Failure of Thiocyanate to Influence The Flux of Sodium Through The Isolated Frog Gastric Mucosa

Isolated stomachs from mammals showed substantial active absorption of sodium (Am.J. Dig. Dis. 14:221-238, 1969) in contrast to isolated frog gastric mucosa. Could the difference have been due to a micro-environment in the latter preparation based on fine structure features that maintained high H-ion concentration at the site of active transport? To answer this, H-ion secretion was inhibited in frog gastric mucosa with 15 mM thiocyanate. Unidirectional fluxes of sodium were not materially affected. These results cast doubt on a possible depression of active sodium absorption by a high H-ion concentration in the microenvironment of the isolated amphibian mucosa

The ball in play demands of international rugby union

Objectives: Rugby union is a high intensity intermittent sport, typically analysed via set time periods or rolling average methods. This study reports the demands of international rugby union via global positioning system (GPS) metrics expressed as mean ball in play (BiP), maximum BiP (max BiP), and whole match outputs. Design: Single cohort cross sectional study involving 22 international players, categorised as forwards and backs. Methods: A total of 88 GPS files from eight international test matches were collected during 2016. An Opta sportscode timeline was integrated into the GPS software to split the data into BiP periods. Metres per min (m.min-1), high metabolic load per min (HML), accelerations per min (Acc), high speed running per min (HSR), and collisions per min (Coll) were expressed relative to BiP periods and over the whole match (>60min). Results: Whole match metrics were significantly lower than all BiP metrics (p < 0.001). Mean and max BiP HML, (p < 0.01) and HSR (p < 0.05) were significantly higher for backs versus forwards, whereas Coll were significantly higher for forwards (p < 0.001). In plays lasting 61s or greater, max BiP m.min-1 were higher for backs. Max BiP m.min-1, HML, HSR and Coll were all time dependant (p < 0.05) showing that both movement metrics and collision demands differ as length of play continues. Conclusions: This study uses a novel method of accurately assessing the BiP demands of rugby union. It also reports typical and maximal demands of international rugby union that can be used by practitioners and scientists to target training of worst-case scenario's equivalent to international intensity. Backs covered greater distances at higher speeds and demonstrated higher HML, in general play as well as 'worst case scenarios'; conversely forwards perform a higher number of collisions

The doubly negative matrix completion problem

An $n\times n$ matrix over the field of real numbers is a doubly negative matrix if it is symmetric, negative definite and entry-wise negative. In this paper, we are interested in the doubly negative matrix completion problem, that is when does a partial matrix have a doubly negative matrix completion. In general, we cannot guarantee the existence of such a completion. In this paper, we prove that every partial doubly negative matrix whose associated graph is a $p$-chordal graph $G$ has a doubly negative matrix completion if and only if $p=1$. Furthermore, the question of completability of partial doubly negative matrices whose associated graphs are cycles is addressed.Spanish DGI - BFM2001-0081-C03-02.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI)

Algebraic inversion of the Dirac equation for the vector potential in the non-abelian case

We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell-Dirac equations, we set up the formalism for non-abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series.Comment: 21pp, uses iopar