Derived equivalence classification of the cluster-tilted algebras of Dynkin type E

We obtain a complete derived equivalence classification of the cluster-tilted algebras of Dynkin type E. There are 67, 416, 1574 algebras in types E6, E7 and E8 which turn out to fall into 6, 14, 15 derived equivalence classes, respectively. This classification can be achieved computationally and we outline an algorithm which has been implemented to carry out this task. We also make the classification explicit by giving standard forms for each derived equivalence class as well as complete lists of the algebras contained in each class; as these lists are quite long they are provided as supplementary material to this paper. From a structural point of view the remarkable outcome of our classification is that two cluster-tilted algebras of Dynkin type E are derived equivalent if and only if their Cartan matrices represent equivalent bilinear forms over the integers which in turn happens if and only if the two algebras are connected by a sequence of "good" mutations. This is reminiscent of the derived equivalence classification of cluster-tilted algebras of Dynkin type A, but quite different from the situation in Dynkin type D where a far-reaching classification has been obtained using similar methods as in the present paper but some very subtle questions are still open.Comment: 19 pages. v4: completely rewritten version, to appear in Algebr. Represent. Theory. v3: Main theorem strengthened by including "good" mutations (cf. also arXiv:1001.4765). Minor editorial changes. v2: Third author added. Major revision. All questions left open in the earlier version by the first two authors are now settled in v2 and the derived equivalence classification is completed. arXiv admin note: some text overlap with arXiv:1012.466

Obstructing mucocele of the cystic duct after transplantation of the liver

A tension mucocele was created in three hepatic homografts by ligating a low-lying cystic duct during transplant cholecystectomy and by incorporating its outflow end into the anastomosis of the common hepatic duct to the recipient common duct or Roux limb of jejunum. The consequent complication of obstruction of the biliary tract that necessitated reoperation and excision of the mucocele in all three patients can be avoided by the simple expedient of completely removing the cystic duct when feasible or providing egress to the secretion of the cystic duct as described

Rigid and Schurian modules over cluster-tilted algebras of tame type

We give an example of a cluster-tilted algebra Λ with quiver Q, such that the associated cluster algebra A(Q) has a denominator vector which is not the dimension vector of any indecomposable Λ-module. This answers a question posed by T. Nakanishi. The relevant example is a cluster-tilted algebra associated with a tame hereditary algebra. We show that for such a cluster-tilted algebra Λ, we can write any denominator vector as a sum of the dimension vectors of at most three indecomposable rigid Λ-modules. In order to do this it is necessary, and of independent interest, to first classify the indecomposable rigid Λ-modules in this case

Effects of glucagon-like peptide-I on glucose turnover in rats

The influences of glucagon-like peptide-I-(7-36) amide (GLP-I; 15 pmol . kg(-1). min(-1)) on glucose turnover were studied in freely moving Wistar rats. In fed rats, GLP-I reduced plasma glucose (from 7.3 +/- 0.2 to 5.6 +/- 0.3 mmol/l; P = 0.017), increased plasma insulin (from 20 +/- 3 to 89 +/- 11 mU/l; P = 0.002), and reduced plasma glucagon (from 44 +/- 1 to 35 +/- 2 pg/ml; P = 0.009) and glucose appearance rate (R(a); from 3.9 1 0.2 to 1.7 +/- 0.7 mu mol . min(-1). 100 g(-1) after 30 min; P = 0.049) without affecting glucose disappearance rate (R(d)). The glucose clearance rate (MCR) was increased (P = 0.048). In 48-h-fasted rats, GLP-I reduced plasma glucose (from 5.0 +/- 0.2 to 4.4 +/- 0.3 mmol/l; P = 0.035) and increased plasma insulin (from 4 +/- 1 to 25 +/- 10 mU/l; P = 0.042) and plasma glucagon (from 43 +/- 3 to 61 +/- 7 pg/ml; P = 0.046). R(a) and R(d) were not significantly affected, although R(a) was lower than R(d) after 15-30 min (P = 0.005) and MCR was increased (P = 0.049). Thus GLP-I reduces R(a) in fed rats and increases MCR in fed and fasted rats. The reduced R(a) seems mediated by an increased insulin-to-glucagon ratio; the increased glucose clearance seems dependent on insulin and a peripheral effect of GLP-I

Betavoltaics using scandium tritide and contact potential difference

Tritium-powered betavoltaic micropower sources using contact potential difference (CPD) are demonstrated. Thermally stable scandium tritide thin films with a surface activity of 15 mCi cm2 were used as the beta particle source. The electrical field created by the work function difference between the ScT film and a platinum or copper electrode was used to separate the beta-generated electrical charge carriers. Open circuit voltages of 0.5 and 0.16 V and short circuit current densities of 2.7 and 5.3 nA cm2 were achieved for gaseous and solid dielectric media-based CPD cells, respectively. © 2008 American Institute of Physics

TBA for non-perturbative moduli spaces

Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton contributions turn out to have the form of Thermodynamic Bethe Ansatz. We explore further this relation and, in particular, we identify the contact potential of quaternionic string moduli space with the free energy of the integrable system and the Kahler potential of the gauge theory moduli space with the Yang-Yang functional. We also show that the corresponding S-matrix satisfies all usual constraints of 2d integrable models, including crossing and bootstrap, and derive the associated Y-system. Surprisingly, in the simplest case the Y-system is described by the MacMahon function relevant for crystal melting and topological strings.Comment: 25 pages, 1 figur

Effet de l’âge et de l’intensité de pâture sur le développement des touffes et la production de biomasse de Panicum maximum var. C1 dans les pâturages artificiels en zone soudanienne et subéquatoriale

L'objectif de l’étude est d’évaluer l’effet du mode d’exploitation sur le développement des organes de régénération des graminées vivaces et leur productivité dans les pâturages artificiels des fermes d’élevage de Kpinnou, de Samiondji et de l’Okpara au Bénin. Les données ont été collectées sur les trois fermes au pic de biomasse au cours du mois d'octobre. Les mesures de densité de touffes et de la surface des plateaux de tallage ainsi que la récolte de biomasse ont été réalisées dans 27 parcelles de Panicum maximum var. C1 âgées de 2 ans, 5 ans et 10 ans en prenant en compte les parcelles fauchées, les parcelles moyennement pâturées et les parcelles fortement pâturées. Les résultats ont montré que le nombre moyen de touffes par m² est plus élevé pour tous les pâturages en condition de surpâturage qu’en condition de non pâture. La moyenne était de 15,68 touffes.m-2 dans les zones surpâturées contre 6,00 touffes.m-2 dans les zones fauchées. La densité moyenne des touffes dans les pâturages en condition de pâture moyenne était de 8,76 touffes.m-2. La surface des plateaux de tallage et la production de biomasse ont évolué inversement à la densité des touffes, en fonction de l’âge et de l’intensité de pâture. La surface moyenne couverte par les plateaux de tallage en condition de fauche était 336,29 cm2.m-2 contre 219,61 cm2.m-2 en condition de surpâture. La surface moyenne couverte au sol dans les zones d'exploitation moyenne était de 251,97 cm2.m-2. Ceci confirme que la pâture a des impacts très évidents sur les pâturages artificiels exploités par le bétail.Mots clés : Groupements végétaux artificiels, pâture, plateaux de tallage, densité de touffes

Valeur pastorale des parcours naturels en zone soudano-guinéenne et stratégie paysanne d’adaptation aux effets de leur invasion par Chromolaena odorata au Bénin

Cette étude sur les pâturages naturels envahis par Chromolaena odorata a été réalisée dans la zone de transition guinéo-congolaise/soudanaise du Bénin. L’objectif de l’étude est d’analyser les connaissances endogènes, les paramètres biologique et agronomique pouvant permettre de déterminer l’effet de l’invasion de C. odorata sur le potentiel pastoral. Les valeurs du coefficient de similitude de Jaccard (<50%), montre que lespâturages aux différents stades d’invasion ne sont pas similaires. La richesse spécifique est plus élevée au niveau des pâturages aux stades 1 et 2 d’invasion. La phytomasse des graminées a varié de 0,37 à 5,62 t MS/ha. Elle est plus élevée dans les pâturages au stade 1 d’invasion. La valeur pastorale (1,12 à 56,9) et la capacité de charge (0,00 à 0,83 kg MS/ha) diminuent avec l’intensité d’invasion par C. odorata. Les éleveurs disposent des connaissances endogènes sur la biologie de C. odorata et adaptent des stratégies d’élevage. Les critères de choix des espaces à pâturer sont par ordre de classification: les graminées consommées sans hésitation, les graminées consommées occasionnellement, le volume et l'accessibilité aux ressources fourragères. Le niveau d’invasion peuvent servir d’indicateurs essentiels de la qualité fourragère des parcours envahis en l’absence de toute analyse bromatologique

Quantum Sine(h)-Gordon Model and Classical Integrable Equations

We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\ \re^{-2\eta}=0$with$p(z)=z^{2\alpha}-s^{2\alpha}$. We show that certain connection coefficients for solutions of the associated linear problem coincide with the$Q$-function of the quantum sine-Gordon$(\alpha>0)$or sinh-Gordon$(\alpha<-1)$ models.Comment: 35 pages, 3 figure