A high-density LED array capable of presenting a density of X LEDsunit area has a first printed circuit board having X2 LEDsarea and X2 apertures arrayed therewith. A geo-cost policy is established for that user or mobile device in which rules and conditions according to the available discounts and class of service are defined. Methods according to the present invention use such devices and function correspondingly. The widget may be redisplayed on a subsequent occasion with a change in the widget without regenerating the client-side code. When at least one of a leading edge and a trailing edge of the sheet material, which is fed in a direction tangential to the rotating drum, is nipped between the circumferential surface of the rotating drum and chucks, nipping by the chucks is sequentially effected from one axial-direction end of the rotating drum to the other axial-direction end of the rotating drum. While both the real portion and the imaginary portion of the dielectric constant change, the change in the imaginary portion is less than the change in the real portion at the wavelength of interest or at the operational wavelength.