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^...

Age and growth of marbled sole Pleuronectes yokohamae werer estimated from growth increments in otolith. The samples were collected with commercial set nets and an experimental bottom trawl net in Kikonai Bay and the nearby waters, southern coast of Hokkaido, from May 1994 to July 1995. Monthly changes in the percentage occurrence of oltoliths with translucent edge in one band and the marginal ...

‎the aim of this paper is to study the convergence of solutions of the‎ ‎following second order difference inclusion‎ ‎begin{equation*}begin{cases}exp^{-1}_{u_i}u_{i+1}+theta_i exp^{-1}_{u_i}u_{i-1} in c_ia(u_i),quad igeqslant 1 u_0=xin m‎, ‎quad‎ ‎underset{igeqslant 0}{sup} d(u_i,x)

Holstein calves, 10 steers (98 +/- 16 kg; Exp. 1) and 14 heifers (122 +/- 7 kg; Exp. 2), were fed either corn-cottonseed hull basal diets (CON; 15.1 and 13.2% CP, respectively) or CON plus 370 micrograms/kg of Cr as Cr-tripicolinate (CrP). After either 58 (Exp. 1) or 56 (Exp. 2) days of ADG and DMI measurement, calves were individually fed 1.4% of their BW every 12 h through the end of each exp...

f, g ∈ L(E) where E is a k vector space of dimension d. We introduce the relation (*): exp(t.f + g) = exp(t.f) ◦ exp(g) for any t ∈ k or N; we study the connections between the relations () and f ◦g = g◦f for d = 2 or 3. Let d = 2: if k = R and if (*) is verified for t ∈ N then f ◦g = g◦f ; we obtain all the couples f , g verifying (*) on C and such as f ◦g 6= g◦f . Our main result is: if d = 3...