Varieties of algebras and algebraic varieties

The paper contains a brief account of ideas and results, which are described in [1] and [2] with details and proofs. The subject of the paper is algebraic geometry in arbitrary algebraic structures.     

Nonconventional carbon additions to azomethines. aryl amination/indoline synthesis by direct aryl radical addition to azomethine nitrogen

[reaction: see text]. The generality of a new method for aryl amination has been defined. Ketimines derived from o-bromophenethylamine cyclize to the N-substituted indoline when treated with nBu3SnH and a radical initiator. The pH-neutral conditions tolerate base- and acid-sensitive functionality. The observed regioselectivity is nonconventional for addition reactions involving carbon radicals and carbon-heteroatom pi-bonds.     

Stimuli-Responsive Hydrogel Microcapsules Harnessing the COVID-19 Immune Response for Cancer Therapeutics

The combination of gene therapy and immunotherapy concepts, along recent advances in DNA nanotechnology, have the potential to provide important tools for cancer therapies. We present the development of stimuli-responsive microcapsules, loaded with a viral immunogenetic agent, harnessing the immune response against the Coronavirus Disease 2019, COVID-19, to selectively attack liver cancer cells (hepatoma) or recognize breast cancer or hepatoma, by expression of green fluorescence protein, GFP. The pH-responsive microcapsules, modified with DNA-tetrahedra nanostructures, increased hepatoma permeation by 50 %. Incorporation of a GFP-encoding lentivirus vector inside the tumor-targeting pH-stimulated miRNA-triggered and Alpha-fetoprotein-dictated microcapsules enables the demonstration of neoplasm selectivity, with approximately 5,000-, 8,000- and 50,000-fold more expression in the cancerous cells, respectively. The incorporation of the SARS-CoV-2 spike protein in the gene vector promotes specific recognition of the immune-evading hepatoma by the COVID-19-analogous immune response, which leads to cytotoxic and inflammatory activity, mediated by serum components taken from vaccinated or recovered COVID-19 patients, resulting in effective elimination of the hepatoma (>85 % yield).     

Hornet flight activity and its correlation with UVB radiation, temperature and relative humidity

During the active season, extending from June to October, hornets emerge from their nest in the field in all the daytime hours. In the beginning of the season, when the number of workers is relatively small, the number of exits from the nest is fairly uniform numerically throughout the day. However, with the increase in hornet population from July onwards, the number of workers emerging from the nest entrance around noon (1100-1300 h) is by 1-2 orders of magnitude greater than the number of those emerging in the morning or evening hours. This disparity persists till September or October, at which time the workers revert to behave as in the beginning of the season. It appears, therefore, that in this period hornet activities outside the nest are coordinated with the meteorological conditions, and in this regard, the highest correlation is with the ultra violet B (UVB) radiation level and to a lesser extent with the temperature. Presumably, also, the greater noon-hour activity in the nests of hornets in the field stems from the digging hornets benefiting from the greater availability of solar energy at noon, mainly that of UVB radiation. We assume that the hornets are able to utilize the UVB radiation, but what part of their body is "absorbing" the UVB energy is still a matter of further investigation.     

The Strong Continuity of Convex Functions

A convex function defined on an open convex set of a finite-dimensional space is known to be continuous at every point of this set. In fact, a convex function has a strengthened continuity property. The notion of strong continuity is introduced in this study to show that a convex function has this property. The proof is based on only the definition of convexity and Jensen’s inequality. The definition of strong continuity involves a constant (the constant of strong continuity). An unimprovable value of this constant is given in the case of convex functions. The constant of strong continuity depends, in particular, on the form of a norm introduced in the space of arguments of a convex function. The polyhedral norm is of particular interest. It is straightforward to calculate the constant of strong continuity when it is used. This requires a finite number of values of the convex function.