Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired considering the conformal symmetry under transformation of an auxiliary metric. By introducing two super-potentials, transform second-order equations system into set first-order equations. With formalism, several types analytical brane solutions are obtained. Then, tensor and pert...

We investigate the behavior of electric potentials on distance-regular graphs, and extend some results of a prior paper, [12]. Our main result, Theorem 4 below, shows(together with Corollary 3) that if distance is measured by the electric resistance between points then all points are close to being equidistant on a distance-regular graph with large valency. A number of auxiliary results are als...

The concept of energy-dependent forces in quantum mechanics is re-analysed. We suggest a simplification of their study via the representation of each self-adjoint and energy-dependent Hamiltonian H = H(E) with real spectrum by an auxiliary non-Hermitian operator K which remains energy-independent. Practical merits of such an approach to the Schrödinger equations with energy-dependent potentials...

AMPA receptors (AMPARs) conduct fast, excitatory currents that depolarize neurons and trigger action potentials. AMPARs took on new importance when it was shown that AMPAR transport can increase or decrease the number of AMPARs at synapses and give rise to synapse plasticity, including long-term potentiation (LTP) and long-term depression (LTD). This review considers how transmembrane AMPAR reg...

A considerable body of evidence has revealed that interstitial cells of Cajal (ICC), identified with c-Kit-immunoreactivity, act as gut pacemaker cells, with spontaneous Ca(2+) activity in ICC as the probable primary mechanism. Namely, intracellular (cytosolic) Ca(2+) oscillations in ICC periodically activate plasmalemmal Ca(2+)-dependent ion channels and thereby generate pacemaker potentials. ...

We construct exact duality transformations in pure SU(N) Hamiltonian lattice gauge theory ($2+1$) dimension. This is obtained by making a series of iterative canonical on the electric vector fields and their conjugate magnetic potentials four links around every plaquette. The resulting dual description terms scalar or plaquette flux loops potentials. Under they both transform like adjoint matte...