For a harmonic map $u : M^3 \to S^1$ on closed, oriented $3$-manifold, we establish the identity \[ 2 \pi \int_{\theta \in S^1} \chi (\Sigma _\theta) \geq \frac{1}{2} \int_{\Sigma_\theta} \left( {\lvert du \rvert}^{-2} \mathit{Hess} (u) \rvert}^2 + R_M \right) \] relating scalar curvature $R_M$ of $M$ to average Euler characteristic level sets $\Sigma_\theta = u^{-1} {\lbrace \theta \rbrace}$. ...

in this paper, some categorical properties of the category ${bf cpo}_{{bf act}text{-}s}$ of all {cpo $s$-acts}, cpo's equipped with actions of a monoid $s$ on them, and strict continuous action-preserving maps between them is considered. in particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. also, we show that the forgetful functor from...

In recent years, there has been significant uptake of meditation and related relaxation techniques, as a means of alleviating stress and fostering an attentive mind. Several electroencephalogram (EEG) studies have reported changes in spectral band frequencies during Qigong meditation indicating a relaxed state. Much less is reported on effects of brain activation patterns induced by Qigong tech...

 In this paper, we consider a flexible skew-generalized normal distribution. This distribution is denoted by $FSGN(/lambda _1, /lambda _2 /theta)$. It contains the normal, skew-normal (Azzalini, 1985), skew generalized normal (Arellano-Valle et al., 2004) and skew flexible-normal (Gomez et al., 2011) distributions as special cases. Some important properties of this distribution are establi...

For a $d$-dimensional random vector $X$, let $p_{n, X}(\theta)$ be the probability that convex hull of $n$ independent copies $X$ contains given point $\theta$. We provide several sharp inequalities regarding and $N_X(\theta)$ denoting smallest for which X}(\theta)\ge1/2$. As main result, we derive totally general inequality $1/2 \le \alpha_X(\theta)N_X(\theta)\le 3d + 1$, where $\alpha_X(\thet...