It is known that the solutions of pure classical 5D gravity with AdS 5 asymptotics can describe strongly coupled large N dynamics in a universal sector of 4D conformal gauge theories. We show that when the boundary metric is flat we can uniquely specify the solution by the boundary stress tensor. We also show that in the Fefferman-Graham coordinates all these solutions have an integer Taylor se...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

We use boundary quantum group symmetry to obtain recursion formulas which determine nondiagonal solutions of the boundary Yang-Baxter equation (reflection equation) of the XXZ type for any spin j. Department of Mathematics, University of York, York YO10 5DD, U.K. Physics Department, P.O. Box 248046, University of Miami, Coral Gables, FL 33124 USA

We present an explicit solution of the Ar T -system for arbitrary boundary conditions. For each boundary, this is done by constructing a network, i.e. a graph with positively weighted edges, and the solution is expressed as the partition function for a family of non-intersecting paths on the network. This proves in particular the positive Laurent property, namely that the solutions are all Laur...

We consider the Navier–Stokes system in a bounded domain with a smooth boundary. Given a time-dependent solution and an arbitrary open subset of the boundary, we prove the existence of a boundary control, supported in the given subset, that drives the system to the given solution in finite time.

We propose a simple mathematical definition and new neural architecture for finding anomalies within discrete sequence datasets. Our model comprises of a modified LSTM autoencoder and an array of One-Class SVMs. The LSTM takes in elements from a sequence and creates context vectors that are used to predict the probability distribution of the following element. These context vectors are then use...

In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the logarithmic stability estimate for the hyperbolic equations without any assumption on an observation sub-boundary.

The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the d-dimensional torus (Z/nZ) for any d ≥ 1. The proof used the symmetric structure of the torus and monotonicity in an essential way. Here we enhance the framework and extend it to general geom...