Unified fields in pentadimensional theory

The theory of Jordan-Thiry is investigated by using a five-dimensional Riemannian manifold V₅ which admits a one-parameter group of isometries. The set of trajectories is supposed to represent the space-time of Relativity.The use of the induced metric in the quotient space leads to essential difficulties. It is necessary to consider a conformal metric and to modify the energy tensor in order to obtain the classical results of relativistic celestial mechanics. Moreover, the conformal metric brings out the evident interpretation of the fifteenth potential like a massless scalar field.A mass term referring to the scalar field is introduced; then the gravitational, electromagnetic, and mesonic scalar fields are unified through the metric of V₅. Several results make the new theory very coherent; in particular, the exact relativistic equations of motion are obtained asymptotically when the matter density vanishes.Exact solutions are searched. The classical Schwarzschild solution and neighbouring solutions are valid in the interior of the matter. Special non-static solutions are also obtained; some of these may be interpreted locally as describing the “collapse” of neutron stars; others ones, analogous to Robertson's metric, can be used to build a cosmology of the unified field.     

Anisotropic surface effects in Au and Cu monocrystals

Electroreflectance spectra at normal incidence of (100) and (110) faces of gold and copper monocrystals are given, in the spectral range from 0.22–0.7 μm. The fractional change in reflectance is different with (110) faces when light is polarized parallel to the [001] direction and parallel to the [$\text{1}\text{10}$] direction while no anisotropy is seen on (100) faces. This shows that electroreflectance is a powerful tool to investigate metal surfaces where the optical electrons are sensitive to the distribution of the surface atoms.     

F/Si distance determination in fluoride-containing octadecasil by Hartmann–Hahn cross-polarization under fast magic-angle spinning

¹⁹F/²⁹Si Hartmann–Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated ²⁹Si–¹⁹F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si–F internuclear distance, r=2.62±0.05 Å, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69±0.04 Å recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of 14 kHz is shown to be necessary for an effective suppression of ¹⁹F–¹⁹F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.     

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

Divergent Synthesis of Bioactive Dithiodiketopiperazine Natural Products Based on a Double C(sp3)−H Activation Strategy

This article provides a detailed report of our efforts to synthesize the dithiodiketopiperazine (DTP) natural products (−)-epicoccin G and (−)-rostratin A using a double C(sp³)−H activation strategy. The strategy's viability was first established on a model system lacking the C8/C8’ alcohols. Then, an efficient stereoselective route including an organocatalytic epoxidation was secured to access a key bis-triflate substrate. This bis-triflate served as the functional handles for the key transformation of the synthesis: a double C(sp³)−H activation. The successful double activation opened access to a common intermediate for both natural products in high overall yield and on a multigram scale. After several unsuccessful attempts, this intermediate was efficiently converted to (−)-epicoccin G and to the more challenging (−)-rostratin A via suitable oxidation/reduction and protecting group sequences, and via a final sulfuration that occurred in good yield and high diastereoselectivity. These efforts culminated in the synthesis of (−)-epicoccin G and (−)-rostratin A in high overall yields (19.6 % over 14 steps and 12.7 % over 17 steps, respectively), with the latter being obtained on a 500 mg scale. Toxicity assessments of these natural products and several analogues (including the newly synthesized epicoccin K) in the leukemia cell line K562 confirmed the importance of the disulfide bridge for activity and identified dianhydrorostratin A as a 20x more potent analogue.     

The commutative cohomology of nilmonoids,revisited

Semigroup Forum - A nilmonoid is a nilsemigroup N with an identity element adjoined. New properties of the canonical presentation of N yield a more precise characterization of 2-cocycles,...     

A door to model reduction in high-dimensional parameter space

Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.