Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-...Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-1)-flat is associated with a point in PG(m-1, sn). An orthogonal array Lsmn((sn)(smn-)(sn-1) can be constructed by using (smn-1)/( sn-1) points in PG(m-1, sn). A set of (st-1)/(s-1) points in PG(m-1, sn) is called a (t-1)-flat over GF(s) if it is isomorphic to PG(t-1, s). If there exists a (t-1)-flat over GF(s) in PG(m-1, sn), then we can replace the corresponding [(st-1)/(s-1)] sn-level columns in Lsmn((sn)(smn-)(sn-1) by (smn-1)/( sn-1) st -level columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. In this paper, we study methods for finding disjoint (t-1)-flats over GF(s) in PG(m-1, sn) in order to construct more mixed orthogonal arrays of strength two. In particular, if m and n are relatively prime then we can construct an Lsmn((sm)smn-1/sm-1-i(sn-1)/ (s-1)( sn) i(sm-1)/ s-1) for any 0i(smn-1)(s-1)/( sm-1)( sn-1) New orthogonal arrays of sizes 256, 512, and 1024 are obtained by using PG(7,2), PG(8,2), and PG(9,2) respectively.展开更多
Throughout the globe,diabetes mellitus（DM） is increasing in incidence with limited therapies presently available to prevent or resolve the significant complications of this disorder.DM impacts multiple organs and af...Throughout the globe,diabetes mellitus（DM） is increasing in incidence with limited therapies presently available to prevent or resolve the significant complications of this disorder.DM impacts multiple organs and affects all components of the central and peripheral nervous systems that can range from dementia to diabetic neuropathy.The mechanistic target of rapamycin（m TOR） is a promising agent for the development of novel regenerative strategies for the treatment of DM.m TOR and its related signaling pathways impact multiple metabolic parameters that include cellular metabolic homeostasis,insulin resistance,insulin secretion,stem cell proliferation and differentiation,pancreatic β-cell function,and programmed cell death with apoptosis and autophagy.m TOR is central element for the protein complexes m TOR Complex 1（m TORC1） and m TOR Complex 2（m TORC2） and is a critical component for a number of signaling pathways that involve phosphoinositide 3-kinase（PI 3-K）,protein kinase B（Akt）,AMP activated protein kinase（AMPK）,silent mating type information regulation 2 homolog 1（Saccharomyces cerevisiae）（SIRT1）,Wnt1 inducible signaling pathway protein 1（WISP1）,and growth factors.As a result,m TOR represents an exciting target to offer new clinical avenues for the treatment of DM and the complications of this disease.Future studies directed to elucidate the delicate balance m TOR holds over cellular metabolism and the impact of its broad signaling pathways should foster the translation of these targets into effective clinical regimens for DM.展开更多
文摘Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-1)-flat is associated with a point in PG(m-1, sn). An orthogonal array Lsmn((sn)(smn-)(sn-1) can be constructed by using (smn-1)/( sn-1) points in PG(m-1, sn). A set of (st-1)/(s-1) points in PG(m-1, sn) is called a (t-1)-flat over GF(s) if it is isomorphic to PG(t-1, s). If there exists a (t-1)-flat over GF(s) in PG(m-1, sn), then we can replace the corresponding [(st-1)/(s-1)] sn-level columns in Lsmn((sn)(smn-)(sn-1) by (smn-1)/( sn-1) st -level columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. In this paper, we study methods for finding disjoint (t-1)-flats over GF(s) in PG(m-1, sn) in order to construct more mixed orthogonal arrays of strength two. In particular, if m and n are relatively prime then we can construct an Lsmn((sm)smn-1/sm-1-i(sn-1)/ (s-1)( sn) i(sm-1)/ s-1) for any 0i(smn-1)(s-1)/( sm-1)( sn-1) New orthogonal arrays of sizes 256, 512, and 1024 are obtained by using PG(7,2), PG(8,2), and PG(9,2) respectively.
基金supported by American Diabetes Association,American Heart Association,NIH NIEHS,NIH NIA,NIH NINDS,and NIH ARRA
文摘Throughout the globe,diabetes mellitus（DM） is increasing in incidence with limited therapies presently available to prevent or resolve the significant complications of this disorder.DM impacts multiple organs and affects all components of the central and peripheral nervous systems that can range from dementia to diabetic neuropathy.The mechanistic target of rapamycin（m TOR） is a promising agent for the development of novel regenerative strategies for the treatment of DM.m TOR and its related signaling pathways impact multiple metabolic parameters that include cellular metabolic homeostasis,insulin resistance,insulin secretion,stem cell proliferation and differentiation,pancreatic β-cell function,and programmed cell death with apoptosis and autophagy.m TOR is central element for the protein complexes m TOR Complex 1（m TORC1） and m TOR Complex 2（m TORC2） and is a critical component for a number of signaling pathways that involve phosphoinositide 3-kinase（PI 3-K）,protein kinase B（Akt）,AMP activated protein kinase（AMPK）,silent mating type information regulation 2 homolog 1（Saccharomyces cerevisiae）（SIRT1）,Wnt1 inducible signaling pathway protein 1（WISP1）,and growth factors.As a result,m TOR represents an exciting target to offer new clinical avenues for the treatment of DM and the complications of this disease.Future studies directed to elucidate the delicate balance m TOR holds over cellular metabolism and the impact of its broad signaling pathways should foster the translation of these targets into effective clinical regimens for DM.
