Tetrads of lines spanning PG(7,2)

Our starting point is a very simple one, namely that of a set L_4 of four mutually skew lines in PG(7,2): Under the natural action of the stabilizer group G(L_4) < GL(8,2) the 255 points of PG(7,2) fall into four orbits omega_1, omega_2, omega_3 omega_4; of respective lengths 12, 54, 108, 81: We show that the 135 points in omega_2 \cup omega_4 are the internal points of a hyperbolic quadric H_7 determined by L_4; and that the 81-set omega_4 (which is shown to have a sextic equation) is an orbit of a normal subgroup G_81 isomorphic to (Z_3)^4 of G(L_4): There are 40 subgroups (isomorphic to (Z_3)^3) of G_81; and each such subgroup H < G_81 gives rise to a decomposition of omega_4 into a triplet of 27-sets. We show in particular that the constituents of precisely 8 of these 40 triplets are Segre varieties S_3(2) in PG(7,2): This ties in with the recent finding that each Segre S = S_3(2) in PG(7,2) determines a distinguished Z_3 subgroup of GL(8,2) which generates two sibling copies S'; S" of S.Comment: Some typos correcte

Tetrads of lines spanning PG(7,2)

Our starting point is a very simple one, namely that of a set L₄ of four mutually skew lines in PG(7,2). Under the natural action of the stabilizer group G(L₄)&lt;GL(8,2) the 255 points of PG(7,2) fall into four orbits ω₁,ω₂,ω₃,ω4, of respective lengths 12,54,108,81. We show that the 135 points ∈ω₂∪ω₄ are the internal points of a hyperbolic quadric H7 determined by L₄, and that the 81-set ω₄ (which is shown to have a sextic equation) is an orbit of a normal subgroup G₈₁≅(Z₃)4 of G(L4). There are 40 subgroups ≅(Z₃)3 of G₈₁, and each such subgroup H&lt;G₈₁ gives rise to a decomposition of ω4 into a triplet {RH,R′H,R′′H} of 27-sets. We show in particular that the constituents of precisely 8 of these 40 triplets are Segre varieties S₃(2) in PG(7,2). This ties in with the recent finding 225-239 --- that each S=S₃(2) in PG(7,2) determines a distinguished Z₃ subgroup of GL(8,2) which generates two sibling copies S′,S′′ of S

Quality Indicators Guiding Secondary Career and Technical Education Programs of Study

The purpose of this study was to examine quality indicators currently guiding the rigor of secondary career and technical education (CTE) programs of study in the United States. Quality indicators are desirable characteristics or expectations for a comprehensive and effective CTE program of study. As of May 2017, we were able to locate publicly accessible secondary CTE quality program standards/guidelines for 38 states. A majority (n=24) updated their secondary CTE quality program standards/guidelines within the last five years (i.e., 2012-2017). Deductive content analysis was conducted to examine the 38 state profiles using the Association of Career and Technical Education (ACTE) Quality CTE Program of Study Framework 4.0 for coding purposes. Common quality elements and key quality indicators were identified from those state documents, which supplements the ACTE Framework. Implications and examples for practice are also discussed

A simplified technique for revascularization of homografts of the liver with a variant right hepatic artery from the superior mesenteric artery

A simplified technique for conversion of a complex hepatic arterial supply into a common channel is described. This technique permits single vessel anastomosis in the recipient of a liver transplant

Liver rejection and its differentiation from other causes of graft dysfunction.

Numerous causes can lead to hepatic dysfunction following orthotopic liver transplantation. The most common cause is rejection, which is usually nonpreventable. The clinical presentation, time of onset, and even treatment are variable. Other causes, such as perioperative ischemic injury, vascular thrombosis, and complications of bile duct reconstruction may be preventable with good surgical technique. Infections can also be minimized by careful adjustment of immunotherapy, avoidance overimmunosuppression, and the judicious use of antibiotics. Hepatic dysfunction following orthotopic liver transplantation requires rapid assessment and proper treatment in order to prevent serious and possibly fatal complications

Influence of selected patient variables and operative blood loss on six-month survival following liver transplantation.

A group of 118 adults who underwent primary, orthotopic transplantation of the liver over a 4-year period served as the subjects of a detailed examination of their ability to survive the first 6 months as a function of their preoperative condition. As a result, a scoring system was developed empirically in an attempt to separate very high-risk from relatively low-risk patients. The scoring method is based on the high degree of correlation between survival probability and various patient characteristics. It allows for additional scoring to account for the dramatic effect of operative blood loss on the eventual outcome. The curve that best describes the relationship between patient scores and survival probability is sigmoidal in shape. Many patients will have scores located on the curve between the inflection points. They represent a group whose relative risk is difficult to estimate but for whom operative blood loss or the occurrence of surgical complications may prove particularly telling