Sorption of nicotinic and isonicotinic acids by the strongly basic anion exchanger АВ-17-8

Thermodynamics and kinetics of sorption with the participation of nicotinic and isonicotinic acids on the strongly basic anion exchanger АВ-17-8 were studied. According to calorimetric measurements, partial (differential) heat of sorption was estimated for anions and zwitterions of pyridinecarboxylic acids upon sorption by the OH-form of the anion exchanger AB-17-8 at 298K. Sorption of zwitterions of pyridinecarboxylic acids by the OH-form of the strongly basic anion exchanger can be presented as the process that involves independent reactions of ion exchange, dissociation of pyridinecarboxylic acid, and neutralization. The kinetics of sorption on the strongly basic anion exchanger with the participation of nicotinic and isonicotinic acids is shown to be controlled by the slow diffusion of the components in the polymer phase. For the organic anion in the phase of the anion exchanger АВ-17-8, the diffusion coefficient is equal to (1.3±0.4)?10^–12 m² s^–1.     

On the construction of multivariate (pre)wavelets

A new approach for the construction of wavelets and prewavelets onR ^d from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors fromL ₂(R ^d ) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the union of a scale of spaces to be used in a multiresolution.     

Entropy of Stationary Measures and Bounded Tangential de-Rham Cohomology of Semisimple Lie Group Actions

Let G be a connected noncompact semisimple Lie group with finite center, K a maximal compact subgroup, and X a compact manifold (or more generally, a Borel space) on which G acts. Assume that ν is a μ -stationary measure on X, where μ is an admissible measure on G, and that the G-action is essentially free. We consider the foliation of K\ X with Riemmanian leaves isometric to the symmetric space K\ G, and the associated tangential bounded de-Rham cohomology, which we show is an invariant of the action. We prove both vanishing and nonvanishing results for bounded tangential cohomology, whose range is dictated by the size of the maximal projective factor G/Q of (X, ν). We give examples showing that the results are often best possible. For the proofs we formulate a bounded tangential version of Stokes’ theorem, and establish a bounded tangential version of Poincaré’s Lemma. These results are made possible by the structure theory of semisimple Lie groups actions with stationary measure developed in Nevo and Zimmer [Ann of Math. 156, 565--594]. The structure theory assert, in particular, that the G-action is orbit equivalent to an action of a uniquely determined parabolic subgroup Q. The existence of Q allows us to establish Stokes’ and Poincaré’s Lemmas, and we show that it is the size of Q (determined by the entropy) which controls the bounded tangential cohomology. Supported by BSF and ISF. Supported by BSF and NSF.     

A structure theorem for boundary-transitive graphs with infinitely many ends

We prove a structure theorem for locally finite connected graphsX with infinitely many ends admitting a non-compact group of automorphisms which is transitive in its action on the space of ends, Ω _X . For such a graphX, there is a uniquely determined biregular treeT (with both valencies finite), a continuous representationφ : Aut(X) → Aut(T) with compact kernel, an equivariant homeomorphism λ : Ω _X → Ω _T , and an equivariant map τ : Vert(X) → Vert(T) with finite fibers. Boundary-transitive trees are described, and some methods of constructing boundary-transitive graphs are discussed, as well as some examples.     

Real-time four-dimensional optical-resolution photoacoustic microscopy with Au nanoparticle-assisted subdiffraction-limit resolution

Photoacoustic microscopy (PAM) offers label-free, optical absorption contrast. A high-speed, high-resolution PAM system in an inverted microscope configuration with a laser pulse repetition rate of 100,000 Hz and a stationary ultrasonic transducer was built. Four-dimensional in vivo imaging of microcirculation in mouse skin was achieved at 18 three-dimensional volumes per second with repeated two-dimensional (2D) raster scans of 100 by 50 points. The corresponding 2D B-scan (50 A-lines) frame rate was 1800 Hz, and the one-dimensional A-scan rate was 90,000 Hz. The lateral resolution is 0.23 ± 0.03 μm for Au nanowire imaging, which is 2.0 times below the diffraction limit.     

Some numerical results on best uniform rational approximation ofx α on [0,1]

Let be a positive number, and letE _n,n (x ;[0,1]) denote the error of best uniform rational approximation from _n,n tox on the interval [0,1]. We rigorously determined the numbers {E _n,n (x ;[0,1])} _n ^=1/30 for six values of in the interval (0, 1), where these numbers were calculated with a precision of at least 200 significant digits. For each of these six values of , Richardson's extrapolation was applied to the products to obtain estimates of

Hydrogen from Formic Acid through Its Selective Disproportionation over Sodium Germanate—A Non‐Transition‐Metal Catalysis System

A robust catalyst for the selective dehydrogenation of formic acid to liberate hydrogen gas has been designed computationally, and also successfully demonstrated experimentally. This is the first such catalyst not based on transition metals, and it exhibits very encouraging performance. It represents an important step towards the use of renewable formic acid as a hydrogen‐storage and transport vector in fuel and energy applications.