A Shock Wave Attached to a Pointed Obstacle in a Steady flow of a Dissociating Gas

A pointed obstacle is assumed symmetrically placed with respect to a uniform supersonic flow ahead of it. It is assumed that an oblique shock wave attached to the leading edge of the obstacle appears form the vertex so that the flow after the shock is along the surface of the obstacle. In this paper a relation between the curvature of an attached shock wave and that of a stream line is discovered. It is concluded that in a steady flow of an ideal dissociating gas, the stream lines at the rear of a straight attached shock wave are necessarily curved lines, whereas in an ordinary gas flow only a straight line flow is possible behind a straight shock

Relation of bone mineral density with homocysteine and cathepsin K levels in postmenopausal women

Background: Homocysteine (HCY) interferes with collagen cross-linking in bones and stimulates osteoclast activity. The activated osteoclasts secrete cathepsin K (CathK), a cysteine protease, in eminent quantity during bone resorption. Hyperhomocysteinemia may effect bone mineral density (BMD) through CathK. We, therefore, examined the relation between HCY and BMD along with CathK, 25-hydroxyvit-D (25[OH]D), intact parathyroid hormone (iPTH), and Vitamin B12. Materials and Methods: We recruited a total of 93 postmenopausal women between the age group of 45–60 years, attending the Endocrinology outpatient department at King George's Medical University, Lucknow. BMD was done by DXA scan using Hologic QDR1000 system. Based on the WHO criteria, patients were segregated into three groups as follows; normal bone mass, osteopenia, and osteoporosis. All women underwent routine biochemical laboratory parameters, HCY, Vitamin B12, and CathK levels. Results: Among 93 postmenopausal women, 56% (52) had osteoporosis. Nineteen percent (18) had normal BMD (mean age, 53.22 ± 8.5 years) and 23 (25%) had osteopenia (mean age 52.86 ± 6.67 years). The mean age in the osteoporetic group was 56.2 ± 6.9 years. The median (interquartile range) levels of HCY in the three groups were 14.5 μmol/L (12.2–24.7), 15.05 μmol/L (12.1–19.9) and 13.2 μmol/L (10.3–17.0), respectively. CathK levels were similar in three groups 7.6 ng/ml (7.0–80.5), 8.3 ng/ml (7.3–8.5), and 8.6 ng/ml (7.2–8.9). Both HCY and CathK were found positively associated with serum phosphorus (r = 0.584, P < 2.01 and r = 0.249, P < 0.05, respectively). Levels of HCY positively correlate with PTH (r = 0.303, P < 0.01) and inversely with Vitamin B12 (r = −0.248, P < 0.05). No significant association was seen between CathK level and 25(OH) D, iPTH, serum calcium. Conclusion: Low bone mass by DXA is a significant problem in postmenopausal females. HCY and CathK do not reliably correlate with bone loss in postmenopausal women although phosphorus metabolism may play a role