In this paper we consider the (ray) representations of group $\mathrm{Aut}$ biholomorphisms Siegel upper half-space $\mathcal U$ defined by $U_s(\varphi) f=(f\circ \varphi^{-1}) (J \varphi^{-1})^{s/2}$, $s\in\mathbb R$, and characterize semi-Hilbert spaces $H$ holomorphic functions on satisfying following assumptions: (a) is strongly decent; (b) $U_s$ induces a bounded ray representation $\math...

The well known analytical formula for $SU(2)$ matrices $U = \exp(i \vec \tau \!\cdot\! \varphi\,) \cos|\vec \varphi\,| + i\vec \hat\varphi \, \sin|\vec \varphi\,|$\\ is extended to the $SU(3)$ group with eight real parameters. resulting involves sum over three roots of a cubic equation, corresponding so-called irreducible case, where one has employ trisection an angle. When going special unitar...

We present an analytical proof that certain natural metric universal covers are Hadamard spaces. If $$\rho \,\mathrm{{d}}s$$ induces a complete distance d on plane domain $$\Omega $$ , and =\varphi \circ u$$ where u is (locally Lipschitz and) subharmonic in $$\varphi positive increasing interval containing $$u(\Omega )$$ with $$\log \varphi convex, then $$(\Omega ,d)$$ has cover $$({\tilde{\Ome...

We classify seven-dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left-invariant purely coclosed G2-structures. This is done by going through the list all algebras given Gong, providing an example a 3-form φ which pure G2-structure (i.e., it satisfies d ∗ = 0 $d*\varphi =0$ , ∧ $\varphi \wedge d\varphi ) for those that admit them; and showing impossi...

The Chern-Simons amended gravity theory appears as a low-energy effective of string theory. includes an anomaly-cancelation correction to the Einstein-Hilbert action. expression consists product $\varphi R \tilde $ Pontryagin density $R with scalar field $\varphi$, where latter is considered background (dynamical construction or non-dynamical construction). Many different solutions Einstein's g...

The standard approach to risk-averse control is use the exponential utility (EU) functional, which has been studied for several decades. Like other functionals, EU encodes risk aversion through an increasing convex mapping $\varphi$ o...