Abstract: An elastic body is modelled as a plurality of models of particles and models of geometric elements. Each particle model has a position attribute. Each geometric element has a boundary defined by two or more of the particles as nodes of the geometric element, nodes being points shared with neighbouring geometric elements. The interior area or volume of the geometric elements is modelled via non-linear interpolation functions that use the positions of the particles of the respective geometric elements as inputs to compute position and/or strain of interior points of the geometric elements. Energy is summed over the interior region of the element, the energy computation based on (a) position and/or stress of the geometric element computed by the non-linear interpolation functions and/or (b) non-linear material parameters that depend on position and/or strain at the interior points of the geometric elements. New positions of the particles are computed based minimizing total energy of the element.

Abstract: An optical system for a camera includes a convex reflector, a decompression lens, and an image sensor. The convex reflector has a first diameter and a non-parabolic, axially symmetric, aspheric surface that provides a virtual curved and compressed image of a scene having a non-parabolic image compression. The decompression lens is positioned to receive the virtual curved and compressed image. The decompression lens is configured to decompress the virtual curved and compressed image into a real image having a parabolic image decompression and project the real image. The image sensor is positioned to receive the real image. The real image has a second diameter at the image sensor that is less than the first diameter. A ratio of the first diameter to the second diameter is between 6.5:1 and 2.3:1. The optical system provides a polychromatic modulation transfer function of 30% or more for 150 cy/mm.

Abstract: An optical system, apparatus, and method for sensing 360-degree horizontal and wide vertical field of view are shown. Powerful optics creates high resolution decompressed images on an image sensor. The compact panoramic camera includes two major optical components: (i) an axially symmetric convex aspheric reflector incorporated into a catadioptric optical element capable of providing a virtual curved image of a 360-degree panoramic scene with a specific image compression and (ii) a decompression lens with hardware aperture. The decompression lens is comprised of three single lens elements and accepts the virtual curved and compressed image and projects it onto the image sensor with high optical resolution and desirable image decompression to achieve a high digital resolution at the same time. Another version of decompression lens is comprised only of a single lens element and projects high resolution decompressed images onto an image sensor.

Abstract: An optical system, apparatus, and method for sensing 360-degree horizontal and wide vertical field of view are shown. Powerful optics creates high resolution decompressed images on an image sensor. The compact panoramic camera includes two major optical components: (i) an axially symmetric convex aspheric reflector incorporated into a catadioptric optical element capable of providing a virtual curved image of a 360-degree panoramic scene with a specific image compression and (ii) a decompression lens with hardware aperture. The decompression lens is comprised of three single lens elements and accepts the virtual curved and compressed image and projects it onto the image sensor with high optical resolution and desirable image decompression to achieve a high digital resolution at the same time. Another version of decompression lens is comprised only of a single lens element and projects high resolution decompressed images onto an image sensor.

Abstract: An optical system, apparatus, and method for sensing 360-degree horizontal and wide vertical field of view are shown. Powerful optics creates high resolution decompressed images on an image sensor. The compact panoramic camera includes two major optical components: (i) an axially symmetric convex aspheric reflector incorporated into a catadioptric optical element capable of providing a virtual curved image of a 360-degree panoramic scene with a specific image compression and (ii) a decompression lens with hardware aperture. The decompression lens is comprised of three single lens elements and accepts the virtual curved and compressed image and projects it onto the image sensor with high optical resolution and desirable image decompression to achieve a high digital resolution at the same time. Another version of decompression lens is comprised only of a single lens element and projects high resolution decompressed images onto an image sensor.

Abstract: A hydrocarbon stream is cracked to produce a hot gaseous stream which is compressed and cooled to condense almost all of the hydrocarbons contained in the stream. A noncondensed stream remaining after the condensation step, comprised predominantly of hydrogen and C.sub.1 to C.sub.3 hydrocarbons, is subjected to pressure swing adsorption or temperature swing adsorption at an adsorption temperature of about 0.degree. to about 250.degree. C. in a bed of adsorbent which selectively adsorbs ethene and propene, thereby adsorbing substantially all of the ethene and propene from the gas stream. The ethene and/or propene is recovered upon bed regeneration. Higher alkenes are separated from alkanes by various methods.

Abstract: A vanadium-containing catalyst system particularly suited to the polymerization of blow moldable olefin polymers. The catalyst system includes a supported, first catalyst component prepared by contacting preheated silica, with (1) a compound or complex which includes at least one carbon to magnesium covalent bond and (2) a compound which includes at least one carbon to Group III metal covalent bond. The sequence of contact of the silica with compound or complex (1) and compound (2) is optional. However, unless the compound or complex (1) and the compound (2) contact the silica simultaneously, the product of this contact is next contacted with whichever of compound (1) or (2) does not initially contact the silica. The product of the step of contacting with compounds (1) and (2) is contacted with a vanadium compound which includes at least one halogen atom. Finally, the product of the vanadium compound contacting step is contacted with an alcohol.

Abstract: The present invention relates to a novel catalyst component for ethylene polymerization comprising vanadium and titanium. Moreover, when the vanadium/titanium containing catalyst of the present invention is employed with an aluminum-containing cocatalyst enhanced activity as well as melt index is obtained.The present invention is directed to a novel halosilane cocatalyst component which, when used in conjunction with an aluminum containing cocatalyst, is effective in increasing the activity of a silica supported titanium/vanadium containing solid catalyst component in the polymerization of ethylene and/or .alpha.-olefins. In addition to the increased catalytic activity, the polymers produced by the present invention exhibit improved melt index values compared with melt index values typically obtained using prior art catalyst systems. Thus, the catalyst system of the instant invention represent an advancement in the art in view of the combination of increased activity, i.e.

Abstract: The present invention is directed to a novel halosilane cocatalyst component which, when used in conjunction with an aluminum containing cocatalyst, is effective in increasing the activity of a supported magnesium/titanium containing catalyst in the polymerization of ethylene and .alpha.-olefins. In addition to the increased catalytic activity, the polymers produced by the present invention are characterized as having an unexpected enhancement in the polymer melt index. Thus, the catalyst system of the instant invention represents an advancement in the art in view of the combination of increased activity, i.e., yield of polymer produced, and physical properties of the polyolefin product.In another aspect of the present invention, a process for polymerizing .alpha.-olefins is disclosed.

Abstract: The present invention is directed to a novel halosilane cocatalyst component which may be used in conjunction with an aluminum-containing cocatalyst to provide enhanced catalytic activity of a vanadium based solid catalyst component in the polymerization of .alpha.-olefins. In addition to the enhancement in the catalytic activity obtaining using the present catalyst system, the resultant polymer produced by the present invention exhibits improved physical properties compared with polymers produced by prior art vanadium based catalyst systems. Thus, the catalyst system of the instant invention represents an advance in the art in view of the combination of increased catalytic activity, i.e. yield of polymer produced, and enhanced physical properties of the polyolefin produced.In accordance with the present invention, a catalyst system is provided which comprises a solid catalyst component and a halosilane cocatalyst component.

Abstract: A novel catalyst support and a method for preparation thereof, characterized by the presence of selected amounts of a hydrocarbon soluble magnesium-containing compound applied to the support relative to solvent, wherein a surface uniformly and essentially continuously moistened with the solvated magnesium compound in a condition of incipient precipitation to permit the formation of a regular essentially continuous distribution of the magnesium compound onto and conforming to the support material. The drying process under these conditions is effective in maintaining to a high degree the effective surface area and pore volume of the material. The support containing the adsorbed magnesium is then dried in a controlled manner to essential incipient wetness conditions providing a regular spatial distribution of stacked reticular magnesium values at a level of one to five molecular monolayers on the support.