1. Terminology. V and M will be differentiable manifolds of dimension n and m respectively; differentiable meaning always of class C. For simplicity, we assume V compact and without boundary. We shall have to consider several categories of maps: (1) the category of continuous maps, (2) the category of topological imbeddings, (3) the category of topological immersions: a map ƒ: F—>M is a topolog...

We describe a new spatio-temporal video autoencoder, based on a classic spatial image autoencoder and a novel nested temporal autoencoder. The temporal encoder is represented by a differentiable visual memory composed of convolutional long short-term memory (LSTM) cells that integrate changes over time. Here we target motion changes and use as temporal decoder a robust optical flow prediction m...

Marshal Ash [3] introduced the concept of (σ, τ) differentiable functions and studied the Riemann generalized derivatives In this article we study the convexity and monotonicity of (σ, τ) differentiable functions, using results by Hincin, Humke and Laczkovich, and using the Riemann generalized derivative. We give conditions such that the classic properties of differentiable functions hold also ...

2. , Functions differentiable on the boundaries of regions, Ann. of Math. vol. 35 (1934) pp. 482-fôS. 3. , Differentiable manifolds, Ann. of Math. vol. 37 (1936) pp. 645-680. 4. f Differentiable functions defined in arbitrary subsets of Euclidean space, Trans. Amer. Math. Soc. vol. 40 (1936) pp. 309-317. Further references are given here. 5. H. O. Hirschfeld, Continuation of differentiable func...

As we shall see later, Thomae’s function is not differentiable on the irrationals. In this note, we address whether there is a modification of Thomae’s function which is differentiable on a subset of the irrationals. In Section 2, we prove that Thomae’s function is not differentiable on the irrationals and define modified versions of Thomae’s function. In Section 3, we show that for each of our...