An Elliptic Non Distributive Algebra

In this paper we extend the results of hyperbolic scator algebra introduced in [5], to consider an elliptic product in a subset of ${\mathbb{R}^{1 + n}}$ which recovers the field of complex numbers when only one director component is present. The product of this algebra, that we call elliptic scator algebra in ${\mathbb{E}^{1 + n}}$ , is associative and commutative provided that divisors of zero are excluded. However, as with the hyperbolic case, the elliptic product is not distributive over addition. We explore the geometry of this algebra by considering some interesting objects, such as spheres.     

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.     

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.     

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.     

A Randomized Homotopy for the Hermitian Eigenpair Problem

Foundations of Computational Mathematics - We describe and analyze a randomized homotopy algorithm for the Hermitian eigenvalue problem. Given an $$n\times n$$ Hermitian matrix $$A$$ , the...     

Performance guarantees of local search for minsum scheduling problems

Mathematical Programming - We study the worst-case performance guarantee of locally optimal solutions for the problem of minimizing the total weighted and unweighted completion time on parallel...