Abstract: Disclosed are pharmaceutical formulations comprising a compound of formula (I): in which R1, R2, R3, and R4 are as described herein, or a pharmaceutically acceptable salt thereof. Also provided are methods for treating pancreatic adenocarcinoma comprising administration of a compound of formula (I), or a pharmaceutically acceptable salt thereof, and methods of detecting the change in expression levels of one or both of FoxA1 and FoxO6 in a pancreatic adenocarcinoma tumor sample from a mammal, wherein the mammal has been administered a compound of formula (I), or a pharmaceutically acceptable salt thereof.

Abstract: One embodiment provides a method for receiving parallel rays at a lens. A first surface of the lens can receive first substantially parallel rays incoming from a first direction. The first surface of the lens also can receive second substantially parallel rays incoming from a second direction that is substantially different than the first direction. The lens can focus the first substantially parallel rays onto a first focal point on a second surface of the lens and focus the second substantially parallel rays onto a second focal point on the second surface of the lens, the second focal point being different than the first focal point.

Abstract: One embodiment provides for a gradient lens having a first substantially hemispherical member comprising a first convex surface and a base and a second substantially hemispherical member projecting away from the base of the first hemispherical member and comprising a second convex surface. The gradient lens also includes a plurality of gradient layers disposed within the first hemispherical member, each gradient layer concentrically aligned to the first hemispherical member and comprising an index of refraction different than that of adjacent gradient layers.

Abstract: An air filter replacement system for existing buildings, vehicles, arenas, and other enclosed airspaces includes a replacement air filter for replacing a standard air filter. The replacement air filter has dimensions and air flow specifications that allow it to replace the standard air filter. The replacement air filter includes a filter material that removes radiological or biological or aerosol particles.

Abstract: A gradient lens capable of focusing electromagnetic rays received at a first lens surface onto a second lens surface. The first lens surface and second lens surface can include convex surfaces protruding in opposite directions from a substantially planar surface. The lens can include a gradient index between the first surface and the planar surface and a gradient index between the two convex surfaces. The lens can include two or more gradient layers, each gradient layer having an index of refraction different than that of adjacent gradient layers. The gradient layers can focus parallel electromagnetic rays incident on the first surface onto a focal point at the second surface of the lens. As the parallel electromagnetic rays pass from one gradient layer to the next, the rays are redirected toward the focal point.

Abstract: A gradient lens capable of focusing electromagnetic rays received at a first lens surface onto a second lens surface. The first lens surface and second lens surface can include convex surfaces protruding in opposite directions from a substantially planar surface. The lens can include a gradient index between the first surface and the planar surface and a gradient index between the two convex surfaces. The lens can include two or more gradient layers, each gradient layer having an index of refraction different than that of adjacent gradient layers. The gradient layers can focus parallel electromagnetic rays incident on the first surface onto a focal point at the second surface of the lens. As the parallel electromagnetic rays pass from one gradient layer to the next, the rays are redirected toward the focal point.

Abstract: An antenna system with an improved antenna feed system is discussed. This multi-beam antenna system can produce a beam of electromagnetic energy propagating in a desired direction by emitting multiple beams of electromagnetic energy that constructively and destructively interfere. The direction of the net beam of electromagnetic energy can be controlled by adjusting the phase and amplitude of the emitted beams of electromagnetic energy which in turn influences the constructive and destructive interference. The phase and amplitude adjustments can be determined by sampling coordinate rotation or similar functions. Aliased components of these functions can be particularly useful in element reduction.