Two Projection Algorithms for Solving the Split Common Fixed Point Problem

Journal of Optimization Theory and Applications - We study the split common fixed point problem for Bregman relatively nonexpansive operators in real reflexive Banach spaces. Using Bregman...     

Electrodeposited Amorphous Tungsten‐doped Cobalt Oxide as an Efficient Catalyst for the Oxygen Evolution Reaction

Thin film of amorphous tungsten‐doped cobalt oxide (W:CoO) was successfully grown on a conducting electrode via an electrochemical oxidation process employing a [Co(WS₄)₂]^2? deposition bath. The W:CoO catalyst displays an attractive performance for the oxygen evolution reaction in an alkaline solution. In an NaOH solution of pH 13, W:CoO operates with a moderate onset overpotential of 230 mV and requires 320 mV overpotential to generate a catalytic current density of 10 mA cm^?2. A low Tafel slope of 45 mV decade^?1 was determined, indicating a rapid O₂‐evolving kinetics. The as‐prepared W:CoO belongs to the best cobalt oxide‐based catalysts ever reported for the oxygen evolution (OER) reaction.     

Hermite–Birkhoff–Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size

A four-stage Hermite–Birkhoff–Obrechkoff method of order 14 with four quantized variable steps, denoted by HBOQ(14)4, is constructed for solving non-stiff systems of first-order differential equations of the form y^′=f(t,y)$y^{\prime }=f(t,y)$ with initial conditions y(_t0)=_y0$y\left(t_0\right)=y_0$. Its formula uses y^′$y^{\prime }$, y^″$y^{″}$ and y^?$y^{?}$ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep- and Runge–Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. To reduce overhead, simple formulae are derived only once to obtain the values of Hermite–Birkhoff interpolation polynomials in terms of Lagrange basis functions for 16 quantized step size ratios. The step size is controlled by a local error estimator. When programmed in C ++, HBOQ(14)4 is superior to the Dormand–Prince Runge–Kutta pair DP(8,7)13M of order 8 in solving several problems often used to test higher order ODE solvers at stringent tolerances. When programmed in Matlab, it is superior to ode113 in solving costly problems, on the basis of the number of steps, CPU time, and maximum global error. The code is available on the URL www.site.uottawa.ca/~remi.     

Visible-Light-Induced Control over Reversible Single-Chain Nanoparticle Folding

We introduce a class of single-chain nanoparticles (SCNPs) that respond to visible light (λ_max=415 nm) with complete unfolding from their compact structure into linear chain analogues. The initial folding is achieved by a simple esterification reaction of the polymer backbone constituted of acrylic acid and polyethylene glycol carrying monomer units, introducing bimane moieties, which allow for the photochemical unfolding, reversing the ester-bond formation. The compaction and the light driven unfolding proceed cleanly and are readily followed by size exclusion chromatography (SEC) and diffusion ordered NMR spectroscopy (DOSY), monitoring the change in the hydrodynamic radius (R_H). Importantly, the folding reaction and the light-induced unfolding are reversible, supported by the high conversion of the photo cleavage. As the unfolding reaction occurs in aqueous systems, the system holds promise for controlling the unfolding of SCNPs in biological environments.     

Convergent assembly of highly potent analogues of bryostatin 1 via pyran annulation: bryostatin look-alikes that mimic phorbol ester function

Highly potent bryostatin analogues which contain the complete bryostatin core structure have been synthesized using a pyran annulation approach as a key strategic element. The A ring pyran was assembled using a pyran annulation reaction between a C1-C8 hydroxy allylsilane and an aldehyde comprising C9-C13. This pyran was transformed to a new hydroxy allylsilane and then coupled with a preformed C ring aldehyde subunit in a second pyran annulation, with concomitant formation of the B ring. This tricyclic intermediate was elaborated to bryostatin analogues which displayed nanomolar to subnanomolar affinity for PKC, but displayed properties indistinguishable from a phorbol ester in a proliferation/attachment assay.     

Model selection of a switching mechanism for financial time series

The threshold autoregressive model with generalized autoregressive conditionally heteroskedastic (GARCH) specification is a popular nonlinear model that captures the well‐known asymmetric phenomena in financial market data. The switching mechanisms of hysteretic autoregressive GARCH models are different from threshold autoregressive model with GARCH as regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. This paper conducts a Bayesian model comparison among competing models by designing an adaptive Markov chain Monte Carlo sampling scheme. We illustrate the performance of three kinds of criteria by comparing models with fat‐tailed and/or skewed errors: deviance information criteria, Bayesian predictive information, and an asymptotic version of Bayesian predictive information. A simulation study highlights the properties of the three Bayesian criteria and the accuracy as well as their favorable performance as model selection tools. We demonstrate the proposed method in an empirical study of 12 international stock markets, providing evidence to strongly support for both models with skew fat‐tailed innovations. Copyright © 2016 John Wiley & Sons, Ltd.     

Even and Odd Charge Coherent States: Higher-Order Nonclassical Properties and Generation Scheme

We examine the higher-order nonclassical properties of the even and odd charge coherent states as well as proposing a scheme to generate these states whose modes can freely travel in open space. We show that the even and odd charge coherent states exhibit both higher-order antibunching and higher-order squeezing. While the two-mode higher-order antibunching occurs in any order and essentially depends on the charge number, the two-mode higher-order squeezing appears only in the even orders. We also prove that these states are genuinely entangled, and they can be generated by means of cross-Kerr media, beam splitters, phase shifts and threshold detectors. We find that the fidelity and the corresponding success probability to generate these states are dependent on the correlative parameters.     

Effect of potassium addition on bimetallic PtSn/θ-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> catalyst for dehydrogenation of propane to propylene

PtSn/θ-Al₂O₃ catalysts with different amounts of K (0.14, 0.22, 0.49, 0.72, and 0.96 wt%) are prepared to investigate the K effects on the PtSn catalyst in propane dehydrogenation (PDH). KPtSn catalyst with 0.xx wt% K, 0.5 wt% Pt and 0.75 wt% Sn is designated as xx-KPtSn. PDH was performed at 873 K and a gas hourly space velocity (GHSV) of 53,000 mL/g_cat h. The temperature-programmed desorption (NH₃-TPD), temperature-programmed reduction (TPR) and CO chemisorption of the KPtSn catalysts with K added revealed the potassium addition blocked the acid sites, promoted the reduction of Sn oxide and decreased the Pt dispersion. The formations of cracking products and higher hydrocarbons on acid sites were suppressed by the K effect of blocking the acid sites. In contrast, K addition at more than 0.72 wt% rather increased cracking products and the amount of coke, resulting in the severe deactivation of catalysts. The high cracking products on the KPtSn catalysts with the high amount of K should not be related to the acid sites, because the acid sites were monotonously decreased with an increase in the amount of K. Instead, the potassium affected the characteristics of PtSn. The interaction between Pt and Sn could be weakened by enriching the reduced Sn, because the K component promoted the reduction of Sn oxide in the TPR experiments. Therefore, the 14-KPtSn catalyst with the low amount of K exhibits the highest stability and selectivity among the prepared KPtSn catalysts due to the compromise of the advantageous (blocking the acid sites) and bad (weakening the interaction between Pt and Sn) effects of the K addition in PDH.