KT-nearfields of rank 2

Summary Nearfields of rank 2 over their kernel which are not Dickson nearfields have recently been constructed by H. Zassenhaus. Here it is shown that KT-nearfields of rank 2 over their kernels and of characteristic 2 are necessarily Dickson nearfields which are coupled to quadratic field extensions and their Dickson group is isomorphic to ₂. Using results of Gröger one obtains all KT-nearfields of rank 2 over the field of rational numbers.     

Linear optical properties of frequency doubling polymers

Measurements of linear optical properties of methylmethacrylate copolymers with non-linear optical 4-alkoxy-4-alkylsulfone stilbene side-chains are presented. From there two methods for phase matching are discussed; one aiming to equalize the refractive indices of the fundamental and the second harmnic wave, the other to suppress the destructive character of the interference. The matter of photo stability of frequency doubling polymers is also discussed.     

Laser-induced electron emission from an Au surface irradiated by single picosecond pulses at λ=2.94 μm. The intermediate region between multiphoton and tunneling effects

The photoinduced electron emission from the surface of a solid gold target irradiated by single picosecond pulses of an erbium laser is investigated. The applied laser intensity (5–120 GW/cm²) corresponds to the intermediate interaction region between the pure multiphoton and tunnel effects, where the decisive Keldysh-parameter, , is in the range 1<<12=n ₀. In the light intensity region which is free of surface heating (I _L<80 GW/cm²), the slope of the measured logarithmic intensity dependence of the photocurrent decreases from the n ₀=12 perturbative value down to n 5. Therefore the experiment shows that the Keldysh-type theories, which have recently been proved to describe correctly the ionization of atoms, are also valid to a certain extent in the case of the photoeffect in metals.     

A contribution to shape theory for the ising model at low temperature

Summary We consider low temperature limits of Gibbs states of the ferromagnetic nearest-neighbour Ising Hamiltonian in the positive orthant of the lattice ^d ,d=1, 2,..., under a negative boundary condition and a small positive external fieldh that decreases linearly with the temperatureT. It is shown that positive and negative spins are separated by a staircase-shaped random boundary. Its explicit distribution is computed in the case that the ratio =h/T exceeds some positive ₀. For < ₀, our results do not rule out infinite negative areas.     

Shock fluctuations in asymmetric simple exclusion

Summary The one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumpsp>q to the right and left, respectively, and with initial product measure with densities < to the left and right of the origin, respectively (with shock initial conditions). We prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times. If this particle is added at another site, then it describes the behavior of a characteristic of the Burgers equation. For vanishing left density (=0) we prove, in the scale t^1/2, that the position of the shock at timet depends only on the initial configuration in a region depending ont. The proofs are based on laws of large numbers for the second class particle.     

The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket

The authors rigorously prove that the exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket is

Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.     

Hydrogen-Related Paramagnetic Centers in Ge-Doped Sol-Gel Silica Induced by γ-Ray Irradiation

We have studied the generation mechanisms of H(II) paramagnetic centers in Ge-doped silica by investigating up to 10⁴ mol ppm sol-gel Ge-doped silica materials. We have considered materials with the same concentrations of Ge but that are produced by two different densification routes that give rise to different concentrations of Ge-related oxygen deficient centers (GeODC(II)). These centers are characterized by an optical absorption band at ∼5.2 eV (B_2β band) and two related emissions at ∼3.2 eV and ∼4.3 eV. The GeODC(II) content was estimated by absorption and emission measurements. The H(II) centers were induced by room temperature γ-ray irradiation and their concentration was determined by electron paramagnetic resonance measurements. The comparison between the two kinds of materials, obtained by different preparations, shows that the GeODC(II) concentration increases with the Ge content and is enhanced by vacuum densification. The comparison of irradiated samples shows that beyond the already known process of conversion of preexisting GeODC(II) into H(II) centers, another generation process of H(II) centers is effective that involves irradiation induced GeODC(II).     

Infrared spectra of two sexithiophenes in neutral and doped states: a theoretical and spectroscopic study

The FT-infrared spectra of two sexithiophenes having their end ,′-positions substituted by n-hexyl or -thiohexyl groups, in neutral and doped states, are studied with the main aim of deriving information about the π-electrons delocalization and about the electronic structure of the charged defects created upon doping with iodine. The analysis of the experimental data is aided by Density Functional Theory calculations. The modifications in the electronic structure of the sexithiophene backbone induced by the n-thiohexyl encapsulation are discussed from the point of view of single molecule interactions in thiol-terminated π-conjugated oligomers bound to metallic or cluster electrodes.     

K18- and CAG-hACE2 Transgenic Mouse Models and SARS-CoV-2: Implications for Neurodegeneration Research

COVID-19, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a global pandemic that might lead to very serious consequences. Notably, mental status change, brain confusion, and smell and taste disorders along with neurological complaints have been reported in patients infected with SARS-CoV-2. Furthermore, human brain tissue autopsies from COVID-19 patients show the presence of SARS-CoV-2 neuroinvasion, which correlates with the manifestation of meningitis, encephalitis, leukocyte infiltration, and neuronal damage. The olfactory mucosa has been suggested as a way of entry into the brain. SARS-CoV-2 infection is also known to provoke a hyper-inflammatory reaction with an exponential increase in the production of pro-inflammatory cytokines leading to systemic responses, even in the absence of direct infection of brain cells. Angiotensin-converting enzyme 2 (ACE2), the entry receptor of SARS-CoV-2, has been extensively demonstrated to be present in the periphery, neurons, and glial cells in different brain regions. To dissect the details of neurological complications and develop therapies helping COVID-19 survivors regain pre-infection quality of life, the development of robust clinical models is highly warranted. Several human angiotensin-converting enzyme 2 (hACE2) transgenic mouse models have been developed and used for antiviral drug screening and vaccine development, as well as for better understanding of the molecular pathogenetic mechanisms of SARS-CoV-2 infection. In this review, we summarize recent results from the studies involving two such mouse models, namely K18- and CAG-hACE2 transgenics, to evaluate the direct and indirect impact of SARS-CoV-2 infection on the central nervous system.