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Titlebook: Handbook of Atomization and Sprays; Theory and Applicati Nasser Ashgriz Book 2011 Springer Science + Business Media, LLC 2011 Laser Doppler

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Countable ModelsAgain we fix an irrational α between zero and one. Since the random graphs .(., .) with .= .. satisfy the Zero-One Law of our Main Theorem 1.4.1 the set .. of sentences that hold almost always form a complete theory. Here we examine an axiomatization of .. and its countable models.
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Discrete (,) Boundary Value ProblemsIn this chapter we shall present discrete analogs of the results established in Chapter 13 for the difference equation (18.1) satisfying the (.) boundary conditions
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The Janson InequalityThe Janson Inequality is a relatively recent result that has proven to be very useful in the study of random graphs. We begin with a general (though hardly the most general) formulation. An important and instructive example of its application is given after the statement of the Inequality.
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Generation PropertiesIn this chapter we continue to study the connection between semigroups and their generators. We characterize generators by the properties of their resolvents. As an important byproduct, we derive a characterization of positive semigroups by the positivity of the resolvent. This is a fundamental result and will be frequently used in the sequel.
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