The rapidly growing field of polynomial optimisation (PO) is concerned with optimisation problems in which the objective and constraint functions are all polynomials. There are applications of PO in a surprisingly wide variety of contexts, including, for example, operational research, statistics, applied probability, quantitative finance, theoretical computer science and various branches of eng...

In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was realized few years ago that certain non-Hermitian parity-time (P T ) symmetric Hamiltonians can exhibit an entirely real spectrum. Much of the...

Background: In earlier experiments the role of the vacuum fields could be demonstrated as the source of complementarity with respect to the temporal properties (Heuer et al., Phys. Rev. Lett. 114:053601, 2015). Methods: Single photon first order interferences of spatially separated regions from the cone structure of spontaneous parametric down conversion allow for analyzing the role of the mode...

Using numerical simulations, here, we demonstrate that a single sheet of graphene with properly designed inhomogeneous, nonuniform conductivity distributions can act as a convex lens for focusing and collimating the transverse-magnetic (TM) surface plasmon polariton (SPP) surface waves propagating along the graphene. Consequently, we show that the graphene can act as a platform for obtaining sp...

For a plane electromagnetic wave at nose-on incidence on a semi-infinite perfectly conducting cone expressions for the surface field components are obtained. These have been programmed for numerical computation and data are presented for the magnitudes and phases as functions of the distance from the tip for three different cone angles. Comparison with results derived from the physical optics a...

We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propag...

In this paper, the angular side-play amount created by radiation pressure acting on active space object has been detailed investigated based on the physical optics, and the results are compared with the results by Mie theory; the correctness of the physical optics model is validated. The curves of angular side-play amount varied with the energy density of incident wave, mass of the object, and ...

BACKGROUND Hyperphosphatemic acidosis and severe electrolyte disturbances caused by phosphate salts (PO) used for mechanical bowel preparation have been described in occasional case reports prior to bowel resection surgery. We hypothesized that PO used preoperatively for bowel preparation may cause more pronounced acid base and electrolyte changes than polyethylene glycol (PG). METHODS Forty ...

Locally partial-ordered spaces (local po-spaces) have been used to model concurrent systems. We provide equivalences for these spaces by constructing a model category containing the category of local po-spaces. We show the category of simplicial presheaves on local po-spaces can be given Jardine's model structure, in which we identify the weak equivalences between local po-spaces. In the proces...