A Hyperbolic Non Distributive Algebra in 1 + 2 Dimensions

We introduce a non distributive algebra over the reals in 1 + 2 dimensions that contains the hyperbolic complex algebra ${\mathbb{H}_2}$ . The algebra has divisors of zero that can be avoided by introducing the necessary conditions. Under these conditions, the proposed addition and product operations satisfy group properties. More stringent restrictions sufficient to satisfy group properties separate the algebra in two subspaces. As an application, the composition of velocities in a deformed Lorentz metric is presented. In this approach, Minkowski light cones are deformed into light bipyramids.     

The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces

We study the initial value problem associated to the dispersion generalized Benjamin–Ono equation. Our aim is to establish persistence properties of the solution flow in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model.     

Spontaneous-search method and short-time dynamics: applications to the Domany-Kinzel cellular automaton

The one-dimensional Domany-Kinzel cellular automaton is investigated by two numerical approaches: (i) the spontaneous-search method, which is a method appropriated for a search of criticality; (ii) short-time dynamics. Both critical frontiers of the system are investigated, namely, the one separating the frozen and active phases, as well as the critical line determined by damage spreading between two cellular automata, that splits the active phase into the nonchaotic and chaotic phases. The efficiency of the spontaneous-search method is established herein through a precise estimate of both critical frontiers, and in addition to that, it is shown that this method may also be used in the determination of the critical exponent ν_⊥. Using the critical frontiers obtained, other exponents are estimated through short-time dynamics. It is verified that the critical exponents of both critical frontiers fall in the universality class of directed percolation.     

q-Gaussians in the porous-medium equation: stability and time evolution

The stability of q-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index q_i, approaches asymptotically the final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for the kurtosis evolves in time according to a q-exponential, with a relaxation index q_rel ≡q_rel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (q_i ≥ 5/3) into a finite-variance one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state.     

A structural study of new tetrakis(1H-pyrazol-1-yl)methanes

Tetrakis(1H-pyrazol-1-yl)methanes are very rare compounds of which only two are known: the unsubstituted 1 obtained classically by Hückel in 1937 from carbon tetrachloride and prepared again several times and the 3,5-dimethyl substituted 2 obtained serendipitously by Pombeiro in 2009. We have now extended this group to include four new derivatives 8, 9, 11 and 12 bearing methyl groups. The X-ray crystal structure of the four compounds has been determined. They have been studied by NMR both in solution (¹H, ¹³C, ¹⁵N) and in the solid state (¹³C and ¹⁵N). DFT calculations of the six compounds (geometries, energies and absolute shieldings) have been used to discuss the experimental observations.     

Boron‐Containing Probes for Non‐optical High‐Resolution Imaging of Biological Samples

Boron has been employed in materials science as a marker for imaging specific structures by electron energy loss spectroscopy (EELS) or secondary ion mass spectrometry (SIMS). It has a strong potential in biological analyses as well; however, the specific coupling of a sufficient number of boron atoms to a biological structure has proven challenging. Herein, we synthesize tags containing closo‐1,2‐dicarbadodecaborane, coupled to soluble peptides, which were integrated in specific proteins by click chemistry in mammalian cells and were also coupled to nanobodies for use in immunocytochemistry experiments. The tags were fully functional in biological samples, as demonstrated by nanoSIMS imaging of cell cultures. The boron signal revealed the protein of interest, while other SIMS channels were used for imaging different positive ions, such as the cellular metal ions. This allows, for the first time, the simultaneous imaging of such ions with a protein of interest and will enable new biological applications in the SIMS field.     

Electrochemical Determination of Sunscreens Agents in Cosmetic Using Square Wave Voltammetry

Sunscreen agents and in particular UV filters are compounds added in different cosmetic formulations, that has the function of preventing damage caused by sun exposition. Therefore, this paper proposes the development of a simple, fast and reliable electroanalytical method utilizing square wave voltammetry (SWV) to the determination of Benzophenone‐3 (BZ‐3), camphor 4‐methylbenzylidene (MBC) and 2‐ethylhexyl‐4‐methoxycinnamate (OMC) in cosmetic samples. The electrochemical system consisted of a cell with three electrodes: work – gold electrode modified, reference – Ag/AgCl_(sat) and auxiliary – platinum, using as supporting electrolyte 4.0 mL of Britton Robinson Buffer 0.04 mol L^?1 (pH=4.0), 1.0 mL of methanol and 5.50×10^?4 mol L^?1 of cetyltrimethylammonium bromide (CTAB). The method was validated using three commercial sunscreen samples and the results showed recovery values between 83 and 98 %. The average values found for the analysed samples were 3.49 % m/m (728 mg L^?1) to BZ‐3, 0.56 % m/m (113 mg L^?1) to MBC and 0.99 % m/m (208 mg L^?1) to OMC. The detection (DL) and quantification (QL) limits were 0.47 mg L^?1 and 1.56 mg L^?1 to BZ‐3, 0.77 mg L^?1 and 2.58 mg L^?1 to MBC and 0.78 mg L^?1 and 2.59 mg L^?1 to OMC, respectively. The sunscreen protector samples were also evaluated by high‐performance liquid chromatography (HPLC) demonstrating a good correlation between the results and compared the results with allowed concentration.     

Nanobody‐Conjugated Nanotubes for Targeted Near‐Infrared In Vivo Imaging and Sensing

Fluorescent nanomaterials such as single‐walled carbon nanotubes (SWCNTs) have many advantages in terms of their photophysics, but it is difficult to target them to specific locations in living systems. In contrast, the green fluorescent protein (GFP) has been genetically fused to proteins in many cells and organisms. Therefore, GFP can be seen not only as a fluorophore but as a universal target/handle. Here, we report the conjugation of GFP‐binding nanobodies to DNA‐wrapped SWCNTs. This approach combines the targeting capabilities of GFP‐binding nanobodies and the nonbleaching near‐infrared fluorescence (850–1700 nm) of SWCNTs. These conjugates allow us to track single Kinesin‐5‐GFP motor proteins in developing embryos of Drosophila melanogaster. Additionally, they are sensitive to the neurotransmitter dopamine and can be used for targeted sensing of dopamine in the nm regime.