In this paper, we prove a monotonicity formula on cigar soliton. Using the monotonicity, obtain three-ball type theorem. There might be some people who have proved theorem Cigar Soliton before, but use new method. We add weight function in norm of u. By doing so, make calculation process much easier because when using integral by part, term that integrates at surface ball would disappear as zero.

In many application areas of machine learning, prior knowledge concerning the monotonicity of relations between the response variable and predictor variables is readily available. Monotonicity may also be an important model requirement with a view toward explaining and justifying decisions, such as acceptance/rejection decisions. We propose a modified nearest neighbour algorithm for the constru...

One of the main problems of interval computations is to compute the range of a given function over given intervals. In general, this problem is computationally intractable (NP-hard) – that is why we usually compute an enclosure and not the exact range. However, there are cases when it is possible to feasibly compute the exact range; one of these cases is when the function is monotonic with resp...

We consider a variant of monotone simultaneous embeddings (MSEs) of directed graphs where all graphs are directed paths and have distinct directions of monotonicity. In contrast to the known result that any two directed paths admit an MSE, there exist examples of three paths that do not admit such an embedding for any possible choice of directions of monotonicity. We prove that if an MSE of thr...