" Wir mssen wissen, wir werden wissen " (We must know, we shall know) Pr[Y ≥ ∆] = Pr[exp(tY) ≥ exp(t∆)] ≤ E [exp(tY)] exp(t∆) , the first part follows by the fact that exp(·) preserve ordering, and the second part follows by the Markov inequality. Observe that E [exp(tX i)] = 1 2 e t + 1 2 e −t = e t + e −t 2 = 1 2 1 + t 1! + t 2 2! + t 3 3! + · · · + 1 2 1 − t 1! + t 2 2! − t 3 3! + · · · = 1 ...

We present an enhancement of exp(ASP), a system that generates explanation graphs for literal l - atom or its default negation ~a given answer set A normal logic program P, which explain why is true (or false) and P. The new system, exp(ASPc), differs from exp(ASP) in it supports choice rules utilizes constraint to provide include information about choices constraints.

four in vitro experiments (exp.) were conducted to evaluate lavender essential oil (leo) effects at 0 (control), 250 (low dose), 500 (medium dose), 750 and 1000 µl per l(high doses) of incubation medium on rumen gas production kinetics (exp.1), ruminal digestibility and fermentation (exp.2), methane production (exp.3) and rumen acidosis (exp.4). the asymptote of gas production (a) increased qua...

for entire functions, the notions of their growth indicators such as ritt order are classical in complex analysis. but the concepts of relative ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. therefore the studies of the growths of entire functions in the light of thei...

In this article we give strong versions for preparation theorems $\mathbb{R}_{\textnormal{an,exp}}$-definable functions outgoing from methods of Lion and Rolin ($\mathbb{R}_{\textnormal{an,exp}}$ is the o-minimal structure generated by all restricted analytic global exponential function). By a deep model theoretic fact Van den Dries, Macintyre Marker every function piecewise given $\mathcal{L}_...

We study the algebra of semigroups Laplacians on Weyl algebra. consider first-order partial differential operators $\nabla^\pm_i$ forming Lie $[\nabla^\pm_j,\nabla^\pm_k]= i\mathcal{R}^\pm_{jk}$ and $[\nabla^+_j,\nabla^-_k] =i\frac{1}{2}(\mathcal{R}^+_{jk}+\mathcal{R}^-_{jk})$ with some anti-symmetric matrices $\mathcal{R}^\pm_{ij}$ define corresponding $\Delta_\pm=g_\pm^{ij}\nabla^\pm_i\nabla^...