Greedy wavelet projections are bounded on BV

Let be the space of functions of bounded variation on with . Let , , be a wavelet system of compactly supported functions normalized in , i.e., , . Each has a unique wavelet expansion with convergence in . If is the set of indicies for which are largest (with ties handled in an arbitrary way), then is called a greedy approximation to . It is shown that with a constant independent of . This answers in the affirmative a conjecture of Meyer (2001).

     

Copolyethers with controlled structure: Mechanism of formation and microstructure

Cationic copolymerization of 3-membered cyclic ethers (oxiranes) with 5-membered cyclic ether (tetrahydrofuran) leads to linear copolyethers containing significant amount of cyclic fraction. When the copolymerization is conducted in the presence of diols, telechelic copolymers are formed by the process in which oxirane is incorporated into copolymer irreversibly by Activated Monomer mechanism, while tetrahydrofuran is incorporated reversibly by Active Chain End mechanism. Thus both kinetic and thermodynamic factors can be used to control the rate of the incorporation of comonomers. Studies of the kinetics of the competing reactions leading to formation of copolymer, studies of copolymer microstructure by ¹³C-NMR and analysis of the composition of the cyclic fraction, led to the correlation between the copolymer microstructure and the amount of cyclic fraction formed. The dependence of the cyclic fraction content on the reaction conditions was therefore explained.     

Branched polyether with multiple primary hydroxyl groups: polymerization of 3-ethyl-3-hydroxymethyloxetane

Cationic polymerization of 3-ethyl-3-hydroxymethyloxetane gives branched, soluble macromolecules with multiple glycolic end groups. There are approximately 3–4 “normal” units per one branched unit.     

Identification of friction in inerter with constant and variable inertance

Meccanica - This paper presents the experimental identification of the friction force in the inerter with constant and variable inertance. The change of intertance is possible due to the...     

Assessing the Productivity of the Direct Conversion of Methane-to-Methanol over Copper-Exchanged Zeolite Omega (MAZ) via Oxygen Looping

The methane-to-methanol (MtM) conversion via the oxygen looping approach using copper-exchanged zeolites has been extensively studied over the last decade. While a lot of research has focussed on maximizing yield and selectivity, little has been directed toward productivity—a metric far more meaningful for evaluating industrial potential. Using copper-exchanged zeolite omega (Cu-omega), a material highly active and selective for the MtM conversion using the isothermal oxygen looping approach, we show that this material exhibits unprecedented potential for industrial valorization. In doing so, we also present a novel methodology combining operando XAS and mass spectrometry for the screening of materials for the MtM conversion in oxygen looping mode.     

Natural radioactivity in groundwater--a review

The issue of natural radioactivity in groundwater is reviewed, with emphasis on those radioisotopes which contribute in a significant way to the overall effective dose received by members of the public due to the intake of drinking water originating from groundwater systems. The term 'natural radioactivity' is used in this context to cover all radioactivity present in the environment, including man-made (anthropogenic) radioactivity. Comprehensive discussion of radiological aspects of the presence of natural radionuclides in groundwater, including an overview of current regulations dealing with radioactivity in drinking water, is provided. The presented data indicate that thorough assessments of the committed doses resulting from the presence of natural radioactivity in groundwater are needed, particularly when such water is envisaged for regular intake by infants. They should be based on a precise determination of radioactivity concentration levels of the whole suite of radionuclides, including characterisation of their temporal variability. Equally important is a realistic assessment of water intake values for specific age groups. Only such an evaluation may provide the basis for possible remedial actions.     

Impedance studies of porous lanthanum-phosphate-bonded nickel electrodes in concentrated sodium hydroxide solution

The hydrogen evolution reaction (HER) was investigated on a lanthanum-phosphate-bonded nickel (LPBN) powder electrode in 30 wt.% NaOH at 70°C using ac impedance and steady-state polarization techniques. Circuits containing one or two constant-phase elements (CPEs) in parallel with a resistance and corresponding to fractal and porous electrode models were tested in order to interpret the ac impedance data. The experimental impedance spectra were well described by the porous electrode model and the circuit containing two CPEs. The results obtained from the ac impedance and steady-state measurements allowed the mechanism and kinetics of the HER to be evaluated. Comparison of these parameters with those obtained on the polycrystalline nickel electrode in 1 M alkaline solution at 25°C indicates that an increase in activity is principally due to an increase in the real surface area.     

Instance-optimality in probability with an -minimization decoder

Let Φ(ω), ωΩ, be a family of n×N random matrices whose entries _i,j are independent realizations of a symmetric, real random variable η with expectation and variance . Such matrices are used in compressed sensing to encode a vector by y=Φx. The information y holds about x is extracted by using a decoder . The most prominent decoder is the ℓ₁-minimization decoder Δ which gives for a given the element which has minimal ℓ₁-norm among all with Φz=y. This paper is interested in properties of the random family Φ(ω) which guarantee that the vector will with high probability approximate x in to an accuracy comparable with the best k-term error of approximation in for the range kan/log₂(N/n). This means that for the above range of k, for each signal , the vector satisfies

with high probability on the draw of Φ. Here, Σ_k consists of all vectors with at most k nonzero coordinates. The first result of this type was proved by Wojtaszczyk [P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math., in press] who showed this property when η is a normalized Gaussian random variable. We extend this property to more general random variables, including the particular case where η is the Bernoulli random variable which takes the values with equal probability. The proofs of our results use geometric mapping properties of such random matrices some of which were recently obtained in [A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491–523].     

Kinetics and mechanism of H+(aq)-assisted aquation of [Cr(N3)(S-pdtra)]− and [Cr(N3(edtrp)]−ions

Two new complex anions, [Cr(N3)(S-pdtra)]– and [Cr(N3)(edtrp)]–, were obtained in solution by N3–/HN3 anation of the aqua analogues (S-pdtra = S-propane-1,2-diamine-N,N,N-triacetate, edtrp = ethylenediamine-N,N,N-tripropionate). Aquation of these species in acidic media leads to the same geometrical isomers as those used for the synthesis. The aquation rate is strongly dependent upon [H] and is substantially higher in D2O than in H2O. Protonation of the coordinated azide was not observed spectrophotometrically. The rate law and activation parameters have been determined and discussed.