Abstract: Embodiments provide methods of conducting operations with an implantable medical device (IMD) and an external controller device for performing authentication operations. In some embodiments, the method comprises: generating or storing an authentication data structure in the external controller device for over-the-air communication between the external device and the IMD, wherein the authentication data structure is generated by: (1) removing attribute fields from a first digital certificate and adding a public key of the external controller device to form an intermediate data structure; (2) creating a digital signature of the first intermediate data structure using a second digital certificate of an issuing certificate authority (CA); and (3) forming the authentication data structure by combining the intermediate data structure, the created digital signature, a public key of the issuing CA, and a digital signature of the public key of the issuing CA created using a third digital certificate of a root CA.

Abstract: Commonly used triethyl aluminum and tri-isobutyl aluminum cocatalysts may be replaced in olefin polymerizations with a cocatalyst conforming to the formula AlRz(Xz)nLzm wherein Rz may be a linear or branched organic moiety having at least 5 carbons and Xz may be a linear or branched organic moiety having at least 5 carbons or heteroatom substituted organic moiety or a heterocyclic moiety having at least 4 atoms and may be anionic (n=2) or dianionic (n=1). One Xz may also be hydrogen. The aluminum complex may also be in the form of an adduct complex where Lz may be a Lewis base and m=1?3. In the absence of a Lewis base, m=0.

Abstract: Commonly used triethyl aluminum and tri-isobutyl aluminum cocatalysts may be replaced in olefin polymerizations with a cocatalyst conforming to the formula AlRz(Xz)nLzm wherein Rz is a linear or branched organic moiety having at least 5 carbons and Xz is a linear or branched organic moiety having at least 5 carbons or heteroatom substituted organic moiety or a heterocyclic moiety having at least 4 atoms and may be anionic (n=2) or dianionic (n=1). Xz may also be hydrogen. The general formula is subject to the proviso that when n=2, each Xz may be the same or different and that both Xz moieties may not be hydrogen. The aluminum complex may also be in the form of an adduct complex where Lz is a Lewis base and m=1-3. Use of the invention enables production of a polyolefin pipe, such as polyethylene pipe, exhibiting improved processing, crack resistance and other desirable properties.

Abstract: Commonly used triethyl aluminum and tri-isobutyl aluminum cocatalysts can be replaced in olefin polymerizations with a cocatalyst conforming to the formula AlRz(Xz)nLzm wherein Rz is a linear or branched organic moiety having at least 5 carbons and Xz is a linear or branched organic moiety having at least 5 carbons or heteroatom substituted organic moiety or a heterocyclic moiety having at least 4 atoms and can be anionic (n=2) or dianionic (n=1). Xz can also be hydrogen. The aluminum complex may also be in the form of an adduct complex where Lz is a Lewis base and m=1-3. The general formula is subject to the proviso that when n=2, each Xz may be the same or different and that both Xz moieties may not be hydrogen. Use of the invention enables production of a polyolefin film, such as polyethylene film, exhibiting improved bubble stability and other desirable properties.