RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Random Activations in Primal-Dual Splittings for Monotone Inclusions with a Priori Information

Journal of Optimization Theory and Applications - In this paper, we propose a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a...     

HPLC monitored synthesis of R2NCH2 substituted benzene derivatives used as (C,N)-ligands for organometallic compounds

2-(Diethylaminomethyl)phenyl bromide and 1,3-bis(dimethylaminomethyl)-benzene, useful ligands for the synthesis of hypervalent organometallic compounds, were prepared and characterized by NMR (¹H, ¹³C, 2D experiments) spectroscopy. Their synthesis was monitored by the HPLC method. The compounds were eluted on a Nucleosil 120 Si column (5 μm, 25×0.4 cm) with n-hexane at room temperature using a 1.0 ml/min flow-rate. The maximum values of absorbance for the studied compounds, excepting the diethylamine, were located in a narrow range around 212 nm, the wavelength used for their UV detection. The diethylamine was detected at 190 nm. The calibration curves are straight lines with correlation factors r>0.995. The HPLC data are in good agreement with those provided by NMR spectroscopy.     

Mass Balance and Compositional Analysis of Biomass Outputs from Cacao Fruits

The global chocolate value chain is based exclusively on cacao beans (CBs). With few exceptions, most CBs traded worldwide are produced under a linear economy model, where only 8 to 10% of the biomass ends up in chocolate-related products. This contribution reports the mass balance and composition dynamics of cacao fruit biomass outputs throughout one full year of the crop cycle. This information is relevant because future biorefinery developments and the efficient use of cacao fruits will depend on reliable, robust, and time-dependent compositional and mass balance data. Cacao husk (CH), beans (CBs), and placenta (CP) constitute, as dry weight, 8.92 ± 0.90 wt %, 8.87 ± 0.52 wt %, and 0.57 ± 0.05 wt % of the cacao fruit, respectively, while moisture makes up most of the biomass weight (71.6 ± 2.29 wt %). CH and CP are solid lignocellulosic outputs. Interestingly, the highest cellulose and lignin contents in CH coincide with cacao’s primary harvest season (October to January). CB contains carbohydrates, fats, protein, ash, and phenolic compounds. The total polyphenol content in CBs is time-dependent, reaching maxima values during the harvest seasons. In addition, the fruit contains 4.13 ± 0.80 wt % of CME, a sugar- and nutrient-rich liquid output, with an average of 20 wt % of simple sugars (glucose, fructose, and sucrose), in addition to minerals (mainly K and Ca) and proteins. The total carbohydrate content in CME changes dramatically throughout the year, with a minimum of 10 wt % from August to January and a maximum of 29 wt % in March.     

Self-similarities in the frequency-amplitude space of a loss-modulated CO2 laser

We show the standard two-level continuous-time model of loss-modulated CO2 lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. Our results suggest that the two-parameter space of class B laser models and that of a certain class of discrete mappings could be isomorphic.     

Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

Intermediate-temperature polymorphic phase transition in KH2PO4: A synchrotron X-ray diffraction study

We have used synchrotron X-ray diffraction to investigate the structural and chemical changes undergone by polycrystalline KH₂PO₄ (KDP) upon heating within the 30-250 °C temperature interval. Our data show evidence of a polymorphic transition at T∼190 °C from the room-temperature tetragonal KDP phase to a new intermediate-temperature monoclinic KDP modification (spacegroup P2₁/m and lattice parameters a=7.590, b=6.209, c=4.530 Å, and β=107.36°). The monoclinic RDP polymorph remains stable upon further heating to 235 °C, and is isomorphic to its RbH₂PO₄ and CsH₂PO₄ counterparts.     

Skew Schubert polynomials

We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schubert polynomials with nonnegative integer coefficients that are precisely the structure constants of the cohomology of the complex flag variety with respect to its basis of Schubert classes. We rederive the construction of Bergeron and Sottile in a purely combinatorial way, relating it to the construction of Schubert polynomials in terms of rc-graphs.

     

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories

We show an accurate procedure to obtain a Fourier transform (FT) with no dc term using a commercial twisted-nematic liquid-crystal display. We focus on the application to holographic storage of binary data pages, where a drastic decrease of the dc term in the FT is highly desirable. Two different codification schemes are considered: binary pi radians phase modulation and hybrid ternary modulation. Any deviation in the values of the amplitude and phase shift generates the appearance of a strong dc term. Experimental results confirm that the calculated configurations provide a FT with no dc term, thus showing the effectiveness of the proposal.