The Benjamin Ono equation with a slowly varying potential is $$ \text{(pBO)} \qquad u_t + (Hu_x-Vu \tfrac12 u^2)_x=0 $V(x)=W(hx)$, $0 0$ are parameters. For initial condition $u_0(x)$ to (pBO) close $Q_{0,1}(x)$, it was shown in previous work by Z. Zhang that the solution $u(x,t)$ remains $Q_{a(t),c(t)}(x)$ and approximate parameter dynamics for $(a,c)$ were provided, on dynamically relevant ti...

A new algorithm for learning invariance manifolds is introduced that allows a neuron to learn a non-linear transfer function to extract invariant or rather slowly varying features from a vectorial input sequence. This is generalized to a group of neurons, referred to as a Gibson-clique, to learn slowly varying features that are uncorrelated. Since the transfer functions are non-linear, this tec...

Intensity nonuniformity in magnetic resonance (MR) images, represented by a smooth and slowly varying function, is a typical artifact that is a nuisance for many image processing methods. To eliminate the artifact, we have to estimate the nonuniformity as a smooth and slowly varying function and factor it out from the given data. We reformulate the problem as a problem of finding a unique smoot...

Abstruct-The random-code capacity region of the multiple-access arbitrarily varying channel subject to both state and input constraints is determined. Consideration of a simple erasure channel shows that the capacity region is not convex in general.

let$ p_{n}(x)= sum_{i=0}^{n} a_{i}x^{i}$ be a random algebraicpolynomial, where $a_{0},a_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. thus $a_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}h_{j}(t)}$, where $h_j(t)$'s are complex slowlyvarying functions.under the assumption that th...

in the paper we establish some new results depending on thecomparative growth properties of composition of entire functionsusing relative $l^{ast }$-order (relative $l^{ast }$-lowerorder) as compared to their corresponding left and right factorswhere $lequiv lleft( rright) $ is a slowly changing function.