poles to the trial polynomial so as to make it a rational interpolant. Its convergence is proved by transforming the problem into an associated boundary value problem. Numerical examples demonstrate that the rational pseudospectral method is often more efficient than the polynomial method. 相似文献
10.
Jean-Paul Penot 《Bulletin des Sciences Mathématiques》2003,127(9):815-833
We introduce a notion of “firm” (or uniform) asymptotic cone to an unbounded subset of a normed space. We relate this notion to a concept of “firm” asymptotic function. We use these notions to study boundedness properties which can be applied to continuity questions for some operations on sets and functions. Such questions arise in stability analysis of Hamilton-Jacobi equations. We present some other applications such as an extension of a theorem of Dieudonné and existence results in optimization and fixed point theory. 相似文献