We prove a variation of Gronwall’s lemma. The formulation and proof of the classical Gronwall’s lemma can be found in [1]. We prove here a variation of this lemma, which we were not able to find in the literature. Lemma 1 Let g : [0,∞[→ R be a continuous function, λ > 0 and C ≥ 0. Assume that ∀u, t 0 ≤ u ≤ t g(t)− g(u) ≤ − ∫ t

We present a robust Farkas lemma, which provides a new generalization of the celebrated Farkas lemma for linear inequality systems to uncertain conical linear systems. We also characterize the robust Farkas lemma in terms of a generalized characteristic cone. As an application of the robust Farkas lemma we establish a characterization of uncertainty-immunized solutions of conical linear program...

This article proves a lemma which shows that two empirical processes will be uniformly close if they are evaluated with a small time lag. A new feature of our lemma is that we allow the empirical processes to be functionally weighted (by fi(t), see Lemma 2). A third lemma for functionally weighted empirical process is also included. AMS 1991 Subject Classification: Primary 62G10. Secondary 62P1...

There are various pumping lemmata for context free languages, the strongest of which is Ogden’s Lemma. It is known that it does not fully characterize context free languages. In an attempt to remedy the situation, Manaster– Ramer, Moshier and Zeitman have strengthened this lemma. As we shall show here, there exist non–semilinear languages that satisfy this stronger lemma and also the lesser kno...

Recently we have developed a new method in graph theory based on the Regularity Lemma. The method is applied to find certain spanning subgraphs in dense graphs. The other main general tool of the method, beside the Regularity Lemma, is the so-called Blow-up Lemma ([24]). This lemma helps to find bounded degree spanning subgraphs in ε-regular graphs. Our original proof of the lemma is not algori...