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ON DIFFERENTIAL STRUCTURES OF POLYNOMIAL SPACES IN CONTROL THEORY

Journal of Systems Science and Systems Engineering 2012年第3期21卷 372-382页

作者： Baltazar Aguirre HERNANDEZ martn eduardo frias-armenta Fernando VERDUZCO Depto.de Matematicas Universidad Autonoma Metropolitana-lztapalapa.Av.Sn.Rafael Atlixco no.186.Col.Vicentinalztapalapa 09340MexicoD.F. Depto.de Matematicas Universidad de Sonora.Blvd.Luis Encinas y Rosales s/n.Col.CentroHermosilloSonoraMexico.

A valuable number of works has been published about Hurwitz and Schur polynomials in order to known better their properties. For example it is known that the sets of Hurwitz and Schur polynomials are open and no convex sets. Besides, the set of monic Schur polynomials is contractible. Now we study this set using ideas from differential topology, and we prove that the space of Schur complex polynomials with positive leading coefficient, and the space of Hurwitz complex polynomials which leading coefficient having positive real part, have structure of trivial vector bundle, and each space of （Schur complex and real, Hurwitz complex） polynomials has a differential structure diffeomorphic to some known spaces.

关键词： Schur polynomials Hurwitz complex polynomials trivial vector bundle

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Regeneration of critical-sized defects, in a goat model, using a dextrin-based hydrogel associated with granular synthetic bone substitute

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Regenerative Biomaterials 2021年第1期8卷 73-82页

作者： Isabel Pereira Jose eduardo Pereira Luis Maltez Alexandra Rodrigues Catarina Rodrigues Manuela Oliveira Dina MSilva Ana Rita Caseiro Justina Prada Ana Colette Mauricio Jose Domingos Santos Miguel Gama CEB Centre of Biological EngineeingUniversity of MinhoCampus de GualtarBraga 4710-057Portugal CECAV Animal and Veterinary Research CentreUniversity of Trias-os-Montes e Alto DouroVila Real 5001-801Portugal Department of Veterinary Sciences University of Tras-os-Montes e Alto DouroVila Real 5001-801Portugal Bios ckin Molecular and Cell Therapies S.A.Laboratorio CriovidaTecMaiaRua Engenheiro Frederico Ulrich 2650Moreira da Maia 4470-605Portugal Departamento de Clinicas Veterinarias Instituto de Ciencias Biomedicas de Abel Salazar(ICBAS)Universidade do Porto(UP)Rua de Jorge Viterbo Ferreiran°228Porto 4050-313Portugal Centro de Estudos de Ciencia Animal(CECA) Instituto de CienciasTecnologias e Agroambiente da Universidade do Porto(ICETA)Rua D.Manuel IApartado 55142Porto 4051-401 Portugal Centro de Investigaqao Vasco da Gama(CIVG)/Escola Universitaria Vasco da Gama(EUVG) Avenida Jose R.Sousa Femandesn°197 LordemaoCoimbra 3020-210Portugal REQUIMTE/LAQV Departamento de Engenharia Metalurgica e MateriaisFaculdade de EngenhariaUniversidade do PortoRua Dr Roberto FriasPorto 4200-495Portugal

The development of injectable bone substitutes(IBS)have obtained great importance in the bone re-generation field,as a strategy to reach hardly accessible defects using minimally invasive techniques and able to fit to irregular topographies.In this scenario,the association of injectable hydrogels and bone graft granules is emerging as a well-established trend.Particularly,in situ forming hydrogels have arisen as a new IBS generation.An in situ forming and injectable dextrin-based hydrogel(HG)was developed,aiming to act as a carrier of granular bone substitutes and bioactive agents.In this work,the HG was associated to a granular bone substitute(Bonelike)and implanted in goat critical-sized calvarial defects(14mm)for 3,6 and 12weeks.The results showed that HG improved the han-dling properties of the Bonelike granules and did not affect its osteoconductive features,neither impairing the bone regener ation process.Human multipotent mesenchymal stromal cells from the umbilical cord,extracellular matrix hydrolysates and the pro-angiogenic peptide LLKKK18 were also combined with the IBS.These bioactive agents did not enhance the new bone formation significantly under the conditions tested,according to micro-computed tomography and histological analysis.

关键词： polysaccharide injec table hydrogel granular ceramics Bonelike' bone regen eration calvarial defect

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