View of the clinic, diagnosis and treatment of familial benign pemphigus (Hailey — Hailey disease). Literature review

The article describes modern views on predisposing factors, histological and genetic changes, the role of ATP2C1 encoding a mutant gene, localized on chromosome 3 in the pathogenesis of Hailey — Hailey disease. Diagnostic criteria, differential diagnostics with other diseases and methods of modern treatment of this disease are presented

Analytical approximation of spectrum for pulse X-ray tubes

Among the main characteristics of the pulsed X-ray apparatuses the spectral energy characteristics are the most important ones: the spectral distribution of the photon energy, effective and maximum energy of quanta. Knowing the spectral characteristics of the radiation of pulse sources is very important for the practical use of them in non-destructive testing. We have attempted on the analytical approximation of the pulsed X-ray apparatuses spectra obtained in the different experimental papers. The results of the analytical approximation of energy spectrum for pulse X-ray tube are presented. Obtained formulas are adequate to experimental data and can be used by designing pulsed X-ray apparatuses

Analysis of innovative technologies in industry: the blockchain and the internet of things

The rapid development of modern information technologies introduces significant changes in the work of all spheres of activity, especially in industry. The technologies, using in industry have been analyzed in the article. The prospects for the development of the blockchain technology and the industrial Internet were considered and possible problems for their implementation and development have been highlighted, such as: high cost, unemployment, long distances and long transit times, cold climate, insuffi quality of cartographic services

D'Alembert sums for vibrating bar with viscous ends

We describe a new method for finding analytic solutions to some initial-boundary problems for partial differential equations with constant coefficients. The method is based on expanding the denominator of the Laplace transformed Green's function of the problem into a convergent geometric series. If the denominator is a linear combination of exponents with real powers one obtains a closed form solution as a sum with finite but time dependent number of terms. We call it a d'Alembert sum. This representation is computationally most effective for small evolution times, but it remains valid even when the system of eigenmodes is incomplete and the eigenmode expansion is unavailable. Moreover, it simplifies in such cases. In vibratory problems d'Alembert sums represent superpositions of original and partially reflected traveling waves. They generalize the d'Alembert type formulas for the wave equation, and reduce to them when original waves can undergo only finitely many reflections in the entire course of evolution. The method is applied to vibrations of a bar with dampers at each end and at some internal point. The results are illustrated by computer simulations and comparisons to modal and FEM solutions.Comment: 18 pages, 8 figure

Torus knots and mirror symmetry

We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.Comment: 30 pages + appendix, 3 figure

String theory and the Kauffman polynomial

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations, i.e. it involves the full HOMFLY skein of the annulus. The conjecture sheds new light on the relationship between the Kauffman and the HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide various non-trivial tests of the conjecture and we sketch the string theory arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos corrected, final version to appear in CM