A note on replacement policy for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.     

Performance of a wavelength-tunable erbium-doped fiber laser using a Sagnac interferometer

We experimentally demonstrate a wavelength-tunable erbium-doped fiber laser that is composed of a ring cavity and a single-mode fiber Sagnac interferometer in a new and simple arrangement. We find that the fiber laser output wavelength is tunable by adjusting the filter effect of the Sagnac fiber loop through a fiber polarization controller set there. The quasi-single-wavelength continuously tunable laser outputs could be achieved within some wavelength range. The multi-wavelength laser outputs could also be observed under some appropriate settings of the polarization controller. A theoretical demonstration of the wavelength tunability about the transmission-type Sagnac loop filter has also been achieved using the Jones calculus theory.     

An effective explicit pressure gradient scheme implemented in the two-level non-staggered grids for incompressible Navier–Stokes equations

In this paper, an improved two-level method is presented for effectively solving the incompressible Navier–Stokes equations. This proposed method solves a smaller system of nonlinear Navier–Stokes equations on the coarse mesh and needs to solve the Oseen-type linearized equations of motion only once on the fine mesh level. Within the proposed two-level framework, a prolongation operator, which is required to linearize the convective terms at the fine mesh level using the convergent Navier–Stokes solutions computed at the coarse mesh level, is rigorously derived to increase the prediction accuracy. This indispensable prolongation operator can properly communicate the flow velocities between the two mesh levels because it is locally analytic. Solution convergence can therefore be accelerated. For the sake of numerical accuracy, momentum equations are discretized by employing the general solution for the two-dimensional convection–diffusion–reaction model equation. The convective instability problem can be simultaneously eliminated thanks to the proper treatment of convective terms. The converged solution is, thus, very high in accuracy as well as in yielding a quadratic spatial rate of convergence. For the sake of programming simplicity and computational efficiency, pressure gradient terms are rigorously discretized within the explicit framework in the non-staggered grid system. The proposed analytical prolongation operator for the mapping of solutions from the coarse to fine meshes and the explicit pressure gradient discretization scheme, which accommodates the dispersion-relation-preserving property, have been both rigorously justified from the predicted Navier–Stokes solutions.     

Synthesis, structure and oxygen-sensing properties of iridium(III)-containing coordination polymers with different cations

Four iridium(III)-containing coordination polymers 1-4 using Ir(ppy)(2)(H(2)dcbpy)PF(6) (L-H(2), ppy = 2-phenylpyridine, H(2)dcbpy = 4,4'-dicarboxy-2,2'-bipyridine) as the bridging ligand, [ZnL(2)]·3DMF·5H(2)O (1), [CdL(2)(H(2)O)(2)]·3DMF·6H(2)O (2), [CoL(2)(H(2)O)(2)]·2DMF·8H(2)O (3) and [NiL(2)(H(2)O)(2)]·3DMF·6H(2)O (4), have been synthesized and structurally characterized. The emissions from 1-4 are ascribed to a metal-to-ligand charge transfer transition (MLCT). The absolute emission quantum yields for 1-4 in single crystals were measured in air to be 0.274, 0.193, 0.001 and 0.002, respectively. The noteworthy oxygen-sensing properties of 1-4 as well as L-H(2) in a single crystal were also evaluated. The Stern-Volmer quenching constant, K(SV) values, of 1-4 and L-H(2) can be deduced to be 0.834, 2.820, 1.328, 1.111 and 2.476, respectively. The results show promising K(SV) values (e.g.2) that are competitive or even larger than those of many known Ir-complexes. Moreover, the short response time (e.g. compound 2) and recovery times toward oxygen of 1-4 have been measured in their single crystal forms. The reversibility experiments for 1-4 were carried out for seven repeated cycles. As a result, >75% recovery of intensity for 1 and 2 on each cycle demonstrates a high degree of reproducibility during the sensing process. It should be noted that iridium(III)-containing coordination polymers with high emission intensity and notable oxygen sensing properties are obscure, especially in the single crystal form. This, in combination with its fine reversibility, leads to success in single crystal oxygen recognition based on photoluminescence imaging. The detection limit could be 0.50% for gaseous oxygen. Moreover, the temperature effect of compound 2 in a single crystal upon application as an oxygen sensor was expected.     

Assembly of Three 2D Metal‐Organic Frameworks (MOFs) Derived from Flexible Ligands, 1,4‐bis(3‐pyridyl)‐2,3‐diaza‐1,3‐butadiene (3‐bpd) and/or 1,2‐bis(4‐pyridyl)ethane (dpe)

Three coordination polymers, {[Cd(3‐bpd)₂(NCS)₂]×C₂H₅OH}_n ( 1 ), {[Cd(3‐bpd)(dpe)(NO₃)₂]×(3‐bpd)}₂ ( 2 ), {[Cd(dpe)₂(NCS)₂]×3‐bpd×2H₂O}_n ( 3 ) (3‐bpd = 1,4‐bis(3‐pyridyl)‐2,3‐diaza‐1,3‐butadiene; dpe = 1,2‐bis(4‐pyridyl)ethane), were prepared and structurally characterized by a single‐crystal X‐ray diffraction method. In compound 1 , each Cd(II) ion is six‐coordinate bonded to six nitrogen atoms from four 3‐bpd and two NCS^? ligands. The 3‐bpd acts as a bridging ligand connecting the Cd(II) ion to generate a 2D layered metal‐organic framework (MOF) by using a rhomboidal‐grid as the basic building units with the 4⁴ topology. In compound 2 , the Cd(II) ion is also six‐coordinate bonded to four nitrogen atoms of two 3‐bpd, two dpe and two oxygen atoms of two NO₃^? ligands. The 3‐bpd and dpe ligands both adopt bis‐monodentate coordination mode connecting the Cd(II) ions to generate a 2D layered MOF by using a rectangle‐grid as the basic building units with the 4⁴ topology. In compound 3 , two crystallographically independent Cd(II) ions are both coordinated by four nitrogen atoms of dpe ligands in the basal plane and two nitrogen atom of NCS^? in the axial sites. The dpe acts as a bridging ligand to connect the Cd(II) ions forming a 2D interpenetrating MOFs by using a square‐grid as the basic unit with the 4⁴ topology. All of their 2D layered MOFs in compounds 1 ‐ 3 are then arranged in a parallel non‐interpenetrating ABAB—packing manner in 1 and 2 , and mutually interpenetrating manner in 3 , respectively, to extend their 3D supramolecular architectures with their 1D pores intercalated with solvent (ethanol in 1 or H₂O in 3 ) or free 3‐bpd molecules in 2 and 3 , respectively. The photoluminescence measurements of 1 ‐ 3 reveal that the emission is tentatively assigned to originate from π‐π* transition for 1 and 2 and probably due to ligand‐center luminescence for compounds 3 , respectively.     

Simultaneous determination of sweeteners and preservatives in preserved fruits by micellar electrokinetic capillary chromatography

A micellar electrokinetic capillary method for the simultaneous determination of the sweeteners dulcin, aspartame, saccharin, and acesulfame-K and the preservatives sorbic acid; benzoic acid; sodium dehydroacetate; and methyl-, ethyl-, propyl-, isopropyl-, butyl-, and isobutyl-p-hydroxybenzoate in preserved fruits is developed. These additives are ion-paired and extracted using sonication followed by solid-phase extraction from the sample. Separation is achieved using a 57-cm fused-silica capillary with a buffer comprised of 0.05 M sodium deoxycholate, 0.02 M borate-phosphate buffer (pH 8.6), and 5% acetonitrile, and the wavelength for detection is 214 nm. The average recovery rate for all sweeteners and preservatives is approximately 90% with good reproducibility, and the detection limits range from 10 to 25 microg/g. Fifty preserved fruit samples are analyzed for the content of sweeteners and preservatives. The sweeteners found in 28 samples was aspartame (0.17-11.59 g/kg) or saccharin (0.09-5.64 g/kg). Benzoic acid (0.02-1.72 g/kg) and sorbic acid (0.27-1.15 g/kg) were found as preservatives in 29 samples.     

Five novel norcembranoids from Sinularia leptoclados and S. parva

Three new norcembrane-based diterpenoids, leptocladolides A (1), B (4) and C (5), along with five known metabolites 6-10, have been isolated from the dichloromethane extract of a Taiwanese soft coral Sinularia leptoclados. Furthermore, a chemical investigation on the dichloromethane extract of S. parva has resulted in the isolation of two new related isomers, 1-epi-leptocladolide A (2) and 7E-leptocladolide A (3), in addition to 1 and 7. The structures of new metabolites 1-5 were elucidated on the basis of extensive spectroscopic analyses and their relative stereochemistries were determined by NOESY experiments. The new metabolites 1 and 3 have been shown to exhibit significant cytotoxic activity against KB and Hepa59T/VGH cancer cell lines.     

Hypervalent Iodine(III) Sulfonate Mediated Synthesis of 2‐Arylimidazo[1,2‐a]Pyrimidines in Liquid PEG‐400

PEG‐400[poly(ethylene glycol‐400)] is used as a “green” recyclable solvent in the one‐pot synthesis of 2‐arylimidazo[1,2‐a]pyrimidines by reaction with ketones, [hydroxyl(2,4‐dinitrobenzenesulfonyloxy)‐iodo]benzene (HDNIB), and 2‐aminopyrimidine. Significant rate enhancements and improved yields have been observed.     

The Regioselectivity of (Dimethylvinylidene)carbene Directed by Aromatic Ring upon the Addition into Aryl Alkenes in the Presence of Other Olefins

Regioselective cycloaddition of (dimethylvinylidene)carbene (1) into aryl alkenes in the presence of other olefins is reported. The reaction is presumably controlled by the phenyl group, which forms an aromatic π-complex with the carbene C-3 orbital, followed by the selective addition of 1 to the closest phenyl-substituted double bond. Also, this selectivity is assumed to be attributed to delocalization of aromatic π electrons which increases the electron density of the conjugated carbon-carbon double bond, thus leading to the facile addition of vinylidenecarbene.     

Control of Luminescence by Tuning of Crystal Symmetry and Local Structure in Mn4+‐Activated Narrow Band Fluoride Phosphors

Mn⁴⁺‐doped fluoride phosphors have been widely used in wide‐gamut backlighting devices because of their extremely narrow emission band. Solid solutions of Na₂(Si_xGe_1?x)F₆:Mn⁴⁺ and Na₂(Ge_yTi_1?y)F₆:Mn⁴⁺ were successfully synthesized to elucidate the behavior of the zero‐phonon line (ZPL) in different structures. The ratio between ZPL and the highest emission intensity υ₆ phonon sideband exhibits a strong relationship with luminescent decay rate. First‐principles calculations are conducted to model the variation in the structural and electronic properties of the prepared solid solutions as a function of the composition. To compensate for the limitations of the Rietveld refinement, electron paramagnetic resonance and high‐resolution steady‐state emission spectra are used to confirm the diverse local environment for Mn⁴⁺ in the structure. Finally, the spectral luminous efficacy of radiation (LER) is used to reveal the important role of ZPL in practical applications.