A greedy algorithm for multicut and integral multiflow in rooted trees

We present an O(min(Kn,n²)) algorithm to solve the maximum integral multiflow and minimum multicut problems in rooted trees, where K is the number of commodities and n is the number of vertices. These problems are NP-hard in undirected trees but polynomial in directed trees. In the algorithm we propose, we first use a greedy procedure to build the multiflow then we use duality properties to obtain the multicut and prove the optimality.     

Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity

We report new results on the diffraction properties of photoinduced gratings in InGaAs/InGaAsP MQW structures. The original feature of this device is that the QWs are enclosed in an asymmetric Fabry–Perot microcavity in order to increase the diffraction efficiency. We observe oscillations in the diffraction efficiency due to resonant effects in the microcavity. The experimental spectra are compared with theory. Diffraction efficiency at 1.55 μm attains a maximum value of 2.7% at a write beam fluence of 260 μ J cm⁻², and then decreases at higher fluences. We explain this phenomenon by an absorption saturation at high excitation.     

Synthesis,characterization, spectroscopy and thermal analysis of rare earth picrate complexes with <Emphasis Type="Italic">L</Emphasis>-lysine

Summary Rare earth picrate (RE) complexes with L-lysine (Lys) were synthesized and characterized. Elemental analysis (CHN), EDTA titrations and thermogravimetry data suggest a general formula RE(pic)₃·2Lys·2H₂O, where RE=La-Lu (without Pm) and Y, pic=picrate). IR spectra suggest that Lys is coordinated to the central ion through the nitrogen of the α-amino group. Parameters obtained from the absorption spectrum of the Nd compound indicated that the metal-ligand bonds are essentially electrostatic. Emission spectrum and biexponential behavior of the luminescence decay of the Eu compound suggest the existence of polymeric species. Thermogravimetric/derivative thermogravimetric (TG/DTG) and differential scanning calorimetry (DSC) curves of all complexes are very similar, with five events. The final products are the corresponding rare earth oxides and their X-ray diffraction patterns are identical to the calcinated oxides.</o:p>     

Thermal decomposition and indirect structural determination of rare earth element picrates with the dtso ligand

The complexes [Ln(pic)₃(DTSO)₃] (Ln=La, Lu and Y; pic=picrate; DTSO=1,3-dithiane-1-oxide) were synthesized and characterized. Indirect structural determination by far infrared spectroscopy is presented. Results from thermal decomposition of these complexes by TG/DTG and DSC techniques are reported. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nature et stabilité des complexes métalliques de cryptands dinucléants en solution II. Polythiamacrotricycles et monocycles apparentés

Nature and Stability of Some Metallic Complexes of Dinucleating Cryptands in Solution II. Polythiamacrotricycles and Related Monocyclic Subunits The stability constants of the Cu²⁺ and Ag⁺ complexes of the cylindrical macrotricycle 1a (1,7,13,19-tetraaza 4,16-dioxa 10,22,27,32-tetrathiatricyclo[17.5.5.5]tetratriacontane) have been determined by pH-metry, as well as those of the Cu²⁺, Co²⁺, Zn²⁺, Cd²⁺, Pb²⁺, and Ag⁺ complexes of the monocyclic subunit 2a (1,7-dimethyl-1,7-diaza 4,10-dithiacyclododecane), in aqueous solutions (NaClO₄) at 25°. In the Cu(II) systems, equilibria were reached slowly, and the results established by pH-metry were confirmed by UV/VIS spectrophotometric studies. The tricycle 1a forms dinuclear cryptates with copper and silver, with overall stability constants log β₂₁₀ (Cu₂- 1a )⁴⁺ = 18.5, log β_21-2 (Cu₂- 1a (OH)₂)²⁺ = 4.8, log β₂₁₀(Ag₂- 1a )²⁺ = 23.0. Ag⁺ also forms a mononuclear (Ag- 1a )⁺ complex, with log β₁₁₀ = 13.1, but no mononuclear species were detected in the Cu- 1a system. The absorption spectra of the bis-Cu(II) complexes of 1a and 2a in aqueous medium, MeOH and propylene carbonate (PC) are given, as well as those, in MeOH and PC, of the bis-copper complexes of the related monocycles 3 and 4 (1,7-diaza-4,10,13-trithiacyclopentadecane and 1.10-diaza 4,7,13,16-tetrathiacyclooctadecane, respectively), and tricycle 5 with two benzyl groups in the lateral chains. The complexing properties of the polyoxa- and polythia macrotricycles (Parts I and II of this series) are compared to those of other bis-chelating ligands, the bicyclic bis-tren and the monocyclic bis-dien.     

Actinide heterobimetallic oxides (Th, U): reduction studies

In our laboratories we have been studying the synthesis and reactivity of binary actinide and lanthanide intermetallic compounds. In this work, the air-oxidation of ThCu₂ and AnNi₂ (An = Th, U) was followed by thermogravimetry (TG) and the products were characterized by X-ray powder diffraction (XRD). The heterobimetallic oxides obtained are described by the formulas 2MO·ThO₂ (M = Cu, Ni) and 2NiO·UO₃. The thermogravimetric analysis under hydrogen of these heterobimetallic oxides show one mass loss for 2MO·ThO₂ and two mass losses for 2NiO·UO₃ over a wide range of temperature (293–1273 K). The characterization by XRD shows that the reduction products are 2M·ThO₂ (M = Cu, Ni) and 2Ni·UO₂, with all the actinides in the 4+ oxidation state. The actinide heterobimetallic oxides were described as copper or nickel supported catalysts.