In this note, we prove the following inequality for norm N(K) of a convex body K in $$\mathbb {R}^n$$ , $$n\ge 2$$ : $$\begin{aligned} \le \frac{\pi ^{\frac{n-1}{2}}}{2 \Gamma \left( \frac{n+1}{2}\right) }\cdot {{\,\mathrm{length}\,}}(\gamma ) + ^{\frac{n}{2}-1}}{\Gamma \frac{n}{2}\right) } \cdot {{\,\mathrm{diam}\,}}(K), \end{aligned}$$ where $${{\,\mathrm{diam}\,}}(K)$$ is diameter K, $$\gamm...

Due to its constantly growing incidence, obesity is an increasingly serious social and medical problem. Available data on the use of novel oral anticoagulants in morbidly obese and obese patients are very limited. However, we tried to summarize the available knowledge on the use of anticoagulants in this subpopulation of patients in everyday clinical practice. Studies on the clinical use of ant...

OBJECTIVE To evaluate the current and ideal body weight perceptions of schoolchildren in relation to their actual body weight and socio-economic status (SES). DESIGN Baseline evaluation of schoolchildren from January 2008 to April 2008 as part of a 3-year longitudinal study. SETTING City and non-city locations, Karnataka State, South India. SUBJECTS Schoolchildren (n 1877) aged between 8 ...

Although the burgeoning discipline of welfare economics is based on essentially utilititarian principles, the foundations of utilitarianism have received little attention in recent years. This paper seeks to reopen the debate by drawing a distinction between Harsanyi’s two defences of utilitarianism, labeling the first a teleological or ideal-observer theory, and the second a nonteleological th...

Let $\mathfrak{g}$ be an algebra over $K$ with a bilinear operation $[\cdot,\cdot]:\mathfrak{g}\times\mathfrak{g}\rightarrow\mathfrak{g}$ not necessarily associative. For $A\subseteq\mathfrak{g}$, let $A^{k}$ the set of elements written combining $k$ $A$ via $+$ and $[\cdot,\cdot]$. We show "sum-bracket theorem" for simple Lie algebras form $\mathfrak{g}=\mathfrak{sl}_{n},\mathfrak{so}_{n},\mat...

In the present work, chemotaxis-Naiver-Stokes system with rapidly decaying diffusivities \begin{document}$ \begin{eqnarray*} { \bf{(KSNS)} }\ \ \left\{ \begin{array}{llll} n_{t}+u\cdot\nabla n = \nabla\cdot(D(n)\nabla n)-\nabla\cdot(S(n)\nabla c), &&x\in\Omega, \, t>0, \\ c_{t}+u\cdot\nabla c \Delta - c+ n, u_{t}+\kappa(u\cdot\nabla)u u +\nabla P+ n\nabla\Phi, \nabla\cdot 0, t>0\ ...