In this article we consider the problem related to positional synthesis and controllability function method more precisely admissible maximum principle. Unlike common approach principle gives discontinuous solutions problem. Let us canonical system of linear equations $\dot{x}_i=x_{i+1}, i=\overline{1,n-1}, \dot{x}_n=u$ with constraints $|u| \le d$. The for an arbitrary $\dot{x} = A x + b u$ ca...

We reveal the existence of the surface plasmonic lattice solitons (surface PLSs) at the boundary of a semi-infinite metallic-dielectric periodic nanostructure. We find that the truncation of the periodic structure imposes a threshold power for the existence of surface PLSs, and significantly enhances the modal localization. The propagation and excitation of surface PLSs as well as their potenti...

We consider a class of bimodal systems which alternate modes on hitting`switch-ing surfaces': the canonical model is a physical thermostat. A suucient condition is obtained for the existence of periodic solutions. The signiicance for this theory of certain anomalous points on the switching surface is shown by an example with no periodic solutions. Further discussion is presented for the importa...

We demonstrate a fast optical modulator capable of switching large amount of optical retardation (a few microns) in less than 1ms. The result is achieved by employing a dual frequency nematic in cells with high pre-tilt alignment and by providing a special addressing scheme that features amplitude and frequency modulated voltage. We explore the effect of surface alignment and dielectric heating...

We proposed a fast liquid crystal display (LCD) in a vertical alignment (VA) mode with continuous multi-domains for wide-viewing characteristics. The fast VA LCD was fabricated by the mixed vertical alignment layer with UV curable reactive mesogen (RM) polymer memorizing the switching directions of the LC molecules. The wide-viewing and fast response characteristics were obtained by axially sym...

We demonstrate nonvolatile resistive switching in single crystalline ZnO nanowires with high ON/OFF ratios and low threshold voltages. Unlike the mechanism of continuous metal filament formation along grain boundaries in polycrystalline films, the resistive switching in single crystalline ZnO nanowires is speculated to be induced by the formation of a metal island chain on the nanowire surface....

We exploit the properties of ultranarrow, Fano-like resonances generated by the coupling of long range surface plasmons with ultrathin (~10 nm), metallic, subwavelength gratings embedded in a nonlinear, cubic material to obtain all-optical switching at telecommunication wavelengths for extremely low input power. We provide an example of a silver metallic grating embedded in a chalcogenide glass...