Periodic schedules for linear precedence constraints

We consider the computation of periodic cyclic schedules for linear precedence constraints graphs: a linear precedence constraint is defined between two tasks and induces an infinite set of usual precedence constraints between their executions such that the difference of iterations is a linear function. The objective function is the minimization of the maximal period of a task.We recall first that this problem may be modelled using linear programming. A polynomial algorithm is then developed to solve it for a particular class of linear precedence graphs called unitary graphs. We also show that a periodic schedule may not exist for unitary graphs. In the general case, a decomposition of the linear precedence graph into unitary components is computed and we assume that a periodic schedule exists for each of these components. Lower bounds on the periods are exhibited and we show that an optimal periodic schedule may not achieve them. The notion of quasi-periodic schedule is then introduced and we prove that this new class of schedules always reaches these bounds.     

Tetrapterosides A and B,two new oleanane‐type saponins from Tetrapleura tetraptera

From the stem bark of Tetrapleura tetraptera, two new oleanane‐type saponins, tetrapteroside A 3‐O‐{6‐O‐[(2E,6S)‐2,6‐dimethyl‐6‐hydroxyocta‐2,7‐dienoyl]‐β‐D ‐glucopyranosyl‐(1 → 2)‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐(1 → 4)‐[β‐D ‐glucopyranosyl‐(1 → 2)]‐β‐D ‐glucopyranosyl}‐3,27‐dihydroxyoleanolic acid (1), and tetrapteroside B 3‐O‐{ β‐D ‐glucopyranosyl‐(1 → 2)‐6‐O‐[(E)‐feruloyl]‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐(1 → 4)‐[β‐D ‐glucopyranosyl‐(1 → 2)]‐β‐D ‐glucopyranosyl}‐3,27‐dihydroxyoleanolic acid (2), were isolated. Further extractions from the roots led to the isolation of four known oleanane‐type saponins. Their structures were elucidated by the combination of mass spectrometry (MS), one and two‐dimensional NMR experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate

Summary. In this paper, we study finite volume schemes for the nonhomogeneous scalar conservation law with initial condition . The source term may be either stiff or nonstiff. In both cases, we prove error estimates between the approximate solution given by a finite volume scheme (the scheme is totally explicit in the nonstiff case, semi-implicit in the stiff case) and the entropy solution. The order of these estimates is in space-time -norm (h denotes the size of the mesh). Furthermore, the error estimate does not depend on the stiffness of the source term in the stiff case. Received October 21, 1999 / Published online February 5, 2001     

A method for 13C‐labeling of metabolic carbohydrates within French bean leaves (Phaseolus vulgaris L.) for decomposition studies in soils

The molecular composition of plant residues is suspected to largely govern the fate of their constitutive carbon (C) in soils. Labile compounds, such as metabolic carbohydrates, are affected differently from recalcitrant and structural compounds by soil‐C stabilisation mechanisms. Producing ¹³C‐enriched plant residues with specifically labeled fractions would help us to investigate the fate in soils of the constitutive C of these compounds. The objective of the present research was to test ¹³C pulse chase labeling as a method for specifically enriching the metabolic carbohydrate components of plant residues, i.e. soluble sugars and starch. Bean plants were exposed to a ¹³CO₂‐enriched atmosphere for 0.5, 1, 2, 3 and 21 h. The major soluble sugars were then determined on water‐soluble extracts, and starch on HCl‐hydrolysable extracts. The results show a quick differential labeling between water‐soluble and water‐insoluble compounds. For both groups, ¹³C‐labeling increased linearly with time. The difference in δ¹³C signature between water‐soluble and insoluble fractions was 7‰ after 0.5 h and 70‰ after 21 h. However, this clear isotopic contrast masked a substantial labeling variability within each fraction. By contrast, metabolic carbohydrates on the one hand (i.e. soluble sugars + starch) and other fractions (essentially cell wall components) on the other hand displayed quite homogeneous signatures within fractions, and a significant difference in labeling between fractions: δ¹³C = 414 ± 3.7‰ and 56 ± 5.5‰, respectively. Thus, the technique generates labeled plant residues displaying contrasting ¹³C‐isotopic signatures between metabolic carbohydrates and other compounds, with homogenous signatures within each group. Metabolic carbohydrates being labile compounds, our findings suggest that the technique is particularly appropriate for investigating the effect of compound lability on the long‐term storage of their constitutive C in soils. Copyright © 2009 John Wiley & Sons, Ltd.     

Copper(II) halide salts and complexes of 4-amino-2-fluoropyridine: synthesis,structure and magnetic properties

Reaction of 4-amino-2-fluoropyridine (2-F-4-AP) with copper halides produced the neutral coordination complexes: (2-F-4-AP)₂CuX₂ (X = Cl(1), Br(2)). 1 crystallizes in the orthorhombic space group Pccn in a distorted square planar geometry. Magnetic susceptibility data were fit to the uniform chain Heisenberg model resulting in C = 0.439(6)emu-K/mole-Oe and J = ?28(1) K. 2 crystallizes in the monoclinic space group C2/m and is closer to distorted tetrahedral. Intermolecular Br?Cu contacts generate a square layer. Magnetic data show very weak ferromagnetic interactions [C = 0.42(1)emu-K/mol-Oe, J = 0.71(2) K]. Similarly, reaction of 2-F-4-AP with copper halides and aqueous HX in alcohol solvents produced the salts (2-F-4-APH)₂CuX₄ (X = Cl(3), Br(4)). 3 crystallizes in the triclinic space group P-1. Crystal packing reveals short Cl?Cl contacts which generate a structural ladder. However, analysis of the magnetic data suggests that only the rails of the ladder produce a viable magnetic superexchange pathway; the uniform Heisenberg chain model provides C = 0.449(1)emu-K/mol-Oe and J = -6.9(1) K. 4 is isostructural and is also best fit by a chain model [J = ?2.7(4) K]. The brominated complex (2-F-3-Br-4-APH)₂CuBr₄·2H₂O, 5, (2-F-3-Br-4-APH = 4-amino-3-bromo-2-fluoropyridinium) was serendipitously produced as a byproduct of the synthesis of 4 and was characterized by single-crystal X-ray diffraction.     

Short and efficient access to imidazo[1,2-a]pyrrolo[3,2-c]pyridine derivatives

Access to N-protected or N-free imidazo[1,2-a]pyrrolo[3,2-c]pyridine derivatives as potential antiviral compounds was achieved in good yields from N-protected 7-amino-8-halo-2-methylimidazo[1,2-a]pyridines by catalytic coupling of terminal acetylenes under mild conditions using [PdCl₂(PPh₃)₂] or [Cu(Phen)(PPh₃)₂]NO₃.     

Presenegenin Glycosides from Securidaca welwitschii

The five new presenegenin glycosides 1 – 5 were isolated from Securidaca welwitschii, together with one known sucrose diester. Compounds 1 – 4 were obtained as pairs of inseparable (E)/(Z)‐isomers of a 3,4‐dimethoxycinnamoyl derivative, i.e., 1 / 2 and 3 / 4 . Their structures were elucidated mainly by 2D‐NMR techniques and mass spectrometry as 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐β‐D ‐xylopyranosyl‐(1→4)‐O‐α‐L ‐rhamnopyranosyl‐(1→2)‐O‐[β‐D ‐glucopyranosyl‐(1→3)]‐4‐O‐[(E)‐3,4‐dimethoxycinnamoyl]‐β‐D ‐fucopyranosyl} ester ( 1 ) and its (Z)‐isomer 2 , 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐β‐D ‐galactopyranosyl‐(1→4)‐O‐β‐D ‐xylopyranosyl‐(1→4)‐O‐3‐O‐acetyl‐α‐L ‐rhamnopyranosyl‐(1→2)‐O‐[β‐D ‐glucopyranosyl‐(1→3)]‐4‐O‐[(E)‐3,4‐dimethoxycinnamoyl]‐β‐D ‐fucopyranosyl} ester ( 3 ) and its (Z)‐isomer 4 , and 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐[O‐β‐D ‐galactopyranosyl‐(1→3)‐O‐β‐D ‐xylopyranosyl‐(1→4)‐O‐α‐L ‐rhamnopyranosyl‐(1→2)‐β‐D ‐fucopyranosyl] ester ( 5 ) (presenegenin=(2β,3β,4α)‐2,3,27‐trihydroxyolean‐12‐ene‐23,28‐dioic acid).     

Toluene steam reforming as tar model molecule produced during biomass gasification with an iron/olivine catalyst

Tar produced during biomass steam reforming is a complex mixture of single to multiple ring aromatic compounds and it is necessary to eliminate them in order to prevent any condensation-polymerisation problem. Tar steam reforming leads to additional hydrogen that improves gas production. Previous works have shown that olivine was active in tar removal during biomass gasification and the iron distribution into the mineral different phases has a real influence on its efficiency. A Fe/olivine catalytic system has been designed to study tar steam reforming. This work presents the Fe/olivine catalyst characterizations (XRD, Mössbauer, TPR) and compares the Fe/olivine and olivine reactivity in toluene steam reforming, a tar model molecule. At 850 °C, an important conversion (95%) was observed for Fe/olivine during 7 h. The strong interaction between iron and olivine, and the equilibrium between Fe⁰/Fe^II/Fe^III seem to be responsible of the catalyst activity and stability in toluene steam reforming.     

Comparative dissociation of peptide polyanions by electron impact and photo-induced electron detachment

We compare product-ion mass spectra produced by electron detachment dissociation (EDD) and electron photodetachment dissociation (EPD) of multi-deprotonated peptides on a Fourier transform and a linear ion trap mass spectrometer, respectively. Both methods, EDD and EPD, involve the electron emission-induced formation of a radical oxidized species from a multi-deprotonated precursor peptide. Product-ion mass spectra display mainly fragment ions resulting from backbone cleavages of C_α-C bond ruptures yielding a and x ions. Fragment ions originating from N-C_α backbone bond cleavages are also observed, in particular by EPD. Although EDD and EPD methods involve the generation of a charge-reduced radical anion intermediate by electron emission, the product ion abundance distributions are drastically different. Both processes seem to be triggered by the location and the recombination of radicals (both neutral and cation radicals). Therefore, EPD product ions are predominantly formed near tryptophan and histidine residues, whereas in EDD the negative charge solvation sites on the backbone seem to be the most favorable for the nearby bond dissociation.