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.     

Numerical implementation of coherence for the example of the “Swiss Cross”

Summary We consider the two-dimensional Helmholtz equation u+u=0 inD with the boundary conditionsu=0 on D. D is the Swiss Cross — a region consisting of five unit squares. A method based on the concept of Coherence is utilized to determine an approximation for the first eigenvalue= ₁ more accurate than calculated by classical difference methods. The numerical result is used to illustrate isoperimetric upper and lower bounds for ₁, and to test some conjectures on its relations with torsional rigidity.Dedicated to the memory of Professor Lathar Collatz     

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.     

Functional inequality characterizing nonnegative concave functions in (0, ∞) k

Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned.     

Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

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.     

Excitation of the Characteristic K Series Radiation,Coherent and Incoherent Scatter of Low Energy Gamma Rays

On the basis of a simplified mathematical model there is calculated the probability of a photon of characteristic K series radiation excited by a photon of low energy gamma radiation hitting the detector. There are also included the probabilities for coherently and incoherently scattered primary radiation considering electron binding energies.