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Chain Event Graphs are probabilistic graphical models designed especially for the analysis of discrete statistical problems which do not admit a natural product space structure.
It is well-known that π2-sectorial operators generally do not admit a bounded H∞ calculus over the right half-plane.
Finally, using a framework developed by Bodlaender et al. (2009) and Fortnow and Santhanam (2011), based upon the notion of compositionality, we show that the tractable cases do not admit a polynomial kernel unless NP⊆coNP∕poly, even restricted to instances without or-vertices with out-degree greater than two.
Unfortunately, matrices that minimize Equation 21, and hence optimize the cutoff rate, do not admit a closed form solution.
The isothermal Lane-Emden equations [8 11] also have strictly nonoscillatory solutions because they do not admit a trivial solution.
The polytropic equations with negative integer values of n and the isothermal Lane-Emden equations [8 11] do not admit a trivial solution, therefore their solutions are all nonoscillatory.
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Subspaces that permit a dual with this transpose do not admit an interior point.
We prove similar results for uniform spectral multipliers of second order elliptic differential operators in divergence form on Rd belonging to a wide class, which contains L. From these results we deduce that operators in this class do not admit an H∞ functional calculus in sectors smaller than Sφp∗.
We also show that this function does not admit a conjugate function.
We show that C X, C) does not admit a shift operator for certain special compact Hausdorff spaces X.
The Riemann initial data are hyperbolic and correspond to a Lax 1-shock that does not admit a viscous profile.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com