Numerical study of an ion-exchanged glass waveguide using both two-dimensional and three-dimensional models

A numerical study is carried out to compare the two-dimensional (2-D) case and three-dimensional (3-D) case for the modelling of an ion-exchanged glass waveguide. It is shown that different waveguide widths on the photomask correspond to different ion concentration distributions after an annealing process. A numerical example is presented of two waveguide sections with different widths indicates that due to the abrupt change of the waveguide width, a 3-D theoretical model is required for an accurate prediction of the parameters of ion-exchanged glass waveguides. The good agreement between the modelled and measured results proves that the developed 3-D numerical model can be beneficially utilized in the generalized design of optical devices based on ion-exchange waveguides.     

Humidity sensor based on a single-mode hetero-core fiber structure

Using a small-core single-mode fiber (SCSMF), a novel relative humidity (RH) sensor based on an SMF28-SCSMF-SMF28 fiber structure was proposed in this paper. By depositing a humidity sensitive material, such as poly (ethylene oxide) (PEO) on the bare SCSMF fiber, the proposed structure can act as an RH sensor with high sensitivity. Experiments demonstrated that the proposed RH sensor with PEO coating can achieve a sensitivity of 430 nm per relative humidity unit (RHU) in the RH range from 80% to 83% RH and a sensitivity of 50 nm per RHU in the RH range from 83% to 95% RH.     

Fiber refractometer based on a fiber Bragg grating and single-mode-multimode-single-mode fiber structure

A refractive index (RI) sensor based on a novel fiber structure that consists of a single-mode-multimode-single-mode (SMS) fiber structure followed by a fiber Bragg grating was demonstrated. The multimode fiber in the SMS structure excites cladding modes within output single-mode fiber (SMF) and recouple the reflected cladding Bragg wavelength to the input SMF core. By measuring the relative Bragg wavelength shift between core and cladding Bragg wavelengths, the RI can be determined. Experimentally we have achieved a maximum sensitivity of 7.33 nm/RIU (RI unit) at RI range from 1.324 to 1.439.     

The Farrell–Jones Conjecture for the solvable Baumslag–Solitar groups

In this paper, we prove the Farrell–Jones Conjecture for the solvable Baumslag–Solitar groups with coefficients in an additive category. We also extend our results to groups of the form, Z[1/p] semidirect product with any virtually cyclic group, where p is a prime number.     

Asymptotically liberating sequences of random unitary matrices

A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asymptotic liberation” under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdú.     

Metal‐Catalyzed “On‐Demand” Production of Carbonyl Sulfide from Carbon Monoxide and Elemental Sulfur

The group 6 molybdenum(II) cyclopentadienyl amidinate (CPAM) bis(carbonyl) complex [Cp*Mo{N(iPr)C(Ph)N(iPr)}(CO)₂] (Cp*=η⁵‐C₅Me₅) serves as a precatalyst for the high‐yielding photocatalytic production of COS from CO and S₈ under near‐ambient conditions (e.g., 10 psi, 25 °C). Further documented is the isolation and structural characterization of several key transition‐metal intermediates which collectively support a novel molybdenum(IV)‐based catalytic cycle as being operative. Finally, in the presence of an excess amount of a primary amine, it is demonstrated that this catalytic system can be successfully used for the “on‐demand” generation and utilization of COS as a chemical reagent for the synthesis of ureas.     

Fluorene-containing tetraphenylethylene molecules as lasing materials

A series of star-shaped oligofluorene molecules, each containing a TPE core, have been specifically designed and produced to show effective aggregation-induced emission (AIE). Each molecule differs either in the number of fluorene units within the arms (e.g., 1 or 4, compounds 4 and 5 ), or the terminal group positioned at the end of each arm (e.g., H, TMS, or TPA, compounds 4 , 6 , and 7 ). Although they are all poor emitters in solution phase they become efficient yellow-green luminogens in the condensed state. Their AIE properties were investigated in THF/H₂O mixtures, with each molecule exhibiting a clear emission enhancement at specific water contents. An all-organic distributed feedback (DFB) laser was fabricated using compound 4 as the gain material and exhibited an average threshold energy fluence of 60 ± 6 μJ/cm² and emission in the green region. Furthermore, piezofluorochromism studies on a thin film of this material displayed a linear dependence of the amplified spontaneous emission (ASE) peak position on applied pressure, indicating potential applications as lasing-based pressure sensors. © 2016 The Authors. Journal of Polymer Science Part A: Polymer Chemistry Published by Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 734–746     

The effect of spatial wandering on experimental laser velocimeter measurements of the end-wall vortices in an axial-flow pump

In a high Reynolds number axial-flow pump, laser velocimeter (LV) measurements were made to study the size and structure of the end-wall vortex. The time mean measurements show that the core size of the end-wall vortex increased with decreasing tip clearance, which is contrary to existing theory. Observations of cavitation in the vortex showed that the flow was unsteady. The vortices emanating from the smaller clearances were observed to wander or meander spatially and to develop kinks more than the vortices emanating from the larger tip clearances. This observed unsteadiness has a significant effect on the time mean size and velocity distribution of the vortex as measured with the LV employing the field point measurement technique. In order to obtain an estimate of the true size and velocity distribution, computational experiments were conducted which modelled a periodically wandering vortex and the LV measurement process. The computational and experimental results show good agreement, including a broadened and reduced tangential velocity distribution. In this paper, the end-wall vortex LV measurements are presented, and the method of analyzing the vortex wandering is described.     

Solution studies of dinuclear polyamine-linked platinum-based antitumour complexes

The aquation profiles of two novel dinuclear polyamine-linked, platinum-based antitumour complexes [{trans-PtCl((15)NH(3))(2)}(2){μ-((15)NH(2)(CH(2))(6)(15)NH(2)(CH(2))(6)(15)NH(2))}](3+) (BBR3007, 1,1/t,t-6,6, 1) and [{trans-PtCl((15)NH(3))(2)}(2){μ-((15)NH(2)(CH(2))(6)(15)NH(2)(CH(2))(2)(15)NH(2)(CH(2))(6)(15)NH(2))}](4+) (BBR3610, 1,1/t,t-6,2,6, 1') have been probed using 2D [(1)H, (15)N] HSQC NMR spectroscopy. Reported herein are the rate constants for the hydrolysis of 1 and 1', as well as the acid dissociation constants of the coordinated aqua ligands in their aquated derivatives. The aquation and anation rate constants for the single step aquation model in 15 mM NaClO(4) (pH 5.4) at 298 K are, for 1, k(1) = 7.2 ± 0.1 ×10(-5) s(-1), k(-1) = 0.096 ± 0.002 M(-1) s(-1) and, for 1', k(1) = 4.0 ± 0.2 × 10(-5) s(-1), k(-1) = 1.4 ± 0.1 M(-1) s(-1). The effect of the linker backbone (Pt(tetra(m)mine vs. polyamine) was evaluated by comparison with previous data for the trinuclear complex [{trans-PtCl(NH(3))(2)}(2)(μ-trans-Pt(NH(3))(2){NH(2)(CH(2))(6)NH(2)}(2))](4+) (1,0,1/t,t,t or BBR3464). The pK(1) for 1,0,1/t,t,t (3.44) is closest to that of 1 (3.12), while the pronounced difference for 1' (4.54), means that 1' is the least aquated of the three complexes at equilibrium. pK(a) values of 5.92 were calculated for the aquated forms of both 1 and 1', which are 0.3 pK units higher than for either 1,0,1/t,t,t, or the dinuclear 1,1/t,t. The higher pK(a) values for both polyamine-linked compounds may be attributed to the formation of macrochelates between the central NH(2) groups and the {PtN(3)O} coordination sphere of the aquated species.     

On graphical partitions and planarity

Chvátal gave a necessary condition for a partition to have a planar realization. It is of interest to find: (i) partitions which satisfy the condition of the theorem but have no planar realization, and also (ii) partitions which satisfy the condition and have only planar realizations. We give a list of all such partitions with 6, 7, 8 and 9 elements. We also give an algorithm for generating all graphs with a given partition, an algorithm for generating all subcompositions of a given composition and some general classes of partitions which have planar realizations only and some which have non-planar realizations only.