BACKGROUND Core outcome sets can increase the efficiency and value of research and, as a result, there are an increasing number of studies looking to develop core outcome sets (COS). However, the credibility of a COS depends on both the use of sound methodology in its development and clear and transparent reporting of the processes adopted. To date there is no reporting guideline for reporting ...

Dual-specificity thyrosine phosphorylation-regulated kinase 1A (DYRK1A) is a strong therapeutic target to ameliorate cognitive functions of Down Syndrome (DS). Genetic normalization of Dyrk1a is sufficient to normalize early cortical developmental phenotypes in DS mouse models. Gyrencephalic human neocortical development is more complex than that in lissencephalic mice; hence, cerebral organoid...

In this paper, we prove that for x ∈ (0,π/2) (cos p1x) 1/(3p1) < sinx x < (cos p0x) 1/(3p0) < · · · < e−x/6 < 2+ cos x

People can reach all kinds of information online including reviews and comments on products, movies, holiday destinations and so on. However, one usually need to go through the reviews to have an objective opinion the positive and the negative aspects of the item reviewed. We aim to provide a method that will extract positive and negative opinions on a specific aspect and compare them in an att...

Background A core outcome set (COS) is a minimal set of outcomes to be reported in a trial. Development is often challenging because patients and clinicians identify many important outcomes and prioritisation is difficult. Delphi surveys (with several rounds) are one approach for prioritising outcomes. Summarised participant responses are provided in subsequent ‘rounds’, allowing initial respon...

The well-known Hadamard method of descent [2, 3] consists of deriving solutions of wave equations in n variables from (known) solutions in more than n variables. To quote Hadamard, (the method) “consists in noticing that he who can do more can do less”. It is the purpose of this paper to exhibit cases in which he who can do less can do more — that sometimes one can build the propagator cos (√ A...

Abstract For any Liouville number $\alpha $ , all of the following are transcendental numbers: ${e}^\alpha $\log _{e}\alpha $\sin \alpha $\cos $\tan $\sinh $\cosh $\tanh $\arcsin and inverse functions evaluated at listed trigonometric hyperbolic functions, noting that wherever multiple values involved, every such value is transcendental. This remains true if ‘Liouville number’ replaced by ‘ U -...

Soil is a major contributor to the biosphere–atmosphere exchange of carbonyl sulfide (COS) and carbon monoxide (CO). COS is [..1 ]a tracer to quantify terrestrial photosynthesis based on the [..2 ]coupled leaf uptake of COS and [..3 ]CO2, but [..4 ]such use requires separating soil COS flux[..5 ], which is unrelated to photosynthesis, from ecosystem COS uptake. For CO, soil is a [..6 ]significa...