Abstract A swimmer embedded on an inertialess fluid must perform a non-reciprocal motion to swim forward. The archetypal demonstration of this unique motion-constraint was introduced by Purcell with the so-called “scallop theorem”. Scallop here is minimal mathematical model composed two arms connected via hinge whose periodic (of opening and closing its arms) not sufficient achieve net displace...

Cyclotron resonance (CR) is considered one of the fundamental phenomena in conducting systems. In this paper, we study CR a gated two-dimensional (2D) electron system (ES). Namely, analyze absorption electromagnetic radiation incident normal to 2DES, where standard dielectric substrate separates 2D sheet and metallic steering electrode ("gate"); whole placed perpendicular magnetic field. Our an...

We consider linear one-dimensional strongly degenerate parabolic equations with measurable coefficients that may be or singular. Taking 0 as the point where strong degeneracy occurs, we assume coefficient a = ( x ) in principal part of equation is such function → / L p (0,1) for some > 1. After establishing spectral estimates corresponding elliptic problem, prove null controllable energy spa...

In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. The fact that the jobs have controllable processing times means that it is possible to reduce the processing time of the jobs by paying a certain cost. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial...

Supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis. In this paper, we discuss the computation of supremal controllable and normal sublanguages. We derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed. As a result, those languages can be computed without app...