A novel design of Dual-Core Photonic Crystal Fiber (DC-PCF) with silica-air microstructures is proposed in this paper. Nonlinearity and confinement loss of DC-PCF are evaluated by using a Full-Vectorial Finite Element Method (FV-FEM) successfully. By optimizing the geometry of three ring DC-PCFs, a high nonlinearity (52w-1km-1) and low confinement loss (0.001dB/km) can be achieved at 1.55μm wav...

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

We establish some multiplicity results for a class of p-sublinear pLaplacian problems involving indefinite eigenvalue problems using Morse theory.

Abstract: In this paper, a method for determination of refractive index in membrane of fuel cell on basis of three-longitudinal-mode laser heterodyne interferometer is presented. The optical path difference between the target and reference paths is fixed and phase shift is then calculated in terms of refractive index shift. The measurement accuracy of this system is limited by nonlinearity erro...

We study the nonlinear elliptic problem −∆u = ρ(x)f(u) in R (N ≥ 3), lim|x|→∞ u(x) = l, where l ≥ 0 is a real number, ρ(x) is a nonnegative potential belonging to a certain Kato class, and f(u) has a sublinear growth. We distinguish the cases l > 0 and l = 0 and we prove existence and uniqueness results if the potential ρ(x) decays fast enough at infinity. Our arguments rely on comparison techn...

We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We use these bounds to study the asymptotic behavior of weakly coupled systems of fully nonlinear parabolic equations. Our results apply to some “asymmetric sy...

We consider the problem of functional programming with data in external memory, in particular as it appears in sublinear space computation. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot compose functions directly for lack of space for the intermediate result, but must instead compute and recomput...

In this paper we consider nonconvex optimization and learning over a network of distributed nodes. We develop a Proximal Primal-Dual Algorithm (Prox-PDA), which enables the network nodes to distributedly and collectively compute the set of first-order stationary solutions in a global sublinear manner [with a rate of O(1/r), where r is the iteration counter]. To the best of our knowledge, this i...