On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times

The structural properties of the moments of the time to ruin are studied in dependent Sparre Andersen models. The moments of the time to ruin may be viewed as generalized versions of the Gerber–Shiu function. It is shown that structural properties of the Gerber–Shiu function hold also for the moments of the time to ruin. In particular, the moments continue to satisfy defective renewal equations. These properties are discussed in detail in the model of Willmot and Woo (2012), which has Coxian interclaim times and arbitrary time-dependent claim sizes. Structural quantities needed to determine the moments of the time to ruin are specified under this model. Numerical examples illustrating the methodology are presented.     

Dark solitons of the Biswas–Milovic equation by the first integral method

This paper studies the Biswas–Milovic equation that is a generalized version of the familiar nonlinear Schrodinger's equation describing the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances with Kerr law nonlinearity by the aid of the first integral method. The dark 1-soliton solution is retrieved by the aid of this method and a couple of other singular periodic solutions are also obtained.     

New classes of second order difference equations solvable by factorization method

Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

Rare-earth Doped Nanoparticles with Narrow NIR-II Emission for Optical Imaging with Reduced Autofluorescence

Fluorescence imaging in the second near-infrared region(900-1700 nm, NIR-II) with a high resolution and penetration depth due to the significantly reduced tissue scattering and autofluorescence has emerged as a useful tool in biomedical fields. Recently, many efforts have been devoted to the development of fluorophores with an emission band covering the long-wavelength end of NIR-II region(1500-1700 nm) to eliminate the autofluorescence. Alternatively, we believe imaging with a narrow bandwidth could also reduce the autofluorescence. As a proof of concept, NaYF₄:Yb,Nd@NaYF₄ downconversion nanoparticles(DCNPs) with sharp NIR-II emission were synthesized. The luminescence of DCNPs showed a half-peak width of 49 nm centered at 998 nm, which was perfectly matched with a (1000±25) nm bandpass filter. With this filter, we were able to retain most of the emissions from the nanoparticles, while the autofluorescence was largely reduced. After PEGylation, the DCNPs exhibited great performance for blood vessel and tumor imaging in living mice with significantly reduced autofluorescence and interference signals. This work provided an alternative way for the low-autofluorescence imaging and emphasized the importance of narrow emitting rare-earth doped nanoparticles for NIR-II imaging.     

Separation between second price auctions with personalized reserves and the revenue optimal auction

When buyer valuations are drawn IID from a known regular distribution, a second price auction with a symmetric reserve price is the revenue-optimal single-item auction. When this distribution is irregular, we provide the first separation result showing that a second price auction with reserves earns at most 0.778 times the revenue of Myerson’s optimal auction, even when the reserves can be asymmetric. Since the lower bound is 0.745 for i.i.d. buyers, our result is nearly tight.     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Structural,magnetic and optical properties of two concomitant molecular crystals

A new 1D complex has been prepared and characterized. X-ray single crystal structure confirms that the Cu(II) ions assemble in alternating chains with Cu … Cu distances of 2.5685(4) and 3.1760(4) Å. The temperature dependence of the magnetic susceptibility reveals an antiferromagnetic interaction between the paddle-wheel copper centers with an exchange of −300 cm⁻¹. The exchange integral was also determined by quantum chemical ab-initio calculations, using polarised and unpolarised basis sets reproducing well the experimental value. The second harmonic generation efficiency of a concomitantly crystallized material was evaluated and was found to be comparable to urea.