Estimation effective de la perte de positivité dans la régularisation des courants

Let (X,ω) be a compact complex Hermitian manifold, and let T?γ be a d-closed (1,1) almost positive current on X. A variant of Demailly's regularization-of-currents theorem states that T is the weak limit of a sequence of (1,1)-currents T_m with analytic singularities of coefficient 1/m, lying in the same cohomology class as T, whose Lelong numbers converge to those of T, and with a loss of positivity decaying to zero. We prove that if the (1,1)-form γ is assumed to be closed and C^∞, the regularizing currents T_m can be chosen such that $\text{T}{}_{\mathrm{m}}\text{?γ?}\text{C}\text{m}$ for a constant C>0 independent of m. To cite this article: D. Popovici, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Mathematical modeling of two-photon thermal fields in laser–solid interaction

In this paper, we have developed an analytical model to study the temperature distributions in IR optical materials heated by laser pulses. Our model takes into account the two-photon absorption (TPA). The calculations are based on a three-dimensional model of heat diffusion in solids using the integral transform method. We find out the rigorous analytical expression of the thermal field when one considers both one- and two-photon absorption. The model is valid for any laser–solid system whose interaction can be described by the generalized Beer–Lambert law. Specific results are presented for an application of the model to ZnSe sample. We find out that TPA can produce detectable temperature variation.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

泛代数的二次扩张

在本文中引入了泛代数的二次扩张的概念，解决了ＴＵ－ＥＣ（Ａ）和ＵＴ－ＥＣ（Ａ）的存在、真类和基数问题，范畴ＴＵ－ＥＣ（Ａ）（及ＵＴ－ＥＣ（Ａ）），并得到了有关二次扩张的几个同构定理，还对一点二次扩张作了讨论。     

Preparation and microwave absorption properties of electroless Co-Ni-P coated strontium ferrite powder

A new type of Co-Ni-P coated strontium ferrite nanocomposite was prepared with electroless plating enhanced by ultrasonic wave at room temperature. The plating process was studied carefully. The morphology, crystal structure and microwave absorption properties of the Co-Ni-P coated powder were studied with field emission scanning electron microscopy (FE-SEM), X-ray diffraction (XRD), energy dispersive analysis of X-rays (EDX) and vector network analyzer. The results show that the strontium ferrite powder was successfully coated with Co-Ni-P alloy and possesses excellent microwave absorption properties. The maximum microwave loss of the composite powder reaches −44.12 dB. The bandwidth with the loss above −10 dB exceeds 13.8 GHz.     

Avoider-Enforcer games

Let p and q be positive integers and let H be any hypergraph. In a (p,q,H) Avoider-Enforcer game two players, called Avoider and Enforcer, take turns selecting previously unclaimed vertices of H. Avoider selects p vertices per move and Enforcer selects q vertices per move. Avoider loses if he claims all the vertices of some hyperedge of H; otherwise Enforcer loses. We prove a sufficient condition for Avoider to win the (p,q,H) game. We then use this condition to show that Enforcer can win the (1,q) perfect matching game on K2n for every q?cn/logn for an appropriate constant c, and the (1,q) Hamilton cycle game on Kn for every q?cnloglogloglogn/lognlogloglogn for an appropriate constant c. We also determine exactly those values of q for which Enforcer can win the (1,q) connectivity game on Kn. This result is quite surprising as it substantially differs from its Maker-Breaker analog. Our method extends easily to improve a result of Lu [X. Lu, A note on biased and non-biased games, Discrete Appl. Math. 60 (1995) 285-291], regarding forcing an opponent to pack many pairwise edge disjoint spanning trees in his graph.     

Calculation of number and free energy of the conformers of linear alkanes with medium and long chains. Implications for catalysis

A method for calculating the number of rotamers of a linear alkane and of the number of rotamers with a given number of gauche conformations along the chain as a function of the total number of atoms in the chain, using general equations, is presented. A graphical method for generating individual rotamers was applied to the homologs up to decane, which has 1134 rotamers. The steric energies calculated by molecular mechanics (MM2 force field) were used as measures of the heat of formation for the coiled conformations relative to the anti conformer for each molecule, whereas the statistical entropy differences were calculated for classes of coiled rotamers grouped by the number of gauche bonds and steric energy. The free energy values calculated from these components show that already at 400 K hexane exists preferentially in conformations containing gauche bonds. For larger chains the free energy advantage for the coiled chains increases very steeply. The implications for the question of reactions of linear alkanes occurring on the surface or inside the channels of small- and medium-pore zeolites are briefly examined.