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See detailCalcium-vitamin D supplementation in clinical trials of osteoporosis should be titrated on the basis of pre-study assessments
Reginster, Jean-Yves ULg; Diez-Perez, A.; Ortolani, S. et al

in Osteoporosis International (2002), 13(S1), 24

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See detailIs it possible to obtain a coherent image of the texture of a porous material?
Noville, Francis ULg; Gommes, Cédric ULg; Doneux, C. et al

in Studies in Surface Science and Catalysis (2002), 144

This study consists in verifying the coherence of a few commonly used analysis methods of nitrogen adsorption-desorption isotherms. These methods were tested on model samples obtained by mechanically ... [more ▼]

This study consists in verifying the coherence of a few commonly used analysis methods of nitrogen adsorption-desorption isotherms. These methods were tested on model samples obtained by mechanically mixing two micro- and mesoporous solids respectively with known, mass proportions. Although the individual analysis methods may lead to discrepancies in the interpretation of the isotherms, their systematic comparison allows drawing a coherent picture of the porous texture. [less ▲]

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See detailCandidate locus for familial abdominal aortic aneurysms by genome-wide DNA linkage analysis
Shibamura, H.; Buxbaum, S.; Olson, J. M. et al

in Circulation (2002), 106(19, Suppl. S), 168

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See detailStructure-modifying drugs in osteoarthritis
Reginster, Jean-Yves ULg; Kvasz, Angela ULg

in Osteoporosis International (2002), 13(Suppl. 1), 49-50

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See detailInfluence of P-glycoprotein on the tissue distribution in rats of the 5-HT1A antagonist p-[18F]MPPF.
Plenevaux, Alain ULg; Lacan, G.; Defraiteur, C. et al

in Society for Neuroscience / Abstracts (2002)

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See detail18F-MPPF Pharmacokinetics in rat hippocampus imaged with MicroPet.
Rubin, D. J.; Way, B.; Lacan, G. et al

in Journal of Nuclear Medicine : Official Publication, Society of Nuclear Medicine (2002), 43(S1), 209

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See detailCharacterization of the Metabolism of Osteoarthritic Chondrocytes Cultured in Alginate Beads
Sanchez, Christelle ULg; Mathy, Marianne ULg; Deberg, Michelle ULg et al

in Osteoarthritis and Cartilage (2002), 10(SA), 34

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See detailPCDD/F and non-ortho PCB body burden of the general population in Wallonia, Belgium: impact of different sources of environmental pollution
Fierens, S.; Mairesse, Hélène; Focant, Jean-François ULg et al

in Organohalogen Compounds (2002), 55

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See detailThe effect on bone turnover of monofluorophosphate (MFP) combined with raloxifene (RLX) as compared to MFP alone in postmenopausal women with low bone mass
Stepan, J.; Payer, J.; Resch, H. et al

in Osteoporosis International (2002), 13(S1), 54

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See detailThe green lacewings in Belgium (Neuroptera : Chrysopidae)
Bozsik, Andras; Mignon, Jacques ULg; Gaspar, Charles

in Acta Zoologica Academiae Scientiarum Hungaricae (2002), 48(Suppl. 2), 53-59

There are merely three published sources of information on the green lacewings in Belgium. The first two were written by a Belgian and a Catalan author at the beginning of the 20th century and the third ... [more ▼]

There are merely three published sources of information on the green lacewings in Belgium. The first two were written by a Belgian and a Catalan author at the beginning of the 20th century and the third was published in 1980. Interestingly, the most recent study reported the fewest species (11), the most previous contained 12 and the second one showed 17 species, This confused situation and the paucity of data initiated the authors to identify the green lacewing collection of the Gembloux University of Agricultural Sciences, where lacewings from different parts of Belgium were preserved, and also to collect chrysopids regularly, Summarising the species reported in the literature and caught during sampling, 18 green lacewing species have been verified in Belgium: Nothochrysa fulviceps, Nothochrysa capitata, Hypochrysa elegans, Nineta flava, Nineta vittata, Nineta pallida, Chrysotropia ciliata, Chrysopa perla, Chrysopa dorsalis, Chrysopa abbreviata, Chrysopa formosa, Chrysopa phlyllochroma, Chrysopa pallens, Dichochrysa flavifrons, Dichochrysa prasina, Dichochrysa ventralis, Chrysoperla carnea, Cunctochrysa albolineata. Considering the known references, one species, Nineta pallida proved to be new for the Belgian fauna. [less ▲]

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See detailPregnancy-associated glycoprotein concentrations during pregnancy and postpartum periods in zébu cattle.
Melo de Sousa, Noelita ULg; Zongo, M.; Pitala, W. et al

in Biotechnologie, Agronomie, Société et Environnement = Biotechnology, Agronomy, Society and Environment [=BASE] (2002), 6(1), 10-11

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See detailEffet de la parité sur les paramètres métaboliques et hormonaux de la femelle de réforme Blanc-Bleu Belge cularde
Cabaraux, Jean-François ULg; Hornick, Jean-Luc ULg; de Behr, V. et al

in Biotechnologie, Agronomie, Société et Environnement = Biotechnology, Agronomy, Society and Environment [=BASE] (2002), 6(1), 5-16

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See detailStrontium ranelate réduit le risque de fracture vertébrale chez des patientes traitées 3 ans pour ostéoporose postménopausique
Meunier, P. J.; Roux, C.; Fardellone, P. et al

in Revue du Rhumatisme (2002), 69

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See detailPrediction of bone mineral density by estrogens precursors, estradiol, SHBG and BMI in elderly women at risk for osteoporotic fractures
Goemaere, S.; Zmierczak, H.; Van Pottelbergh, I. et al

in Osteoporosis International (2002), 13(S1), 102

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See detailAnalyse des potentialités du transport fluvial dans un marché multimodal et intermodal
Marchal, Jean ULg; Zhang, Zhaomin; Marchal, Jean-Christophe ULg

in Revue PIANC (2002)

L’article identifie en profondeur les facteurs déterminants, et l’ampleur de leur influence, relatifs à une utilisation plus intensive du mode de transport fluvial et au concept de développement durable ... [more ▼]

L’article identifie en profondeur les facteurs déterminants, et l’ampleur de leur influence, relatifs à une utilisation plus intensive du mode de transport fluvial et au concept de développement durable. Il est donc important de comprendre quelles sont les barrières qui empêchent le glissement de marchandises de la route vers la voie d’eau sur le réseau belge où des conditions spécifiques économiques, administratives, organisationnelles, politiques et d’infrastructure existent. Il est aussi fondamental d’être attentif aux facteurs relatifs à la capacité du mode fluvial à s’intégrer dans des chaînes de transport intermodales. L’article se subdivise en trois parties, à savoir : - possibilités de glissement de marchandises sur les corridors fluviaux belges. - obstacles au glissement. - conditions préalables au glissement; exigences nécessaires pour une pleine intégration de la navigation intérieure dans les chaînes intermodales de transport; proposition de mesures concrètes. [less ▲]

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See detailRegulation by reactive oxygen species of pro-inflammatory genes in chondrocytes
Henrotin, Yves ULg; Mathy, Marianne ULg; Sanchez, Christelle ULg et al

in Osteoarthritis and Cartilage (2002), 10(Suppl A), 34

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See detailUsing the OST index to identify women at risk of osteoporosis : a validation study in Belgium
Ben Sedrine, Wafa ULg; Reginster, Jean-Yves ULg

in Osteoporosis International (2002), 13(S1), 109-110

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See detailEnhanced Platelet Reactivity to Collagen and Shear Stress in Transgenic Mice Overexpressing the Platelet P2X1 Ion Channel
Oury, Cécile ULg; Kuijpers, Marijke; Toth-Zsamboki, Emese et al

in Blood (2002), 100

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See detailMetabolic stress as a paradigm to elucidate genotype-environment interaction in psychosis
Marcelis, Machteld; Cavalier, Etienne ULg; Gielen, Jacques et al

in Acta Psychiatrica Scandinavica (2002), 105(Suppl. 411), 91

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See detailIncreased platelet reactivity to collagen in transgenic mice overexpressing the P2X1 ion channel.
Oury, Cécile ULg; Kuijpers, marijke; Toth-Zsamboki, Emese et al

in Haematologica (2002), 87

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See detailCD40 engagement enhances eosinophil survival through induction of cellular inhibitor of apoptosis protein 2 expression: possible involvement in allergic inflammation
Bureau, Fabrice ULg; Seumois, G.; Jaspar, F. et al

in Pflügers Archiv : European Journal of Physiology (2002), 443

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See detailNF-kB activity, and IL-8 and GM-CSF expression, in the milk of chorionic mastitis-affected cows
Boulanger, Delphine; Bureau, Fabrice ULg; Lekeux, Pierre ULg

in Pflügers Archiv : European Journal of Physiology (2002), 443

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See detailComparison between three therapeutic strategies in the bovine respiratory disease complex
Boutet, Philippe ULg; Coghe, J.; Borceux, J. P. et al

in Pflügers Archiv : European Journal of Physiology (2002), 443

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See detailCorrelation between exercise parameters and oxidant markers in horses
Kirschvink, Nathalie; Art, Tatiana ULg; De Moffarts, Brieux et al

in Pflügers Archiv : European Journal of Physiology (2002), 443

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See detailArterial revascularization therapy study: a randomized trial of stenting in multivessel coronary disease versus bypass surgery. 3 year results
Legrand, Victor ULg; Serruys, P. W. S.; Bilocleau, L. et al

in European Heart Journal (2002), 23(Suppl. S), 263-263

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See detailFDG-PET imaging for monitoring rheumatoid arthritis treated by infliximab injections.
BECKERS, Catherine ULg; RIBBENS, Clio ULg; ANDRE, Béatrice ULg et al

in Journal of Nuclear Medicine (The) (2002), 43

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See detail18F-fluoro-L-tyrosine : a potential tracer for whole-body tumor imaging with PET.
HUSTINX, Roland ULg; LEMAIRE, C.; JERUSALEM, Guy ULg et al

in Journal of Nuclear Medicine (The) (2002), 43

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See detailEffects of BM-573, a dual thromboxane A(2) receptor antagonist and thromboxane synthase inhibitor, on osteogenic sarcoma cell-induced platelet aggregation
de Leval, X.; David, Jean-Louis ULg; Neven, P. et al

in Blood (2001, November 16), 98(11, Part 2), 43

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See detailAlkaline phosphatase positive reticular cell network recovery after radiation-induced marrow aplasia in mice
Almohamad, K.; Thiry, Anne-Marie ULg; Boniver, Jacques ULg et al

in Blood (2001, November 16), 98(11, Part 2), 141

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See detailHST Observations of Aurora from the Magnetic Footprints of Io, Ganymede, and Europa during the Millennium Campaign
Clarke, J. T.; Grodent, Denis ULg; Connerney, J. et al

in Bulletin of the American Astronomical Society (2001, November 01)

UV images of Jupiter's aurora obtained with the HST STIS instrument reveal much detail in the distribution of emissions from Io's magnetic footprint on Jupiter, including extended trails of emission in ... [more ▼]

UV images of Jupiter's aurora obtained with the HST STIS instrument reveal much detail in the distribution of emissions from Io's magnetic footprint on Jupiter, including extended trails of emission in the downstream direction. Emissions are also seen from the magnetic footprints of Ganymede and Europa, relatively much fainter and point-like in spatial extent. Knowledge of the statistical properties of these emissions, in terms of their locations and brightnesses, was greatly advanced in a comprehensive series of images obtained during the Millennium campaign in Dec. 2000 - Jan. 2001. These images provide sufficient spatial coverage to give a good indication of the auroral oval locations mapping to Io and Ganymede, and a few points mapping to Europa. The observed variations in footprint properties provide indications of the nature of the electrodynamic interactions of the satellites with Jupiter's magnetic field. These and other indicators also show the direction that magnetic field models should take to better describe Jupiter's internal magnetic field. Contributing evidence comes from the locus of footprint latitudes, and their deviations from the VIP4 model. The latitudinal distance between the Io and Ganymede footprint loci indicates variations in the local field strength, with larger separations corresponding to a weaker field. These separations, and the distance from and distortion of the main oval, indicate an anomalously weak field region in the north near 90[SUP]o[/SUP] longitude. This work has been supported by NASA in STScI grants GO-08171-97A and GO-08657-01A to the University of Michigan. [less ▲]

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See detailSpatial and temporal variations of the Jovian auroral electrons deduced from HST-STIS ultraviolet spectroscopy
Gérard, Jean-Claude ULg; Gustin, Jacques ULg; Grodent, Denis ULg et al

in Bulletin of the American Astronomical Society (2001, November 01)

Jovian auroral spectra have been observed with the Space Telescope Imaging Spectrometer (STIS) in both hemispheres since 1997, including during the recent Cassini Jupiter millenium campaign. The time ... [more ▼]

Jovian auroral spectra have been observed with the Space Telescope Imaging Spectrometer (STIS) in both hemispheres since 1997, including during the recent Cassini Jupiter millenium campaign. The time-tagged G140L STIS spectra used for this study cover the 1100-1700 Ì· range which includes the Lyman (B-X) bands and continuum and the Werner (C-X) bands. Time-dependent spectroscopy with spatial resolution along the 25 arcsec slit makes it possible to follow spectral and temporal variations in different regions of the aurora. FUV images observed on the same HST orbit were obtained to put the spectral data into the global morphology context. Synchronous observations of spectral domains absorbed or not by CH4 and other hydrocarbons are used to determine the FUV color ratio and the depth of the auroral emission relative to the methane homopause. Large variations of the color ratio across the auroral oval are observed. The time evolution of the mean electron energy and its possible correlation with the precipitated energy flux are investigated. It is found that the mean electron energy generally positively correlates with the auroral brightness. In contrast, flares occasionally observed in the polar cap can correspond to a softening or a hardening of the precipitation. The mean electron energy associated with the Io trail is approximately constant and shows less hydrocarbon absorption than the higher latitude aurora. [less ▲]

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See detailDevelopment of a flow cytometry method for the characterization of yeast cells surface hydrophobicity
Aguedo, Mario ULg; Waché, Y.; Sequeira-Le Grand, A. et al

in Morphologie : Bulletin de l'Association des Anatomistes (2001, October), 85(270), 30

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See detailA Stable and Flexible TCP-friendly congestion control protocol for layered multicast transmission
El Khayat, Ibtissam; Leduc, Guy ULg

in Lecture Notes in Computer Science (2001, September 04), 2158

We propose an improvement of our RLS (Receiver-driven Layered multicast with Synchronization points) protocol, called CIFL for “Coding-Independent Fair Layered mulaticast”, along two axes. In CIFL, each ... [more ▼]

We propose an improvement of our RLS (Receiver-driven Layered multicast with Synchronization points) protocol, called CIFL for “Coding-Independent Fair Layered mulaticast”, along two axes. In CIFL, each receiver of a layered multicast transmission will try and find the adequate number of layers to subscribe to, so that the associated throughput is fair towards TCP and stable in steady-state. The first improvement is that CIFL is not specific to any coding scheme. It can work as well with an exponentially distributed set of layers (where the throughput of each layer i equals the sum of the throughputs of all layers below i), or with layers of equal throughputs, or any other scheme. The second improvement is the excellent stability of the protocol which avoids useless join attempts by learning from its unsuccessful previous attempts in the same (or better) network conditions. Moreover, the protocol tries and reaches its ideal TCP-friendly as soon as possible by computing its target throughput in a clever way when an incipient congestion is confirmed. [less ▲]

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See detailUse of fluorescent polyethylene glycols (PEGs) to assess intestinal permeability in vitro
Loret, S; Pirson, L; Nollevaux, G et al

in Pflügers Archiv : European Journal of Physiology (2001, September)

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See detailSoup 'n Old Clothes : The Arts of Frank Zappa and Captain Beefheart
Delville, Michel ULg

in Oficina de poesia : Revista de palavra e da imagem (2001, May 29)

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See detailFurther exploration of the mere exposure effect in Alzheimer's disease
Willems, Sylvie ULg; Adam, Stéphane ULg; Van der Linden, Martial et al

in Journal of Cognitive Neuroscience (2001, March 25), Suppl. 58

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See detailLes pénétrations percutanées de fluides projetés sous pression
Beaujean, M.; Thiry, A.; RADERMECKER, Régis ULg

in Journal des Maladies Vasculaires (2001, March), 26(Suppl 1), 153

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See detailOne year experience of the Belgian Liver Intestine Comittee (BLIC) intranet database
Lerut, Jan; Roggen, F.; De Hemptinne, Bernard et al

in Acta Gastro-Enterologica Belgica (2001, January), 64(1), 7

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See detailRadiofrequency ablation of liver tumors: short term evaluation
Detry, Olivier ULg; Detroz, Bernard ULg; Preud'Homme, Laurence ULg et al

in Acta Gastro-Enterologica Belgica (2001, January), 64(1), 11

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See detail120 laparoscopic sigmoidectomies in diverticulitis: a 9 years experience
Detroz, Bernard ULg; Moscato; Detry, Olivier ULg et al

in Acta Gastro-Enterologica Belgica (2001, January), 64(1), 49

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See detailLiver transplantation in Jehovah's witnesses
Detry, Olivier ULg; Honoré, Pierre ULg; De Roover, Arnaud ULg et al

in Acta Gastro-Enterologica Belgica (2001, January), 64(1), 53

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See detailStricturoplasty in Crohn disease: short and long term follow up
Laurent, Stanislas; Detry, Olivier ULg; Detroz, Bernard ULg et al

in Acta Gastro-Enterologica Belgica (2001, January), 64(1), 73

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See detailIntraperitoneal hyperthermic chemotherapy (IPHC) for treatment of peritoneal carcinomatosis
Detroz, Bernard ULg; Marchettini, P.; Joris, Jean ULg et al

in Acta Gastro-Enterologica Belgica (2001, January), 64(1), 80

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See detailDevelopment of routine RT-PCR ELOSA tests for fruit tree certification.
Kummert, Jean; Vendrame, Marina; Lepoivre, Philippe ULg et al

in Acta Horticulturae (2001), (550 (Vol. 1)),

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See detailConstructing Automata from Temporal Logic Formulas: A Tutorial
Wolper, Pierre ULg

in Lecture Notes in Computer Science (2001), 2090

This paper presents a tutorial introduction to the construction of finite-automata on infinite words from linear-time temporal logic formulas. After defining the source and target formalisms, it describes ... [more ▼]

This paper presents a tutorial introduction to the construction of finite-automata on infinite words from linear-time temporal logic formulas. After defining the source and target formalisms, it describes a first construction whose correctness is quite direct to establish, but whose behavior is always equal to the worst-case upper bound. It then turns to the techniques that can be used to improve this algorithm in order to obtain the quite effective algorithms that are now in use. [less ▲]

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See detailMagnetic properties of melt-textured DyBCO single domains
Vanderbemden, Philippe ULg; Ausloos, Marcel ULg; Cloots, Rudi ULg

in Materials Research Society Symposium Proceedings (2001), 659

This communication aims at reporting the superconducting properties of several bulk melt-processed DyBa2Cu3O7-x samples determined by using various measuring techniques. The original single domain ... [more ▼]

This communication aims at reporting the superconducting properties of several bulk melt-processed DyBa2Cu3O7-x samples determined by using various measuring techniques. The original single domain material was first cut into 9 similar cubic samples which have been characterized by AC susceptibility, flux profiles and DC magnetization. The results indicate good quality melt-processed (RE)BCO materials with Tc = 89 K. Next, the effect of post oxygen annealing treatments on these samples was studied. The influence of the non-uniformity of the oxygen content on the magnetic property anisotropy is discussed. Finally, additional magnetic measurements were carried out by using a couple of parallel pick-up coils wound on the same sample. From the results we conclude that geometric effects have to be taken into account in order to extract the critical current density from the magnetic properties. [less ▲]

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See detailA model for assessing water chemistry by using aquatic bryophyte assemblages in north-eastern France
Vanderpoorten, Alain ULg; Thiébaut, G.; Trémolières, M. et al

in Verhandlungen der Internationalen Vereinigung für Theoretische und Angewandte Limnologie = Proceedings of the International Association of Theoretical and Applied Limnology (2001), 27

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See detailSustained fracture benefit with five years of risedronate in postmenopausal women
Hosking, D; Sorensen, OD; Mulder, H et al

in BONE (2001), S28

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See detailEfficacy of risedronate in decreasing the incidence of femoral neck and intertrochanteric fractures in older women with osteoporosis
Eastell, R; McClung, MR; Reginster, Jean-Yves ULg et al

in Journal of Bone and Mineral Research (2001), 16(S1), 219

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See detailDioxin Body Burden of Populations Living in the Vicinity of Two Municipal Solid Waste Incinerators (MSWI) in Belgium
Fierens, S.; mairesse, H.; Focant, Jean-François ULg et al

in Organohalogen Compounds (2001), 52

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See detailLevels and Profile of PCDD/Fs and cPCBs in Belgian Breast Milk
Focant, Jean-François ULg; Pirard, C.; Andre, J.-E. et al

in Organohalogen Compounds (2001), 52

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See detailAn improved Clean-up Strategy for Simultaneous Analysis of PCDDs, PCDFs, and PCBs in Biological Samples.
Pirard, C.; Focant, Jean-François ULg; Eppe, Gauthier ULg et al

in Organohalogen Compounds (2001), 50

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See detailTowards Biological or Physico-chemical Screening for Dioxins?
Focant, Jean-François ULg; De Pauw, Edwin ULg

in Organohalogen compounds (2001), 50

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See detailComparison of PCDD/Fs and cPCBs levels in commercial pasteurized cow's milk in Wallonia (Belgium)
Focant, Jean-François ULg; Pirard, C.; Andre, J.-E. et al

in Organohalogen Compounds (2001), 51

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See detailExtraction and Clean-Up of Milk Samples for PCDD/Fs and cPCBs Analysis
Focant, Jean-François ULg; De Pauw, Edwin ULg

in Organohalogen Compounds (2001), 50

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See detailPTV-LV Injection Coupled to Capillary GC Ion Trap MS/MS as Alternative Method for PCDD/Fs Analysis in Foods.
Eppe, Gauthier ULg; Focant, Jean-François ULg; Pirard, C. et al

in Organohalogen compounds (2001), 50

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See detailEnantioselective synthesis of 2-[18F]fluoro-L-Tyrosine by catalytic phase-transfer alkylation.
Lemaire, Christian ULg; Gillet, S.; Ooi, T. et al

in Journal of Labelled Compounds & Radiopharmaceuticals (2001), 44

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See detailEvaluation of classical NSAIDS and COX-2 selective inhibitors on purified ovine enzymes and human whole blood
de Leval, X; Dogne, JM; Delarge, J et al

in Clinical Rheumatology (2001), 20

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See detailTi deposits in anorthosite; geochemical constraints on the economic value
Duchesne, Jean-Clair; Vander Auwera, Jacqueline ULg

in Proceedings of the Biennial SGA Meeting (2001), 6

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See detail"Acomyinae": new molecular evidences for a muroid taxon (Rodentia : Muridae)
Chevret, P.; Catzeflis, F.; Michaux, Johan ULg

in African Small Mammals (2001)

The taxonomic position of the spiny mouse (genus Acomys) within the Murinae (Rodentia) was first challenged by the immunological data of SARICH (1985). Subsequent molecular data have also excluded Acomys ... [more ▼]

The taxonomic position of the spiny mouse (genus Acomys) within the Murinae (Rodentia) was first challenged by the immunological data of SARICH (1985). Subsequent molecular data have also excluded Acomys from the murine rodents, in association with two murine genera (Uranomys and Lophuromys) and a "dendromurine" Deomys; this group was designed as "Acomyinae". We present here complementary DNA/DNA hybridization results, mitochondrial gene sequences (12S rRNA) and nuclear gene sequences (LCAT), which confirm the existence of an "Acomyine" clade, that comprises Acomys, Uranomys, Lophuromys and Deomys. But there is still no morphological synapomorphy that can define this group. We also evidenced that the Murinae, Gerbillinae and Acomyinae are sister groups but we were not able to decipher their relationships. [less ▲]

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See detailEthanol-induced brain extracellular taurine release: an osmoregulatory mechanism?
Quertemont, Etienne ULg; Devitgh, Audrey; De witte, Philippe

in Alcohol & Alcoholism (2001), 36

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See detailImplications of acetaldehyde in ethanol reinforcing and discriminative effects
Quertemont, Etienne ULg; Rios, Ananda; Macias, Enrique et al

in Alcohol & Alcoholism (2001), 36

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See detailEthanol-induced taurine release in rats genetically selected for ethanol preference and sensitivity
Quertemont, Etienne ULg; Colombo, Giancarlo; De Witte, Philippe

in Alcohol & Alcoholism (2001), 36

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See detailResearch on hydrodynamics of inland navigation at the University of Liège
Marchal, Jean ULg; Shen, Yide ULg

in Research on hydrodynamics of inland navigation at the University of Liège (2001)

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See detailNeurochemical and behavioral effects of ethnaol-conditioned stimuli: implication for alcohol consumption
Quertemont, Etienne ULg; De Witte, Philippe

in Cahiers de l'I.R.E.B. (2001), 15

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See detailCounting the Solutions of Presburger Equations without Enumerating Them
Boigelot, Bernard ULg; Latour, Louis

in Lecture Notes in Computer Science (2001), 2494

The Number Decision Diagram (NDD) has recently been proposed as a powerful representation system for sets of integer vectors. In particular, NDDs can be used for representing the sets of solutions of ... [more ▼]

The Number Decision Diagram (NDD) has recently been proposed as a powerful representation system for sets of integer vectors. In particular, NDDs can be used for representing the sets of solutions of arbitrary Presburger formulas, or the set of reachable states of some systems using unbounded integer variables. In this paper, we address the problem of counting the number of distinct elements in a set of vectors represented as an NDD. We give an algorithm that is able to perform an exact count without enumerating explicitly the vectors, which makes it capable of handling very large sets. As an auxiliary result, we also develop an efficient projection method that allows to construct efficiently NDDs from quantified formulas, and thus makes it possible to apply our counting technique to sets specified by formulas. Our algorithms have been implemented in the verification tool LASH, and applied successfully to various counting problems. [less ▲]

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