In this paper, we demonstrate a source of photon pairs based on four-wave-mixing in photonic crystal fibres. Careful engineering of the phase matching conditions in the fibres enables us to create photon pairs at 597 nm and 860 nm in an intrinsically factorable state showing no spectral correlations. This allows for heralding one photon in a pure state and hence renders narrow band filtering ob...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

Plantholt and Tipnis (1991) proved that for any even integer r, a regular multigraph G with even order n, multiplicity μ(G) ≤ r and degree high relative to n and r is 1-factorable. Here we extend this result to include the case when r is any odd integer. Häggkvist and Perković and Reed (1997) proved that the One-factorization Conjecture for simple graphs is asymptotically true. Our techniques y...

In this paper we present a new method to construct a polynomial u(x) ∈ Z[x] which will make Φk(u(x)) reducible. We construct a finite separable extension of Q(ζk), denoted as E. By primitive element theorem, there exists a primitive element θ ∈ E such that E = Q(θ). We represent the primitive k-th root of unity ζk by θ and get a polynomial u(x) ∈ Q[x] from the representation. The resulting u(x)...

In this paper, all possible sparse chemical reaction network structures of a classical 3-dimensional Lorenz system are computed assuming a given chemical complex set. The original non-kinetic equations are transformed into kinetic form using two different approaches: firstly, using a statedependent time-rescaling and secondly, by applying the theory of X-factorable systems. Using the notions of...

We study photon pair generation through scalar spontaneous four-wave mixing in single-mode fibre and for frequency-degenerate pumps; we concentrate on source geometries which fulfil full group velocity matching (GVM), i.e. where the pump, signal and idler propagate at identical group velocities. We discuss two experimental techniques which permit the attainment of full GVM, and discuss the resu...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.