Higher correlations of divisor sums related to primes II: variations of the error term in the prime number theorem

We calculate the triple correlations for the truncated divisorsum _R(n). The _R(n) behave over certain averages just as theprime counting von Mangoldt function (n) does or is conjecturedto do. We also calculate the mixed (with a factor of (n)) correlations.The results for the moments up to the third degree, and thereforethe implications for the distribution of primes in short intervals,are the same as those we obtained (in the first paper with thistitle) by using the simpler approximation _R(n). However, when_R(n) is used, the error in the singular series approximationis often much smaller than what _R(n) allows. Assuming the GeneralizedRiemann Hypothesis (GRH) for Dirichlet L-functions, we obtainan _±-result for the variation of the error term in theprime number theorem. Formerly, our knowledge under GRH wasrestricted to -results for the absolute value of this variation.An important ingredient in the last part of this work is a recentresult due to Montgomery and Soundararajan which makes it possiblefor us to dispense with a large error term in the evaluationof a certain singular series average. We believe that our resultson the sums _R(n) and _R(n) can be employed in diverse problemsconcerning primes.     

Electrochemical stability of self-assembled alkylphosphate monolayers on conducting metal oxides

Alkylphosphate self-assembled monolayers (SAMs) were prepared on Nb-doped SrTiO(3) (Nb-STO) conducting metal oxide substrates. Unlike thiols on gold, the alkylphosphate SAMs on Nb-STO exhibited an electrochemical stability over a wide voltage range from -2 to 2 V. Cyclic voltammetry showed that the SAM modification inhibited the electrochemical activity of the underlying conducting substrate with an efficiency dependent on the chain length. Impedance spectroscopy showed that SAM-modified Nb-STO substrates have a significantly higher resistance than bare substrates.     

Sodium magnesium amidoborane: the first mixed-metal amidoborane

The first example of a mixed-metal amidoborane Na(2)Mg(NH(2)BH(3))(4) has been successfully synthesized. It forms an ordered arrangement in cation coordinations, i.e., Mg(2+) bonds solely to N(-) and Na(+) coordinates only with BH(3). Compared to ammonia borane and monometallic amidoboranes, Na(2)Mg(NH(2)BH(3))(4) can release 8.4 wt% pure hydrogen with significantly less toxic gases.     

On the coupling of the homotopy perturbation method and Laplace transformation

In this paper, a Laplace homotopy perturbation method is employed for solving one-dimensional non-homogeneous partial differential equations with a variable coefficient. This method is a combination of the Laplace transform and the Homotopy Perturbation Method (LHPM). LHPM presents an accurate methodology to solve non-homogeneous partial differential equations with a variable coefficient. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as HPM, VIM, and ADM. The approximate solutions obtained by means of LHPM in a wide range of the problem’s domain were compared with those results obtained from the actual solutions, the Homotopy Perturbation Method (HPM) and the finite element method. The comparison shows a precise agreement between the results, and introduces this new method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.     

Near‐IR Absorbing BODIPY Derivatives as Glutathione‐Activated Photosensitizers for Selective Photodynamic Action

Enhanced spatiotemporal selectivity in photonic sensitization of dissolved molecular oxygen is an important target for improving the potential and the practical applications of photodynamic therapy. Considering the high intracellular glutathione concentrations within cancer cells, a series of BODIPY‐based sensitizers that can generate cytotoxic singlet oxygen only after glutathione‐mediated cleavage of the electron‐sink module were designed and synthesized. Cell culture studies not only validate our design, but also suggest an additional role for the relatively hydrophobic quencher module in the internalization of the photosensitizer.     

A new approach to separation and pre-concentration of some trace metals with co-precipitation method using a triazole

A new co-precipitation method was developed to separate and pre-concentrate Fe(3+), Cu(2+), Cr(3+), Zn(2+), and Pb(2+) ions using an organic co-precipitant, 3-benzyl-4-p-nitrobenzylidenamino-4,5-dihydro-1,2,4-triazole-5-on (BPNBAT) without adding any carrier element, following flame atomic absorption spectrometric (FAAS) determinations. Effect of some analytical conditions, such as pH of the solution, quantity of the co-precipitant, standing time, centrifugation rate and time, sample volume, and interference of concomitant ions were investigated over the recovery yields of the metal ions. The recoveries of the analyte ions were in the range of 95-102%. The detection limits, corresponding to three times the standard deviation of the blank, were found to be in the range of 0.3-2.0 microg L(-1). The precision of the method, evaluated as the relative standard deviation (R.S.D.) obtained after analyzing a series of 10 replicates, was between 1.6% and 6.0% for the trace metal ions. The method was validated by analyzing two certified reference materials and spiked addition. The proposed procedure was applied for the trace metal ions in some environmental samples.     

Dimensionally stable Nafion–polyethylene composite membranes for direct methanol fuel cell applications

Nafion^® impregnated Solupor^®, microporous UHMWPE film, (N-PE), Nafion^®117 (N117) and a membrane prepared using a DE2020 Nafion^® dispersion (DE2020) were characterized with respect to their swelling degree (SD), methanol cross-over, proton conductivity and DMFC performance at various methanol concentrations in order to understand the effect of impregnation of an ion-conductive polymer membrane to the fuel cell performance.     

Bidirectional switching of near IR emitting boradiazaindacene fluorophores

Two novel distyryl-boradiazaindacene dyes with dimethylaminostyryl and pyridylethenyl substituents display opposite spectral shifts on protonation with TFA in organic solvents. This bidirectional switching of the dyes can be shown to be directly related to ICT donor and acceptor characteristics of the substituents attached to the BODIPY core. The observed spectral response of these dyes could be very useful in the design of novel NIR fluorescent ratiometric probes for pH.     

The effect of concentration on Li diffusivity and conductivity in rutile TiO2

Li transport characteristics are studied by means of density functional theory (DFT) and molecular dynamics (MD) simulations in order to investigate concentration effects on Li chemical diffusivity and conductivity in TiO(2) rutile. Our MD simulations predict one-dimensional diffusion of Li ions via jumps between the octahedral sites along the channels parallel to the c-axis. The diffusion barrier and diffusion coefficient (at room temperature) for the isolated Li, determined by means of DFT calculations, correspond to 60 meV and 9.1 × 10(-6) cm(2) s(-1), respectively. Such a small barrier suggests rapid mass transport along the channels. MD simulations are performed to evaluate the concentration dependent diffusivity profiles. The changes in Li energetics and dynamics are studied as a function of Li content, which is varied primarily between 10% and 50%. In addition, we consider a couple of compositions over 50% although this is above the intercalation limit. Our results suggest that Li diffusivity is strongly dependent on the Li?∶?TiO(2) ratio, and it decreases with increasing Li concentration. For instance, at room temperature, we find Li diffusivity for high concentrations (50% Li) to be three orders of magnitude slower than that for lower concentrations (10% Li). Our analyses on the energetics and dynamics suggest that the changes in the diffusivities originate from successive increases in the barriers with increasing concentration. The decrease in diffusivity as a function of increasing Li content is attributed to the fact that additional Li ions successively block the energetically preferred vacant sites along the channels. Our analyses also show that increasing Li concentration enhances the Li-Li repulsion within the channels, and as a result, diffusion is hindered. We also compare concentration-dependent diffusivities for Li diffusion in anatase, rutile and amorphous TiO(2). Interestingly, we find differing concentration dependence of the diffusivity in these chemically identical but structurally non-equivalent TiO(2) polymorphs. Our study suggests that these differences result from intrinsic structural characteristics of TiO(2) polymorphs, which ultimately contribute to intercalation limit, diffusivity, ionic conductivity, and the electrochemical performance in energy storage applications.