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The memristor has attracted phenomenal worldwide attention since its debut on 1 May 2008 issue of Nature in view of its many potential applications, e.g. super-dense nonvolatile computer memory and neural synapses. The Hewlett–Packard memristor is a passive nonlinear two-terminal circuit element that maintains a functional relationship between the time integrals of current and voltage, respectively, viz. charge and flux. In this paper, we derive several nonlinear oscillators from Chua's oscillators by replacing Chua's diodes with memristors.

In classical electrodynamics, extended with gradients of the electric and magnetic fields, a linear soliton is presented which bears features of the Kerr-Newman electron of electro-gravity. This is considered as a model for the electron, having a ring shape, with diameter equal to the Compton length ħ/mc and thickness smaller by the fine structure constant. The soliton has a finite mass, a spin-½, a g = 2 factor, and an electric quadrupole moment that is also “twice too large”. From this setup, all relativistic corrections to the classical version of the Pauli Hamiltonian are derived. There appears an additional, spin-dependent quadrupolar force that may vanish on the average. Particle-antiparticle annihilation may become explained on the basis of electromagnetic attraction.

Effect of maximum amount of charge a compact star can hold, is studied here. We analyze the different features in the renewed stellar structure and discuss the reasons why such huge charge is possible inside a compact star. We studied a particular case of a polytropic equation of state (EOS) assuming the charge density is proportional to the mass density. Although the global balance of force allows a huge charge, the electric repulsion faced by each charged particle forces it to leave the star, resulting in the secondary collapse of the system to form a charged black hole.

Let $\gamma \equiv {\{{\gamma }_{ij}\}}_{(i,j)\in I}$, with $I\subseteq {\mathbb{Z}}_{+}\times {\mathbb{Z}}_{+}$ and $\overline{{\gamma }_{ij}}={\gamma }_{ji}$, be a given complex-valued sequence. The complex moment problem (respectively, the general complex moment problem) associated with $\gamma$ consists in determining necessary and sufficient conditions for the existence of a positive Borel measure (respectively, a charge) $\mu$ on $ℂ$ such that

In this paper, we investigate the notion of recursiveness in the two variable case. We obtain several useful results that we use to deduce new necessary and sufficient conditions for the truncated complex moment problem to admit a solution. In particular, we show that the general complex moment problem always has a solution. A concrete construction of the solution and an illustrating example are also given.