Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to nonassociativity. Our reflections keep wandering back to the $Brahmagupta$ $Fibonacc$ two square identity and then via the $Euler$ four square identity up to the $Degen$ $Ggraves$ $Cayley$ eight square identity. These glimpses of history incline and invite us to retell the story on how about one month after quaternions have been carved on the $Broughamian$ bridge octonions were discovered by $John$ $Thomas$ $Ggraves$, jurist and mathematician, a friend of $William$ $Rowan$ $Hamilton$. As for today we just mention en passant quaternionic and octonionic quantum mechanics, generalization of $Cauchy$ $Riemann$ equations for octonions and triality principle and $G_2$ group in spinor language in a descriptive way in order not to daunt non specialists. Relation to finite geometries is recalled and the links to the 7stones of seven sphere, seven imaginary octonions units in out of the $Plato$ cave reality applications are appointed . This way we are welcomed back to primary ideas of $Heisenberg$, $Wheeler$ and other distinguished fathers of quantum mechanics and quantum gravity foundations.Comment: 26 pages, 7 figure

On solutions of the matrix equations X−AXB=C and X−AXB=C

AbstractThis paper studies the solutions of complex matrix equations X−AXB=C and X−AXB=C, and obtains explicit solutions of the equations by the method of characteristic polynomial and a method of real representation of a complex matrix respectively

Rise in cesarean section rate over a 20-year period in a public sector hospital in northern Thailand

OBJECTIVE: To determine a trend of cesarean section rate (CSR) and main contributing factors in a public sector hospital, representing northern part of Thailand. METHODS: A retrospective descriptive analysis was conducted by assessing the database of maternal-fetal medicine unit, which had prospectively been collected for 20 years. Trends were evaluated using data for the years 1992–2011. Private sector patients were excluded. RESULTS: A total of 50,872 public sector patients were available for analysis. The number of deliveries was gradually decreased from 3,802 in 1992 to 1,748 in 2011. Of them, 7,480 underwent cesarean section, CSR of 14.7 %. However, the CSR was significantly increased from 11.3 % in 1992 to 23.6 % in 2011 (p value <0.001). The CSRs indicated by cephalopelvic disproportion (CPD) and previous CSs were mainly responsible for a marked increase over the study period. CSR due to CPD was increased from 3.2 % in 1992 to 7.9 % in 2011 (p value <0.0001). While CSR due to other indications either breech presentation, fetal distress and twin pregnancies were only slightly, but significantly increased in the last decades but they are relatively constant in the recent years. CONCLUSIONS: In our public sector, CSR has gradually increased. The main reasons of such an increase were likely to be associated with over-diagnosis of CPD and subsequent repeated CS, while other indications played only a minimal role. To achieve the appropriate CSR, audit system for diagnosis of CPD must be instituted

Maternal Death at Maharaj Nakorn Chiang Mai Hospital, the 17 Years Experience

Objective: To analyze the characteristics, leading causes and trend of maternal deaths at Maharaj Nakorn Chiang Mai Hospital between the 20th and the 21st centuries. Study design: Retrospective descriptive study. Methods: The database of Maternal-Fetal Medicine unit and medical records, between January 1991 and December 2007, were reviewed for maternal death cases, causes of death and the causes were categorized into subgroups. Results: There were 72,952 live births and 50 cases of maternal deaths. The overall maternal mortality ratio (MMR) was 65:100,000 live births. Thirty-four (68%) were referral cases. Between the 20th century (1991-1999) and the 21st century (2000-2007), MMR had been dropped from 67/100 000 live births to 62 /100 000 live births. The direct maternal death was the most common cause of death and the top five leading causes were postpartum hemorrhage (PPH), amniotic fluid embolism, heart diseases, septic abortion and severe pre-eclampsia, respectively. Direct maternal death was decreased (MMR from 46.1 to 33.5%) but indirect maternal death were increased (MMR from 9.6 to 23.9%). Conclusion: The trend of MMR at Maharaj Nakorn Chiang Mai Hospital appeared to be minimal changed during the 17 years period. The direct maternal death tends to be decreased but the indirect maternal death tends to be significantly increased. PPH was the most common cause of death in both centuries

Prenatal Sonographic Diagnosis of Focal Musculoskeletal Anomalies

Focal musculoskeletal anomalies vary, and can manifest as part of a syndrome or be accompanied by numerous other conditions such as genetic disorders, karyotype abnormalities, central nervous system anomalies and other skeletal anomalies. Isolated focal musculoskeletal anomaly does, however, also occur; its early prenatal diagnosis is important in deciding prenatal care, and also helps in counseling parents about the postnatal effects of numerous possible associated anomalies. We have encountered 50 cases involving focal musculoskeletal anomalies, including focal limb dysplasia [radial ray abnormality (n=3), mesomelic dysplasia (n=1)]; anomalies of the hand [polydactyly (n=8), syndactyly (n=3), ectrodactyly (n=1), clinodactyly (n=6), clenched hand (n=5)]; anomalies of the foot [clubfoot (n=10), rockerbottom foot (n=5), sandal gap deformity (n=1), curly toe (n=2)]; amniotic band syndrome (n=3); and anomalies of the focal spine [block vertebra (n=1), hemivertebra (n=1)]. Among these 50 cases, five [polydactyly (n=1), syndactyly (n=2) and curly toe (n=2)] were confirmed by postnatal physical evaluation, two (focal spine anomalies) were diagnosed after postnatal radiologic examination, and the remaining 43 were proven at autopsy

Comparisons of serum non-transferrin-bound iron levels and fetal cardiac function between fetuses affected with hemoglobin Bart’s disease and normal fetuses

ObjectiveTo compare the levels of Non-transferrin bound iron (NTBI) in fetuses with anemia, using Hb Bart’s disease as a study model, and those in unaffected fetuses and to determine the association between fetal cardiac function and the levels of NTBI.Patients and methodsA prospective study was conducted on pregnancies at risk of fetal Hb Bart’s disease. All fetuses underwent standard ultrasound examination at 18–22 weeks of gestation for fetal biometry, anomaly screening and fetal cardiac function. After that, 2 ml of fetal blood was taken by cordocentesis to measure NTBI by Labile Plasma Iron (LPI), serum iron, hemoglobin and hematocrit. The NTBI levels of both groups were compared and the correlation between NTBI and fetal cardiac function was determined.ResultsA total of 50 fetuses, including 20 fetuses with Hb Bart’s disease and 30 unaffected fetuses were recruited. There was a significant increase in the level of serum iron in the affected group (median: 22.7 vs. 9.7; p-value: 0.013) and also a significant increase in NTBI when compared with those of the unaffected fetuses (median 0.11 vs. 0.07; p-value: 0.046). In comparisons of fetal cardiac function, myocardial performance (Tei) index of both sides was significantly increased in the affected group (left Tei: p = 0.001, Right Tei: p = 0.008). Also, isovolumetric contraction time (ICT) was also significantly prolonged (left ICT: p = 0.00, right ICT: p = 0.000). Fetal LPI levels were significantly correlated inversely with fetal hemoglobin levels (p = 0.030) but not significantly correlated with the fetal serum iron levels (p = 0.138). Fetal LPI levels were also significantly correlated positively with myocardial performance index (Tei) of both sides (right Tei: R = 0.000, left Tei: R = 0.000) and right ICT (R = 0.013), but not significantly correlated with left ICT (R = 0.554).ConclusionAnemia caused by fetal Hb Bart’s disease in pre-hydropic stage is significantly associated with fetal cardiac dysfunction and increased fetal serum NTBI levels which are significantly correlated with worsening cardiac dysfunction. Nevertheless, based on the limitations of the present study, further studies including long-term data are required to support a role of fetal anemia as well as increased fetal serum NTBI levels in development of subsequent heart failure or cardiac compromise among the survivors, possibly predisposing to cardiovascular disease in adult life

Standard Model Extension and Casimir effect for fermions at finite temperature

AbstractLorentz and CPT symmetries are foundations for important processes in particle physics. Recent studies in Standard Model Extension (SME) at high energy indicate that these symmetries may be violated. Modifications in the lagrangian are necessary to achieve a hermitian hamiltonian. The fermion sector of the standard model extension is used to calculate the effects of the Lorentz and CPT violation on the Casimir effect at zero and finite temperature. The Casimir effect and Stefan–Boltzmann law at finite temperature are calculated using the thermo field dynamics formalism

Prenatal Ultrasound Findings of Fetal Neoplasms

A variety of neoplasms can develop in each tetal organ. Most fetal neoplasms can be detected by careful prenatal ultrasonographic examination. Some neoplosms show specific ultrasonographic findings suggesting the differential diagnosis, but others do not. Knowledge of the presence of a neoplasm in the fetus may alter the prenatal management of a pregnancy and the mode of delivery, and facilitates immediate postnatal treatment. During the last five years, we experienced 32 cases of fetal neoplasms in a variety of organs. We describe their typical ultrasonographic findings with correlating postnatal CT, MRI, and pathologic findings