Higher order log-concavity in Euler’s difference table

For 0≤k≤n, let be the entries in Euler’s difference table and let . Dumont and Randrianarivony showed equals the number of permutations on [n] whose fixed points are contained in {1,2,…,k}. Rakotondrajao found a combinatorial interpretation of the number in terms of k-fixed-points-permutations of [n]. We show that for any n≥1, the sequence is essentially 2-log-concave and reverse ultra log-concave.     

NaCl interaction with interfacially polymerized polyamide films of reverse osmosis membranes: A solid-state Na NMR study

²³Na nuclear magnetic resonance (NMR) spectroscopy of NaCl-exchanged polyamide (PA) films comparable to those of the active skin layer of many reverse osmosis (RO) membranes provides novel insight into the structural environments and dynamical behavior of Na⁺ in such films. Unsupported PA films were synthesized via interfacial polymerization of trimesoyl chloride in hexane and m-phenylenediamine in aqueous solution, and SEM, FT-IR, and ¹³C NMR data demonstrate successful thin film polymerization. Compositional data confirm this conclusion and demonstrate equal Na and Cl incorporation during NaCl exchange from aqueous solution. The ²³Na NMR spectra for freshly made polymer samples exchanged in 1 M NaCl solution show significant relative humidity (RH) dependence. At near 0% RH, there are resonances for crystalline NaCl and rigidly held Na⁺ in the PA. With increasing RH, a resonance for solution-like dynamically averaged Na⁺ appears and above 51% RH is the only signal observed. The slightly negative chemical shift of this resonance suggests a dominantly hydrous environment with some atomic-scale coordination by atoms of the polymer. The greatly reduced ²³Na T₁ relaxation rates for this resonance relative to bulk solution and crystalline NaCl confirm close association with the polymer. Variable temperature ²³Na NMR spectra for a sample equilibrated at 97% RH obtained from −80 to 20 °C show the presence of rigidly held Na⁺ in a hydrated environment at low temperatures and replacement of this resonance by the dynamically averaged signal at temperatures above about −20 °C. The results provide support for the solution–diffusion model for RO membranes transport and demonstrate the capabilities of multi-nuclear NMR methods to investigate molecular-scale structure and dynamics of the interactions between dissolved species and RO membranes.     

在溴化钾粉末中掺入大量α-炭化硅压片的异常红外透射光谱研究

在光谱学实践中，通常由于带测样品颗粒在本征吸收峰附近产生可观的附加散射消光，致使表观吸收峰偏离实际位置，从而得到不的光谱，这就是我们常要采取措施尽量避免的克里斯坦森（Christiansen）效,这一就是在制作压片（例如溴化钾）时，待测样品含量要少（少于2％）。在一次实验中，当在KBr粉末中掺入大量（而非正常要求的少许）的α-SiC微粉后，得到了一个在1052.33cm^-1处有一个尖峰的中红外透射谱。我们发现，这个新现象非常有趣，它与克里斯坦森效应表面上相反，但都可用Lorentz色散模型给予精确地解释。于是称它为反克里斯坦森效应，在该效应出现的频率处两种材料的折射率相等，且吸收系数都非常小。这个新现象也非常有意义，它可用来制造新型的带通滤波器以及准确测定某些材料的折射率等。     

Minima of initial segments of infinite sequences of reals

Suppose that 〈x_k〉_k∈? is a countable sequence of real numbers. Working in the usual subsystems for reverse mathematics, RCA₀ suffices to prove the existence of a sequence of reals 〈u_k〉_k∈? such that for each k, u_k is the minimum of {x₀, x₁, …, x_k}. However, if we wish to prove the existence of a sequence of integer indices of minima of initial segments of 〈x_k〉_k∈?, the stronger subsystem WKL₀ is required. Following the presentation of these reverse mathematics results, we will derive computability theoretic corollaries and use them to illustrate a distinction between computable analysis and constructive analysis. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Combining reverse osmosis and pulsed electrical current electrodialysis for improved recovery of dissolved organic matter from seawater

Dissolved organic carbon (DOC) in the oceans is one of the largest dynamic reservoirs of carbon on earth, comparable in size to the atmospheric reservoir of carbon (as CO₂) in the atmosphere, or to the amount of carbon in all terrestrial and aquatic biota. The concerted efforts of earth scientists, atmospheric scientists, and biologists who study global biogeochemical cycles and the earth's climate have yielded a rather detailed understanding of carbon in the atmosphere and in biota. Marine dissolved organic matter (DOM) is far less well characterized, principally because it exists as a highly diluted mixture of perhaps millions of organic compounds in a highly saline aqueous solution. Prior to 2007, only around 1/3 of marine DOM was typically recovered from seawater for research purposes, regardless of the method of isolation. In 2007, reverse osmosis (RO) and electrodialysis (ED) were coupled to achieve recoveries of 64–93% of marine DOM. The level of residual salts in the concentrated samples, however, still precluded the characterization of marine DOM by solid-state NMR, mass spectrometry, or even elemental analysis. This paper describes a major improvement to the RO/ED method, in which pulsed ED is used (at sea) to reach roughly 100-fold greater removal of salts compared to non-pulsed ED while maintaining comparable recoveries of DOM.     

Estimation of the Lipschitz constant of a function

A number of global optimisation algorithms rely on the value of the Lipschitz constant of the objective function. In this paper we present a stochastic method for estimating the Lipschitz constant. We show that the largest slope in a fixed size sample of slopes has an approximate Reverse Weibull distribution. Such a distribution is fitted to the largest slopes and the location parameter used as an estimator of the Lipschitz constant. Numerical results are presented.     

Quantum dots-based reverse phase protein microarray

CdSe nanocrystals, also called quantum dots (Qdots) are a novel class of fluorophores, which have a diameter of a few nanometers and possess high quantum yield, tunable emission wavelength and photostability. They are an attractive alternative to conventional fluorescent dyes. Quantum dots can be silanized to be soluble in aqueous solution under biological conditions, and thus be used in bio-detection. In this study, we established a novel Qdot-based technology platform that can perform accurate and reproducible quantification of protein concentration in a crude cell lysate background. Protein lysates have been spiked with a target protein, and a dilution series of the cell lysate with a dynamic range of three orders of magnitude has been used for this proof-of-concept study. The dilution series has been spotted in microarray format, and protein detection has been achieved with a sensitivity that is at least comparable to standard commercial assays, which are based on horseradish peroxidase (HRP)-catalyzed diaminobenzidine (DAB) chromogenesis. The data obtained through the Qdot method has shown a close linear correlation between relative fluorescence unit and relative protein concentration. The Qdot results are in almost complete agreement with data we obtained with the well-established HRP-DAB colorimetric array (R² = 0.986). This suggests that Qdots can be used for protein quantification in microarray format, using the platform presented here.     

Convexification and Concavification for a General Class of Global Optimization Problems

A kind of general convexification and concavification methods is proposed for solving some classes of global optimization problems with certain monotone properties. It is shown that these minimization problems can be transformed into equivalent concave minimization problem or reverse convex programming problem or canonical D.C. programming problem by using the proposed convexification and concavification schemes. The existing algorithms then can be used to find the global solutions of the transformed problems.