Gravitational Field Equations on Fefferman Space–Times

The total space \({\mathfrak M} \approx {\mathbb H}_1 \times S^1\) of the canonical circle bundle over the 3-dimensional Heisenberg group \({\mathbb H}_1\) is a space–time with the Lorentzian metric \(F_{\theta _0}\) (Fefferman’s metric) associated to the canonical Tanaka–Webster flat contact form \(\theta _0\) on \({\mathbb H}_1\). The matter and energy content of \(\mathfrak M\) is described by the energy-momentum tensor \({T}_{\mu \nu }\) (the trace-less Ricci tensor of \(F_{\theta _0}\)) as an effect of the non flat nature of Feferman’s metric \(F_{\theta _0}\). We study the gravitational field equations \(R_{\mu \nu } - (1/2) \, R \, g_{\mu \nu } = {T}_{\mu \nu }\) on \({\mathfrak M}\). We consider the first order perturbation \(g = F_{\theta _0} + \epsilon \, h\), \(\epsilon<< 1\), and linearize the field equations about \(F_{\theta _0}\). We determine a Lorentzian metric g on \({\mathfrak M}\) which solves the linearized field equations corresponding to a diagonal perturbation h.     

Approximation by the Complex form of a Link Operator Between the Phillips and the Szász–Mirakjan Operators

Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho &gt;...     

Fluctuation forces in a three-layer medium with rough boundaries. III. Aspects of perturbation theory in the Casimir range

The problem of calculating the Casimir force that acts in a system of two metallic plates with rough boundaries separated by an insulating layer is considered. An algorithm for constructing a perturbation series in the small function of the roughness profile is developed.Scientific Council on the Problem Complex Kibernetika, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 3, pp. 474–482, June, 1992.     

Green light radiation effects on free radicals inhibition in cellular and chemical systems

Free radicals generation is inhibited through green light (GL) irradiation in cellular systems and in chemical reactions. Standard melanocyte cultures were UV-irradiated and the induced cellular reactive oxygen species (ROS) were quantified by the fluorescence technique. The same cell cultures, previously protected by a 24h GL exposure, displayed a significantly lower ROS production. A simple chemical reaction is subsequently chosen, in which the production of free radicals is well defined. Paraffin wax and mineral oil were GL irradiated during thermal degradation and the oxidation products checked by chemiluminescence [CL] and Fourier transform infrared spectra [FT-IR]. The same clear inhibition of the radical oxidation of alkanes is recorded. A quantum chemistry modeling of these results is performed and a mechanism involving a new type of Rydberg macromolecular systems with implications for biology and medicine is suggested.