Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence

This paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients.The work of the first and third authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEstOE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Polynomials over quaternions and coquaternions: a unified approach

This paper aims to present, in a unified manner, results which are valid on both the algebras of quaternions and coquaternions and, simultaneously, call the attention to the main differences between these two algebras. The rings of one-sided polynomials over each of these algebras are studied and some important differences in what concerns the structure of the set of their zeros are remarked. Examples illustrating this different behavior of the zero-sets of quaternionic and coquaternionic polynomials are also presented.(undefined)info:eu-repo/semantics/publishedVersio

Evaluation schemes in the ring of quaternionic polynomials

In this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.Research at CMAT was financed by Portuguese Funds through FCT - Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC’s (Fundação para a Ciência e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on “Competitiveness and Internationalization - COMPETE 2020” under the PT2020 Partnership Agreement.info:eu-repo/semantics/publishedVersio

Microbiome assembly of avian eggshells and their potential as transgenerational carriers of maternal microbiota

The microbiome is essential for development, health and homeostasis throughout an animal's life. Yet, the origins and transmission processes governing animal microbiomes remain elusive for non-human vertebrates, oviparous vertebrates in particular. Eggs may function as transgenerational carriers of the maternal microbiome, warranting characterisation of egg microbiome assembly. Here, we investigated maternal and environmental contributions to avian eggshell microbiota in wild passerine birds: woodlark Lullula arborea and skylark Alauda arvensis. Using 16S rRNA gene sequencing, we demonstrated in both lark species, at the population and within-nest levels, that bacterial communities of freshly laid eggs were distinct from the female cloacal microbiome. Instead, soil-borne bacteria appeared to thrive on freshly laid eggs, and eggshell microbiota composition strongly resembled maternal skin, body feather and nest material communities, sources in direct contact with laid eggs. Finally, phylogenetic structure analysis and microbial source tracking underscored species sorting from directly contacting sources rather than in vivo-transferred symbionts. The female-egg-nest system allowed an integrative assessment of avian egg microbiome assembly, revealing mixed modes of symbiont acquisition not previously documented for vertebrate eggs. Our findings illuminated egg microbiome origins, which suggested a limited potential of eggshells for transgenerational transmission, encouraging further investigation of eggshell microbiome functions in vertebrates

Significance of glycolytic metabolism-related protein expression in colorectal cancer, lymph node and hepatic metastasis

Background: Colorectal cancer (CRC) is one of the most common malignancies and a leading cause of cancer death worldwide. Most cancer cells display high rates of glycolysis with production of lactic acid, which is then exported to the microenvironment by monocarboxylate transporters (MCTs). The main aim of this study was to evaluate the significance of MCT expression in a comprehensive series of primary CRC cases, lymph node and hepatic metastasis. Methods: Expressions of MCT1, MCT4, CD147 and GLUT1 were studied in human samples of CRC, lymph node and hepatic metastasis, by immunohistochemistry. Results: All proteins were overexpressed in primary CRC, lymph node and hepatic metastasis, when compared with non-neoplastic tissue, with exception of MCT1 in lymph node and hepatic metastasis. MCT1 and MCT4 expressions were associated with CD147 and GLUT1 in primary CRC. These markers were associated with clinical pathological features, reflecting the putative role of these metabolism-related proteins in the CRC setting. Conclusion: These findings provide additional evidence for the pivotal role of MCTs in CRC maintenance and progression, and support the use of MCTs as biomarkers and potential therapeutic targets in primary and metastatic CRC.This work was supported by the Fundação para a Ciência e a Tecnologia (FCT) grant ref. PTDC/SAU-FCF/104347/2008, under the scope of ‘Programa Operacional Temático Factores de Competitividade’ (COMPETE) of ‘Quadro Comunitário de Apoio III’ and co-financed by the Fundo Europeu De Desenvolvimento Regional (FEDER). Ricardo Amorim was recipient of the fellowship SFRH/BD/98002/2013, from Fundação para a Ciência e a Tecnologia (FCT Portugal).info:eu-repo/semantics/publishedVersio

On the roots of coquaternions

In this paper we give a complete characterization of the nth roots of a coquaternion q. In particular, we show that the number and type of roots-isolated and/or hyperboloidal-depend on the nature of q, on the parity of n and (eventually) on the sign of the real part of q. We also show how the coquaternionic formalism can be used to obtain, in a simple manner, explicit expressions for the real nth roots of any 2 x 2 real matrix.Research at CMAT was financed by Portuguese Funds through FCT - Fundacao para a Ciencia e a Tecnologia, within the Project UID/MAT/00013/2013. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC's (Fundacao para a Ciencia e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on "Competitiveness and Internationalization-COMPETE 2020" under the PT2020 Partnership Agreement.info:eu-repo/semantics/publishedVersio

Comparação do equilíbrio postural estático entre sujeitos saudavéis e lombálgicos Comparison of static postural balance between healthy subjects and those with low back pain

OBJETIVO: Comparar o equilíbrio postural estático entre portadoras de lombalgia crônica e indivíduos saudáveis, através do deslocamento do centro de pressão. MÉTODOS: Participaram do estudo 15 mulheres com lombalgia (Grupo lombalgia) e 15 mulheres saudáveis (Grupo saudável). Elas foram orientadas a permanecer em posição ortostática sobre a plataforma de força durante 30 segundos. Foram analisadas a área e a velocidade de deslocamento do centro de pressão de ambos os grupos. A análise dos dados foi realizada através do Teste t de Student, com significância de 5%. RESULTADOS: Os indivíduos com lombalgia crônica apresentaram maior área de deslocamento do centro de pressão em relação aos saudáveis, porém não houve diferença significativa em relação à velocidade de deslocamento do centro de pressão. CONCLUSÃO: Indivíduos com lombalgia crônica apresentam alteração do equilíbrio estático em relação a saudáveis. Nível de evidência III, Estudos Prognósticos.<br>OBJECTIVE: To compare the static postural balance between women suffering from chronic low back pain and healthy subjects, by moving the center of pressure. METHODS: The study included 15 women with low back pain (LBP group) and 15 healthy women (healthy group). They were instructed to remain in standing on the force platform for 30 seconds. We analyzed the area and the speed of displacement of center of pressure of both groups. Data analysis was performed using the Student t-test, with significance of 5%. RESULTS: Individuals with chronic low back pain showed a larger area of displacement of the center of pressure relative to the healthy ones but there was no significant difference in the speed of displacement of the center of pressure. CONCLUSION: Individuals with chronic low back pain had alterations in static balance with respect to healthy ones. Level of Evidence III, Prognostic Studies