Differential Equations with Infinitely Many Derivatives and the Borel Transform

Differential equations with infinitely many derivatives, sometimes also referred to as “nonlocal” differential equations, appear frequently in branches of modern physics such as string theory, gravitation and cosmology. We properly interpret and solve linear equations in this class with a special focus on a solution method based on the Borel transform. This method is a far-reaching generalization of previous studies of nonlocal equations via Laplace and Fourier transforms, see for instance (Barnaby and Kamran, J High Energy Phys 02:40, 2008; Górka et al., Class Quantum Gravity 29:065017, 2012; Górka et al., Ann Henri Poincaré 14:947–966, 2013). We reconsider “generalized” initial value problems within the present approach and we disprove various conjectures found in modern physics literature. We illustrate various analytic phenomena that can occur with concrete examples, and we also treat efficient implementations of the theory.     

Antioxidant capacity and in vitro prevention of dental plaque formation by extracts and condensed tannins of Paullinia cupana

Chemical evaluation of the semi-purified fraction from the seeds of guaraná, Paullinia cupana H.B.K. var. sorbilis (Mart.) Ducke, yielded the following compounds: caffeine, catechin, epicatechin, ent-epicatechin, and procyanidins B1, B2, B3, B4, A2, and C1. Measurement of the antioxidant activity by reduction of the DPPH radical confirmed the anti-radical properties of the aqueous (AqE) and crude (EBPC) extracts and semi-purified (EPA and EPB) fractions. The EPA fraction showed radical-scavenging activity (RSA) and protected DPPH from discoloration at 5.23 +/- 0.08 (RSD% = 1.49) microg/mL, and for the phosphomolybdenum complex showed a higher Relative Antioxidant Capacity (RAC) at 0.75 +/- 0.01 (1.75). The EPA fraction had a total polyphenolics content of 65.80% +/- 0.62 (RSD% = 0.93). The plant drug showed 5.47% +/- 0.19 (RSD% = 3.51) and 6.19% +/- 0.08 (RSD% = 1.29) for total polyphenolics and methylxanthines, respectively. In vitro assessment of the antibacterial potential of the Paullinia cupana extracts against Streptococcus mutans showed that these could be used in the prevention of bacterial dental plaque.     

Gas phase activation energy for unimolecular dissociation of biomolecular ions determined by focused RAdiation for gaseous multiphoton ENergy transfer (FRAGMENT)

We present a novel approach for the determination of activation energy for the unimolecular dissociation of a large (>50 atoms) ion, based on measurement of the unimolecular dissociation rate constant as a function of continuous-wave CO(2) laser intensity. Following a short ( approximately 1 s) induction period, CO(2) laser irradiation produces an essentially blackbody internal energy distribution, whose 'temperature' varies inversely with laser intensity. The only currently available method for measuring such activation energies is blackbody infrared radiative dissociation (BIRD). Compared with BIRD, FRAGMENT: (a) eliminates the need to heat the surrounding ion trap and vacuum chamber to each of several temperatures (each requiring hours for temperature equilibration); (b) offers a three-fold wider range of effective blackbody temperature; and (c) extends the range of applications to include initially cold ions (e.g., gas-phase H/D exchange). Our FRAGMENT-determined activation energy for dissociation of protonated bradykinin, 1.2 +/- 0.1 eV, agrees within experimental error to the value, 1.3 +/- 0.1 eV, previously reported by Williams et al. from BIRD experiments. Copyright 1999 John Wiley & Sons, Ltd.     

Spacecraft motion around artificial equilibrium points

The main goal of this paper is to describe the motion of a spacecraft around an artificial equilibrium point in the circular restricted three-body problem. The spacecraft is under the gravitational influence of the Sun and the Earth, as primary and secondary bodies, subjected to the force due to the solar radiation pressure and some extra perturbations. Analytical solutions for the equations of motion of the spacecraft are found using several methods and for different extra perturbations. These solutions are strictly valid at the artificial equilibrium point, but they are used as approximations to describe the motion around this artificial equilibrium point. As an application of the method, the perturbation due to the gravitational influence of Jupiter and Venus is added to a spacecraft located at a chosen artificial equilibrium point, near the \(L_3\) Lagrangian point of the Sun–Earth system. The system is propagated starting from this point using analytical and numerical solutions. Comparisons between analytical–analytical and analytical–numerical solutions for several kinds of perturbations are made to guide the choice of the best analytical solution, with the best accuracy.     

A numerical mapping of energy gains in a powered Swing-By maneuver

The present paper studies the effects of a powered Swing-By maneuver, considering the particular and important situations where there are energy gains for the spacecraft. The objective is to map the energy variations obtained from this maneuver as a function of the three parameters that identify the pure gravity Swing-By with a fixed mass ratio (angle of approach, periapsis distance and velocity at periapsis) and the three parameters that define the impulsive maneuver (direction, magnitude and the point where the impulse is applied). The mathematical model used here is the version of the restricted three-body problem that includes the Lemaître regularization, to increase the accuracy of the numerical integrations. It is developed and implemented by an algorithm that obtains the energy variation of the spacecraft with respect to the largest primary of the system in a maneuver where the impulse is applied inside the sphere of influence of the secondary body, during the passage of the spacecraft. The point of application of the impulse is a free parameter, as well as the direction of the impulse. The results make a complete map of the possibilities, including the maximum gains of energy, but also showing alternatives that can be used considering particularities of the mission.     

A simple two steps ytterbium triflate‐catalysed preparation of 2,2‐dimethyl‐2h‐chromenes from salicylaldehydes and 2‐methylpropene

The preparation of various 2,2‐dimethyl‐2H‐chromenes was achieved in two steps via an ytterbium triflate‐catalysed reaction between salicylaldehydes, trimethylorthoformate and 2‐methylpropene. From salicylaldehyde, two reaction products were characterised: 4‐methoxy‐2,2‐dimethylchroman and 2‐(1,3‐dimethoxy‐3‐methylbutyl)phenol. The former compound probably results from a Lewis acid‐catalysed [2+4] cycloaddition between the intermediate quinonemethide and 2‐methylpropene whereas the latter may occur via a reaction related to a carbonyl‐ene reaction between the quinonemethide and 2‐methylpropene. Both compounds were subjected to a catalytic acidic treatment leading to 2,2‐dimethyl‐2H‐chromene. Starting from various salicylaldehydes, the scope of this method was investigated.     

Estimation-induced correlations of the Zernike coefficients of the eye aberration

The statistical properties of the estimated eye aberrations differ in general from the actual ones owing to the cross coupling and aliasing generated in the estimation process. In particular, the estimated Zernike aberration coefficients may show fictitious correlations that are not present in the incoming wavefronts. This fact should be taken into account when analyzing estimated aberration datasets, searching for correlations related to physiological eye features. We give an analytical model for this effect and evaluate its magnitude for a particular example, assuming that the true aberration statistics follows a Kolmogorov power law.