In this paper, we consider systems of singularly perturbed integro-differential equations with a rapidly oscillating right-hand side, including an integral operator slowly varying kernel. Differential type and inhomogeneity coefficient at unknown function are studied. The main goal work is to generalize the Lomov’s regularization method reveal influence side on asymptotics solution original pro...

Contemporary algebra is self-contradictory. Indeed, it offers the algorithms of solving algebraic equations using either the real or the complex numbers, which are, however, mutually exclusive. For instance, even the simplest quadratic equation c bx ax y 2    in the case of a negative discriminant ac b 4 2  has no solution on the set of real numbers, but does have a solution on the set of c...

In this article, we show that the magneto-hydrodynamic system (MHD) in R with variable density, variable viscosity and variable conductivity has a local weak solution in the Besov space Ḃ N p1 p1,1 (R )×Ḃ N p2 −1 p2,1 (R )×Ḃ N p2 −1 p2,1 (R ) for all 1 < p2 < +∞ and some 1 < p1 ≤ 2N 3 if the initial density approaches a positive constant. Moreover, this solution is unique if we impose the restr...

ome cells can induce the production of their own protective blanket. The signal comes from active neurons in the central nervous system (CNS), and triggers the differentiation of oligodendrocyte precursor cells (OPCs)—thus yielding the cells that cover the neurons with a protective sheath of myelin. Now, Beth Stevens, Douglas Fields, and colleagues (National Institutes of Health, Bethesda, MD) ...

This paper discusses a novel dynamic resonant wall shear stress sensor concept based on an oscillating sensor operating near resonance. The interaction between the oscillating sensor surface and the fluid above it is modelled using the unsteady laminar boundary layer equations. The numerical experiment shows that the effect of the oscillating shear stress is well correlated by the Hummer number...

Signals exhibiting amplitude as well as frequency modulation at widely separated time scales arise in radio frequency (RF) applications. A multivariate model yields an adequate representation by decoupling the time scales of involved signals. Consequently, a system of differential algebraic equations (DAEs) modelling the electric circuit changes into a system of partial differential algebraic e...