Conservation laws for the Maxwell-Dirac equations with a dual Ohm's law

Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov, we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and magnetic charges obey linear conductivity laws (dual Ohm's law). We find that this linear system allows for conservation laws which are non-local in time

Symmetries and conservation laws

Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed

Symmetrier och konserveringslagar

Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed

Ett aktivt och hållbart lärande i matematik

Undvik att lära ut metoder som endast fungerar i speciella fall, utan lär hellre ut generella metoder. Det ger studenterna en mer hållbar grund att bygga vidare på i sina fortsatta studier

Ett aktivt och hållbart lärande i matematik

Undvik att lära ut metoder som endast fungerar i speciella fall, utan lär hellre ut generella metoder. Det ger studenterna en mer hållbar grund att bygga vidare på i sina fortsatta studier

Changes in Anti-SARS-CoV-2 IgG Subclasses over Time and in Association with Disease Severity

IgG is the most prominent marker of post-COVID-19 immunity. Not only does this subtype mark the late stages of infection, but it also stays in the body for a timespan of at least 6 months. However, different IgG subclasses have different properties, and their roles in specific anti-COVID-19 responses have yet to be determined. We assessed the concentrations of IgG1, IgG2, IgG3, and IgG4 against different SARS-CoV-2 antigens (N protein, S protein RBD) using a specifically designed method and samples from 348 COVID-19 patients. We noted a statistically significant association between severity of COVID-19 infection and IgG concentrations (both total and subclasses). When assessing anti-N protein and anti-RBD IgG subclasses, we noted the importance of IgG3 as a subclass. Since it is often associated with early antiviral response, we presumed that the IgG3 subclass is the first high-affinity IgG antibody to be produced during COVID-19 infection

Alterations in B Cell and Follicular T-Helper Cell Subsets in Patients with Acute COVID-19 and COVID-19 Convalescents

Background. Humoral immunity requires interaction between B cell and T follicular helper cells (Tfh) to produce effective immune response, but the data regarding a role of B cells and Tfh in SARS-CoV-2 defense are still sparse. Methods. Blood samples from patients with acute COVID-19 (n = 64), convalescents patients who had specific IgG to SARS-CoV-2 N-protein (n = 55), and healthy donors with no detectable antibodies to any SARS-CoV-2 proteins (HC, n = 44) were analyses by multicolor flow cytometry. Results. Patients with acute COVID-19 showed decreased levels of memory B cells subsets and increased proportion plasma cell precursors compared to HC and COVID-19 convalescent patients, whereas for the latter the elevated numbers of virgin naïve, Bm2′ and “Bm3+Bm4” was found if compared with HC. During acute COVID-19 CXCR3+CCR6− Tfh1-like cells were decreased and the levels of CXCR3−CCR6+ Tfh17-like were increased then in HC and convalescent patients. Finally, COVID-19 convalescent patients had increased levels of Tfh2-, Tfh17- and DP Tfh-like cells while comparing their amount with HC. Conclusions. Our data indicate that COVID-19 can impact the humoral immunity in the long-term