The self-similar gravitational collapse solutions to the Einstein-axion-dilaton system have already been found out. Those become invariants after combining spacetime dilation with transformations of internal SL(2, R). We apply nonlinear statistical models estimate functions that appear in physics Black Holes axion-dilaton four dimensions. These include polynomial regression, nonparametric kerne...

This paper presents a complete pipeline for learning continuous motion control policies for a mobile robot when only a non-differentiable physics simulator of robot-terrain interactions is available. The multi-modal state estimation of the robot is also complex and difficult to simulate, so we simultaneously learn a generative model which refines simulator outputs. We propose a coarse-to-fine l...

∆u = ∂2u ∂x1 + ∂2u ∂x2 where x = (x1, x2) ∈ IR 2 are Cartesian coordinates. Even though the Poisson equation looks very special it is an important model case representing several problems from physics based on energy minimisation. Variations of the techniques we will study apply to a wide class of second order so-called elliptic problems. It is known that there are cases where no classical (i.e...

The problem is from mesoscopic physics: let p : Σ → R3 be an embedded surface in R3, we assume that (1) Σ is orientable, complete, but non-compact; (2) Σ is not totally geodesic; (3) Σ is asymptotically flat in the sense that the second fundamental form goes to zero at infinity. On can build a quantum layer Ω over such a surface Σ as follows: as a differentiable manifold, Ω = Σ × [−a, a] for so...

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...

In this paper, within the scope of local fractional derivative theory, bidirectional propagation system equations are researched. Compared with unidirectional nonlinear waves in a pipeline, studied paper can better describe channel. This study is groundbreaking and offers more possibilities for simulation pipeline. The exact traveling wave solutions non-differentiable type defined on Cantor set...

Fractional calculus and applications have application areas in many different fields such as physics, chemistry, engineering well mathematics. The of arithmetic carried out classical analysis fractional is very important terms obtaining more realistic results the solution problems. In this study, we prove an identity involving generalized integrals by using differentiable functions. By utilizin...

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 ...