Polymorphism of sorbitol

The polymorphism of sorbitol was investigated, confirming the existence of four anhydrous crystalline phases plus the hydrate. The crystallised melt (CM), the alpha form, and the gamma form were obtained via a dry route. The CM was confirmed to be a crystalline state with a spherulite morphology. The alpha form was obtained via direct conversion from the CM, in contrast to more complicated routes previously reported, and was found to have a very high crystallinity. Gamma crystals were obtained by seeding the melt at high temperature; however, crystallinity was clearly less than for alpha crystals.     

Polynomial time approximation schemes and parameterized complexity

In this paper, we study the relationship between the approximability and the parameterized complexity of NP optimization problems. We introduce a notion of polynomial fixed-parameter tractability and prove that, under a very general constraint, an NP optimization problem has a fully polynomial time approximation scheme if and only if the problem is polynomial fixed-parameter tractable. By enforcing a constraint of planarity on the W-hierarchy studied in parameterized complexity theory, we obtain a class of NP optimization problems, the planar W-hierarchy, and prove that all problems in this class have efficient polynomial time approximation schemes (EPTAS). The planar W-hierarchy seems to contain most of the known EPTAS problems, and is significantly different from the class introduced by Khanna and Motwani in their efforts in characterizing optimization problems with polynomial time approximation schemes.     

An anomalous reaction of 7-chloro-2-hydrazono-5-phenyl-1,2-dihydro-3H-1,4-benzodiazepine with sodium acetate and 1,1′-carbonyldiimidazole

The addition of 7-chloro-2-hydrazono-5-phenyl-1,2-dihydro-3H-1,4-benzodiazepine 3 to a mixture of sodium acetate and 1,1′-carbonyldiimidazole 1 at room temperature gave, in moderate yields, carbonyl-1,1′-bis[7-chloro-5-phenyl-1,2-dihydro-3H-1,4-benzodiazepin-2-ylidene hydrazone] 7 instead of the expected 2-acetylhydrazono-7-chloro-5-phenyl-1,2-dihydro-3H-1,4-benzodiazepine 4 .     

On the stretch factor of Delaunay triangulations of points in convex position

Let S be a finite set of points in the Euclidean plane. Let G be a geometric graph in the plane whose point set is S. The stretch factor of G is the maximum ratio, among all points p and q in S, of the length of the shortest path from p to q in G over the Euclidean distance |pq|. Keil and Gutwin in 1989 [11] proved that the stretch factor of the Delaunay triangulation of a set of points S in the plane is at most 2π/(3cos(π/6))≈2.42. Improving on this upper bound remains an intriguing open problem in computational geometry.In this paper we consider the special case when the points in S are in convex position. We prove that in this case the stretch factor of the Delaunay triangulation of S is at most ρ=2.33.     

Conductance Photoswitching of Metal–Organic Frameworks with Embedded Spiropyran

Conductive metal–organic frameworks (MOFs) as well as smart, stimuli‐responsive MOF materials have attracted considerable attention with respect to advanced applications in energy harvesting and storage as well as in signal processing. Here, the conductance of MOF films of type UiO‐67 with embedded photoswitchable nitro‐substituted spiropyrans was investigated. Under UV irradiation, the spiropyran (SP) reversibly isomerizes to the open merocyanine (MC) form, a zwitterionic molecule with an extended conjugated π‐system. The light‐induced SP–MC isomerization allows for remote control over the conductance of the SP@UiO‐67 MOF film, and the conductance can be increased by one order of magnitude. This research has the potential to contribute to the development of a new generation of photoelectronic devices based on smart hybrid materials.     

Influence of impurities on the crystallization of dextrose monohydrate

The effects of impurities on dextrose monohydrate crystallization were investigated. Crystal nucleation and growth kinetics in the presence of impurities were studied using an in-line focused beam reflectance monitoring (FBRM) technique and an in-line process refractometer. Experimental data were obtained from runs carried out at different impurity levels between 4 and 11 wt% in the high dextrose equivalent (DE) syrup. It was found that impurities have no significant influence on the solubility of dextrose in water. However, impurities have a clear influence on the nucleation and growth kinetics of dextrose monohydrate crystallization. Nucleation and growth rate were favored by low levels of impurities in the syrup.     

Vertex Cover: Further Observations and Further Improvements

Recently, there has been increasing interest and progress in lowering the worst-case time complexity for well-known NP-hard problems, particularly for the Cover problem. In this paper, new properties for the problem are indicated, and several simple and new techniques are introduced, which lead to an improved algorithm of time O(kn + 1.2852^k) for the problem. Our algorithm also induces improvement on previous algorithms for the problem on graphs of small degree.     

Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network

In this work, we demonstrate for the first time that it is possible to transfer simultaneously an ultra-stable optical frequency and precise and accurate timing over 540 km using a public telecommunication optical fiber network with Internet data. The optical phase is used to carry both the frequency information and the timestamps by modulating a very narrow optical carrier at 1.55 μm with spread spectrum signals using two-way satellite time transfer modems. The results in terms of absolute time accuracy (250 ps) and long-term timing stability (20 ps) well outperform the conventional Global Navigation Satellite System or geostationary transfer methods.