It is necessary and sufficient condition that there exist formal power series H ( t ) = ∑ n = 0 ∞ h n t n + 1, h 0 ≠ 0, and A i ( t ) = ∑ n = 0 ∞ a n ( i ) t n ( not all a 0 ( i ) are zero ).
A diglossia or dichotomy also exists between formal literary varieties and spoken varieties.
Up to 400 worshippers, including a good sprinkling of the wealthy youngsters who are busy gentrifying the nearby wharfs and warehouses, attend its main Sunday service: numbers have doubled in the last three years or so, in a sign that a market exists for formal singing and well-turned sermons.
In summary, unless a perceived balance of power between interlocutors exists, more formal language will tend to be used.
In this sense, there exists a formal adjointness star operation such that X ∗ = X, R ∗ = q − 1 L = q − 1 R − 1, L ∗ = q R. (34).
there exists a formal power series A ( t ) = ∑ n = 0 ∞ a n t n ( a 0 ≠ 0 ) such that A ( t ) exp ( x t ) = ∑ n = 0 ∞ P n ( x ) t n.
Similarly, Aghion et al. (2010) suggest how countries with higher levels of trust require lower levels of regulation, arguing, therefore, that a link exists between formal institutional development and the level of trust.
Fortunately, Yirong Liu and Jibin Li [21] found that there always exists a formal inverse integrating factor for three-order nilpotent critical points in 2009, and they gave a new definition of the focal values under the generalized triangle polar coordinates and the method of commuting Lyapunov constants using the inverse integral factors for the three-order nilpotent critical point.
Then there exists a formal power series (hat{G} epsilon)inmathbb {F}[!![epsilon]!!]) which is the common q-Gevrey asymptotic expansion of order (1/k) of the functions (G_{p} epsilon)) on (mathcal{E}_{p}), which is common for all (0le plevarsigma-1).
Moreover, while the premise that this is how pneumonia starts in humans is logical, there exists no formal proof.
