"Extracting" the Key Fragment in ETS-10 Crystallization and Its Application in AM-6 Assembly

The mechanism of crystallization of microporous titanosilicate ETS-10 was investigated by Raman spectroscopy combined with (29) Si magic-angle spinning (MAS) NMR spectroscopy, DFT calculations, and SEM imaging. The formation of three-membered ring species is shown to be the key step in the hydrothermal synthesis of ETS-10. They are formed by means of a complex process that involves the interaction of silicate species in the reaction mixture, which promotes the dissolution of TiO(2) particles. These insights into the mechanism of ETS-10 growth led to the successful development of a new synthesis route to the vanadosilicate AM-6 that involves the use of intermediates that contain three-membered ring species as an initiator.     

Synthesis of oligoribonucleic acid conjugates using a cyclooctyne phosphoramidite

The conjugation of a ribonucleic acid 16-mer with the cationic amphiphilic peptide penetratin and an anionic hyaluronan tetrasaccharide by means of Cu-free "click" chemistry is reported. The alkyne-functionalized 16-mer was prepared by automated solid-phase synthesis, using a newly developed strained cyclooctyne phosphoramidite in the final coupling. Cycloaddition of the alkyne functionalized RNA to the azide containing biomolecules led to a clean conversion into the corresponding nucleic acid conjugates.     

Prophet Regions for Discounted,Uniformly Bounded Random Variables

Abstract

Let X ₁, X ₂,… be any sequence of [0,1]-valued random variables. A complete comparison is made between the expected maximum E(max _j≤n Y _j ) and the stop rule supremum sup _t E Y _t for two types of discounted sequences: (i) Y _j  = b _j X _j , where {b _j } is a nonincreasing sequence of positive numbers with b ₁ = 1; and (ii) Y _j  = B ₁… B _j?1 X _j , where B ₁, B ₂,… are independent [0,1]-valued random variables that are independent of the X _j , having a common mean β. For instance, it is shown that the set of points {(x, y): x = sup _t E Y _{{(x, y): x=sup t E Y} and y = E(max _j≤n Y _j ), for some sequence X ₁,…,X _n and Y _j  = b _j X _j }, is precisely the convex closure of the union of the sets {(b _j x, b _j y): (x, y) ∈ C _j }, j = 1,…,n, where C _j  = {(x, y):0 ≤ x ≤ 1, x ≤ y ≤ x[1 + (j ? 1)(1 ? x ^1/(j?1))]} is the prophet region for undiscounted random variables given by Hill and Kertz [8 Hill , T.P. , and R.P. Kertz . 1983 . Stop rule inequalities for uniformly bounded sequences of random variables . Trans. Amer. Math. Soc. 278 : 197 – 207 . [CSA]  [Google Scholar]]. As a special case, it is shown that the maximum possible difference E(max _j≤n β ^j?1 X _j ) ? sup _t E(β ^t?1 X _t ) is attained by independent random variables when β ≤ 27/32, but by a martingale-like sequence when β > 27/32. Prophet regions for infinite sequences are given also.     

Sister Beiter and Kloosterman: A tale of cyclotomic coefficients and modular inverses

For a fixed prime p$p$, the maximum coefficient (in absolute value) M(p)$M\left(p\right)$ of the cyclotomic polynomial _Φpqr(x)${\Phi }_{pqr}\left(x\right)$, where r$r$ and q$q$ are free primes satisfying r>q>p$r>q>p$ exists. Sister Beiter conjectured in 1968 that M(p)≤(p+1)/2$M\left(p\right)\le (p+1)/2$. In 2009 Gallot and Moree showed that M(p)≥2p(1−?)/3$M\left(p\right)\ge 2p(1-?)/3$ for every p$p$ sufficiently large. In this article Kloosterman sums (‘cloister man sums’) and other tools from the distribution of modular inverses are applied to quantify the abundancy of counter-examples to Sister Beiter’s conjecture and sharpen the above lower bound for M(p)$M\left(p\right)$.     

Hollow silica spheres with an ordered pore structure and their application in controlled release studies

Herein we report the synthesis and characterization of hollow silica spheres with a narrow size distribution, uniform wall thickness, and a worm-like pore structure. The formation of these spheres was monitored by confocal laser scanning microscopy and dynamic light scattering. A model for the molecular build-up of these silica hollow spheres is derived from these data in combination with studies of the as-made particles by transmission electron microscopy, scanning electron microscopy, pore size analysis, thermogravimetric analysis, and solid-state nuclear magnetic resonance. We further demonstrate that these spheres can be used for the encapsulation and subsequent release of different dye molecules.     

Valence-to-core X-ray emission spectroscopy identification of carbide compounds in nanocrystalline Cr coatings deposited from Cr(III) electrolytes containing organic substances

Valence-to-core X-ray emission spectroscopy was applied to study a composition of chromium coatings electrodeposited from Cr(III) sulfate electrolytes with the addition of formic or oxalic acid. It was shown that the obtained crystallographically amorphous deposits contain chromium carbide compounds. These results indicate that nanodimensional Cr crystallites formed during the electrodeposition process are characterized by very high electrocatalytic activity.     

On the presence of Fe(IV) in Fe-ZSM-5 and FeSrO3-x --unequivocal detection of the 3d4 spin system by resonant inelastic X-ray scattering

The contribution of a 3d(4) spin configuration to the valence electronic structure of Fe compounds can be probed via spin-selective Fe K-pre-edge absorption spectra, using resonant inelastic X-ray scattering (RIXS). The 3d(4) configuration of Fe(IV) can be unequivocally detected even in a mixture with the high-spin 3d(5) configuration of Fe(III). This is demonstrated on the perovskite FeSrO(3-x) with formal oxidation state Fe(IV). When the technique was applied to an Fe-ZSM-5 catalyst during reaction with N(2)O, no 3d(4) configuration was detected. The formation of Fe(IV) upon reaction of Fe-ZSM-5 with N(2)O can, therefore, be ruled out.     

Some heuristics and results for small cycles of the discrete logarithm

Brizolis asked the question: does every prime have a pair such that is a fixed point for the discrete logarithm with base ? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on and . In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

     

Growth of ultrathin films of cadmium telluride and tellurium as studied by electrochemical atomic force microscopy

Time dependent, cathodic electrodeposition of ultrathin CdTe and Te films has been studied in 50 mM H(2)SO(4) + 1 mM CdSO(4) + 0.1 mM TeO(2) solutions at room temperature under potential control using electrochemical atomic force microscopy (EC-AFM). The films were also characterized electrochemically and with X-ray diffraction. The growth mechanism and the composition of the films depends on the applied potentials. Island-like growth mode was observed for CdTe films when the deposition potential was -0.35 V (SHE). At a more positive deposition potential of 0.138 V (SHE), Cd was not co-deposited into the film but affected the dynamic growth mode of the deposit. At this voltage smooth Te films were obtained. Depending on the applied potential, Cd acts either as a co-deposition element for CdTe film growth, or as a mediator for layer-by-layer growth of Te films.