Stability of Optically Injected Two‐State Quantum‐Dot Lasers

Simultaneous two‐state lasing is a unique property of semiconductor quantum‐dot (QD) lasers. This not only changes steady‐state characteristics of the laser device but also its dynamic response to perturbations. In this paper we investigate the dynamic stability of QD lasers in an external optical injection setup. Compared to conventional single‐state laser devices, we find a strong suppression of dynamical instabilities in two‐state lasers. Furthermore, depending on the frequency and intensity of the injected light, pronounced areas of bistability between both lasing frequencies appear, which can be employed for fast optical switching in all‐optical photonic computing applications. These results emphasize the suitability of QD semiconductor lasers in future integrated optoelectronic systems where a high level of stability is required.     

Hydrogels Incorporating GdDOTA: Towards Highly Efficient Dual T(1) /T(2) MRI Contrast Agents

Do not tumble dry: Gadolinium-DOTA encapsulated into polysaccharide nanoparticles (GdDOTA?NPs) exhibited high relaxivity (r(1) =101.7?s(-1) mM(-1) per Gd(3+) ion at 37?°C and 20?MHz). This high relaxation rate is due to efficient Gd loading, reduced tumbling of the Gd complex, and the hydrogel nature of the nanoparticles. The efficacy of the nanoparticles as a T(1) /T(2) dual-mode contrast agent was studied in C6 cells.     

A performance study of radio-opaque personal protective fabrics for the reduction of transmittance of gamma-rays and neutrons

Commercial radio-opaque combat (CRC) fabrics, for incorporation into personal protective equipment used by first responders and armed forces, are marketed as having the ability to provide a level of protection against specific types of radiation. For a CRC material, a standard combat uniform and a multi-layered chemical, biological, radiological, nuclear (CBRN) protective material, the present work examines chemical composition and radiation protection against gamma-rays and neutron fluxes. Significant reduction in gamma-ray transmittance occurs only for the CRC fabric (46–514 keV) with gamma-ray attenuation coefficients of 3.10 to <0.10 cm² g⁻¹. Reduction in neutron transmittance, for all three fabrics, could not be assessed with certainty as the measured transmittance was obscured by large statistical uncertainties.     

On second-order periodic elliptic operators in divergence form

We consider second-order, strongly elliptic, operators with complex coefficients in divergence form on . We assume that the coefficients are all periodic with a common period. If the coefficients are continuous we derive Gaussian bounds, with the correct small and large time asymptotic behaviour, on the heat kernel and all its H?lder derivatives. Moreover, we show that the first-order Riesz transforms are bounded on the -spaces with . Secondly if the coefficients are H?lder continuous we prove that the first-order derivatives of the kernel satisfy good Gaussian bounds. Then we establish that the second-order derivatives exist and satisfy good bounds if, and only if, the coefficients are divergence-free or if, and only if, the second-order Riesz transforms are bounded. Finally if the third-order derivatives exist with good bounds then the coefficients must be constant. Received in final form: 28 February 2000 / Published online: 17 May 2001     

Extending shelling orders and a hierarchy of functions of unimodal simple polytopes

Let P be a simplicial d-polytope with n facets ((d − 1)-dimensional faces) in R^d. A shelling of P is an ordering of the facets of P such that the intersection of each facet F with the union of all facets that precede it the ordering is a nonempty union of (d − 2)-faces of F. The following open question was raised by Tverberg and is recorded in [4]. Suppose for some k < n, there is an ordering of k of the facets of P so that the intersection of each of these facets with the union of all of the facets that precede it in the ordering is a nonempty union of (d − 2)-faces. Can this initial “segment” be extended to a shelling of all the facets? This question is open even in the case that P is the dual of the d-dimensional hypercube. The question in this case has resurfaced several times since G. Danaraj and V. Klee (1978) in a variety of forms. It is related to the hierarchies of completely unimodal pseudo-Boolean functions studied in P.L. Hammer et al. (1988), the author (1988) and D. Wiedemann (1986). (A pseudo-Boolean function is a function mapping the vertices of the d-dimensional hypercube into the reals). In this paper, the hierarchies are compared and combined. This hierarchy is then extended to general simple polytopes, and the relationship to the above open question is explained.     

Normals in a Minkowski Plane

In this paper we will establish bounds on the average number of normals through a point in a convex body in a Minkowski plane for certain classes of convex bodies. Also, a related Euler relation is discussed.