Wall-Crossing in Coupled 2d-4d Systems

We introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS states in an N=2 supersymmetric 4d gauge theory coupled to a supersymmetric surface defect. When the theory and defect are compactified on a circle, we get a 3d theory with a supersymmetric line operator, corresponding to a hyperholomorphic connection on a vector bundle over a hyperkahler space. The 2d-4d wall-crossing formula can be interpreted as a smoothness condition for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can be determined for 4d theories of class S, that is, for those theories obtained by compactifying the six-dimensional (0,2) theory with a partial topological twist on a punctured Riemann surface C. For such theories there are canonical surface defects. We illustrate with several examples in the case of A_1 theories of class S. Finally, we indicate how our results can be used to produce solutions to the A_1 Hitchin equations on the Riemann surface C.Comment: 170 pages, 45 figure

Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto

STUDY OF SENSORS FOR DETECTING EXPLOSIVE SUBSTANCES

Results of the study of sensitivity of fluorescent сhemosensory substances to impact of nitroaromatic explosives and synthesis methods are described

ELECTROCHEMICAL DETERMINATION OF NITROBENZENE IN HONEY SAMPLES ON A GLASS-CARBON ELECTRODE MODIFIED WITH CNT AND DERIVATIVES OF 1,3- / 1,4-DIAZINES

In this work, the effect of modification of a glassy carbon electrode with CNTs and 1,3-1,4-diazine derivatives on the electrochemical reduction of nitrobenzene was investigated

DEVICE FOR NITROAROMATIC SUBSTANCE DETECTING AND IDENTIFICATION

Designing and modeling of optic-related part of device for nitroaromatic substance detection are described

Strong protective effect of the APOL1 p.N264K variant against G2-associated focal segmental glomerulosclerosis and kidney disease

African Americans have a significantly higher risk of developing chronic kidney disease, especially focal segmental glomerulosclerosis -, than European Americans. Two coding variants (G1 and G2) in the APOL1 gene play a major role in this disparity. While 13% of African Americans carry the high-risk recessive genotypes, only a fraction of these individuals develops FSGS or kidney failure, indicating the involvement of additional disease modifiers. Here, we show that the presence of the APOL1 p.N264K missense variant, when co-inherited with the G2 APOL1 risk allele, substantially reduces the penetrance of the G1G2 and G2G2 high-risk genotypes by rendering these genotypes low-risk. These results align with prior functional evidence showing that the p.N264K variant reduces the toxicity of the APOL1 high-risk alleles. These findings have important implications for our understanding of the mechanisms of APOL1-associated nephropathy, as well as for the clinical management of individuals with high-risk genotypes that include the G2 allele