In this paper, we present a simple, yet effective, attention and memory mechanism that is reminiscent of Memory Networks and we demonstrate it in question-answering scenarios. Our mechanism is based on four simple premises: a) memories can be formed from word sequences by using convolutional networks; b) distance measurements can be taken at a neuronal level; c) a recursive softmax function can...

This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization find superconductor minimizes a certain cost functional under given target on electric field over specific domain interest. For governing PDE-model, we consider elliptic curl-curl variational inequality (VI) second kind with L1-type nonlin...

The classical Trudinger-Moser inequality says that for functions with Dirichlet norm smaller or equal to 1 in the Sobolev space H 0 (Ω) (with Ω ⊂ R a bounded domain), the integral ∫ Ω e 2 dx is uniformly bounded by a constant depending only on Ω. If the volume |Ω| becomes unbounded then this bound tends to infinity, and hence the Trudinger-Moser inequality is not available for such domains (and...

Throughout this paper, we assume that X is a uniformly convex Banach space and X∗ is the dual space of X. Let J denote the normalized duality mapping form X into 2 ∗ given by J x {f ∈ X∗ : 〈x, f〉 ‖x‖2 ‖f‖2} for all x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. It is well known that if X is uniformly smooth, then J is single valued and is norm to norm uniformly continuous on any b...

We address the Mach limit problem for Euler equations in analytic spaces. prove that, given data, solutions to compressible are uniformly bounded a suitable norm and then show that convergence toward incompressible solution holds norm. also same results hold more generally Gevrey data with norms.

We study the asymptotic behavior, at small viscosity ε, of the NavierStokes equations in a 2D curved domain. The Navier-Stokes equations are supplemented with the slip boundary condition, which is a special case of the Navier friction boundary condition where the friction coefficient is equal to two times the curvature on the boundary. We construct an artificial function, which is called a corr...

We introduce an iterative algorithm for finding a common minimum norm fixed point of a finite family of asymptotically nonextensive nonself mappings. A strong convergence theorem of common element is established in a uniformly smooth and uniformly convex Banach space. Mathematics Subject Classification: 47H09; 47H05

We give examples of finite time blowup in sup-norm and total variation for 3 × 3systems of strictly hyperbolic conservation laws. The exact solutions are explicitly constructed. In the case of sup-norm blowup we also provide an example where all other p-norms, 1 ≤ p < ∞, remain uniformly bounded. Finally we consider appropriate rescalings for the different types of blowup.

We study the connection between uniformly convex functions f : X → R bounded above by ‖ · ‖p, and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X → R bounded above by ‖ · ‖2 if and only if X admits an equivalent norm with modulus of convexity of power type 2.

If a normalized Kähler-Ricci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M , dimC M = n ≥ 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.