The Multiple-partners Assignment Game with Heterogeneous Sells and Multi-unit Demands: Competitive Equilibria

A multiple-partners assignment game with heterogeneous sells and multi-unit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by only using linear programming. We show that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all equilibrium assignments, and vice versa. We also show that the set of (restricted) equilibrium price vectors has a natural lattice structure and we study how this structure is translated into the set of agents' utilities that are attainable at equilibrium.Matching, Assignment Game, Indivisible Goods, Competitive Equilibrium, Lattice

Gallai-Edmonds decomposition of unicyclic graphs from null space

In this paper, we compute the Gallai-Edmonds decomposition of a unicyclic graph G using linear algebraic tools. More precisely, the Gallai-Edmonds decomposition of G is obtained from the null space associated with adjacency matrices of its subtrees

Independence and matching numbers of unicyclic graphs from null space

We characterize unicyclic graphs that are singular using the support of the null space of their pendant trees. From this, we obtain closed formulas for the independence and matching numbers of a unicyclic graph, based on the support of its subtrees. These formulas allows one to compute independence and matching numbers of unicyclic graphs using linear algebra methods

Independence and Matching Numbers of Unicyclic Graphs From Null Space

We characterize unicyclic graphs that are singular using the support of the null space of their pendant trees. From this, we obtain closed formulas for the independence and matching numbers of a unicyclic graph, based on the support of its subtrees. These formulas allows one to compute independence and matching numbers of unicyclic graphs using linear algebra methods

Development of Polylactic Acid Thermoplastic Starch Formulations Using Maleinized Hemp Oil as Biobased Plasticizer

[EN] In this study, hemp seed oil was reacted with maleic anhydride in an ene reaction to obtain maleinized hemp seed oil (MHO). The use of MHO as a plasticizer and compatibilizer has been studied for polylactic acid (PLA) and thermoplastic starch (TPS) blends (80/20, respectively). By mechanical, thermal and morphological characterizations, the addition of MHO provides a dual effect, acting as plasticizer and compatibilizer between these two partially miscible biopolymers. The addition of MHO up to 7.5 phr (parts by weight of MHO per hundred parts of PLA and TPS) revealed a noticeable increase in the ductile properties, reaching an elongation at break 155% higher than the PLA/TPS blend. Furthermore, contrary to what has been observed with maleinized oils such as linseed oil, the thermal properties do not decrease significantly as a result of the plasticizing effect, due to the compatibilizing behavior of the MHO and the natural antioxidants present in the oil. Finally, a disintegration test was carried out in aerobic conditions at 58 degrees C, for 24 days, to demonstrate that the incorporation of the MHO, although causing a slight delay, does not impair the biodegradability of the blend, obtaining total degradation in 24 days.M. Herrero-Herrero wishes to thank Ministerio de Economia y Competitividad for his grant, BES-2016-078024. J. Gomez-Caturla wish to thank Universitat Politecnica de Valencia for his FPI grant.Lerma-Canto, A.; Gómez-Caturla, J.; Herrero-Herrero, M.; Garcia-Garcia, D.; Fombuena, V. (2021). Development of Polylactic Acid Thermoplastic Starch Formulations Using Maleinized Hemp Oil as Biobased Plasticizer. Polymers. 13(9):1-17. https://doi.org/10.3390/polym13091392S11713

Alkaloids Analysis of Habranthus cardenasianus (Amaryllidaceae), Anti-Cholinesterase Activity and Biomass Production by Propagation Strategies

Plants in the Amaryllidaceae family synthesize a diversity of bioactive alkaloids. Some of these plant species are not abundant and have a low natural multiplication rate. The aims of this work were the alkaloids analysis of a Habranthus cardenasianus bulbs extract, the evaluation of its inhibitory activity against cholinesterases, and to test several propagation strategies for biomass production. Eleven compounds were characterized by GC-MS in the alkaloid extract, which showed a relatively high proportion of tazettine. The known alkaloids tazettine, haemanthamine, and the epimer mixture haemanthidine/6-epi-haemanthidine were isolated and identified by spectroscopic methods. Inhibitory cholinesterases activity was not detected. Three forms of propagation were performed: bulb propagation from seed, cut-induced bulb division, and micropropagated bulbs. Finally, different imbibition and post-collection times were evaluated in seed germination assays. The best propagation method was cut-induced bulb division with longitudinal cuts into quarters (T1) while the best conditions for seed germination were 0-day of post-collection and two days of imbibition. The alkaloids analyses of the H. cardenasianus bulbs showed that they are a source of anti-tumoral alkaloids, especially pretazettine (tazettine) and T1 is a sustainable strategy for its propagation and domestication to produce bioactive alkaloids.Fil: Zaragoza Puchol, José Daniel. Universidad Nacional de San Juan; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; ArgentinaFil: Ortiz, Javier Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan; ArgentinaFil: Orden, Alejandro Agustin. Universidad Nacional de San Luis; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Investigaciones en Tecnología Química. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Instituto de Investigaciones en Tecnología Química; ArgentinaFil: Sánchez, Marianela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Palermo, Jorge Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Tapia, Aníbal Alejandro. Universidad Nacional de San Juan; ArgentinaFil: Bastida, Jaume. Universidad de Barcelona. Facultad de Farmacia; EspañaFil: Feresin, Gabriela Egly. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan; Argentin

Alkaloids Analysis of Habranthus cardenasianus (Amaryllidaceae), Anti-Cholinesterase Activity and Biomass Production by Propagation Strategies

Plants in the Amaryllidaceae family synthesize a diversity of bioactive alkaloids. Some of these plant species are not abundant and have a low natural multiplication rate. The aims of this work were the alkaloids analysis of a Habranthus cardenasianus bulbs extract, the evaluation of its inhibitory activity against cholinesterases, and to test several propagation strategies for biomass production. Eleven compounds were characterized by GC-MS in the alkaloid extract, which showed a relatively high proportion of tazettine. The known alkaloids tazettine, haemanthamine, and the epimer mixture haemanthidine/6-epi-haemanthidine were isolated and identified by spectroscopic methods. Inhibitory cholinesterases activity was not detected. Three forms of propagation were performed: bulb propagation from seed, cut-induced bulb division, and micropropagated bulbs. Finally, different imbibition and post-collection times were evaluated in seed germination assays. The best propagation method was cut-induced bulb division with longitudinal cuts into quarters (T1) while the best conditions for seed germination were 0-day of post-collection and two days of imbibition. The alkaloids analyses of the H. cardenasianus bulbs showed that they are a source of anti-tumoral alkaloids, especially pretazettine (tazettine) and T1 is a sustainable strategy for its propagation and domestication to produce bioactive alkaloids. Keywords: Amaryllidaceae; bioactive alkaloids; GC-MS; propagation methods; biomass productio

The Multiple-partners assignment game with heterogeneous sales and multi-unit demands : competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium

Some Results for the (Signless) Laplacian Resolvent

The recently introduced concept of resolvent energy of a graph [6,7] is based on the adjacency matrix. We now consider the analogous resolvent energies based on the Laplacian and signless Laplacian matrices, and determine some of their basic properties.Fil: Cafure, Antonio Artemio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Universidad de Buenos Aires. Ciclo Básico Común; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Jaume, Daniel Alejandro. Universidad Nacional de San Luis. Facultad de Ciencias Físico- Matemáticas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis; ArgentinaFil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pastine, Adrián Gabriel. Michigan Technological University; Estados UnidosFil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; BrasilFil: Gutman, Ivan. University Of Kragujevac; Serbia. State University of Novi Pazar; Serbi