Space curves defined by curvature–torsion relations and associated helices

The relationships between certain families of special curves, including the general helices, slant helices, rectifying curves, Salkowski curves, spherical curves, and centrodes, are analyzed. First, characterizations of proper slant helices and Salkowski curves are developed, and it is shown that, for any given proper slant helix with principal normal n, one may associate a unique general helix whose binormal b coincides with n. It is also shown that centrodes of Salkowski curves are proper slant helices. Moreover, with each unit–speed non–helical Frenet curve in the Euclidean space E3, one may associate a unique circular helix, and characterizations of the slant helices, rectifying curves, Salkowski curves, and spherical curves are presented in terms of their associated circular helices. Finally, these families of special curves are studied in the context of general polynomial/rational parameterizations, and it is observed that several of them are intimately related to the families of polynomial/rational Pythagorean–hodograph curves

A community based cross sectional study on feasibility of lay interviewers in ascertaining causes of adult deaths by using verbal autopsy in rural Wardha

Background & objectives: 1) To study the causes of adult (15 years and above) deaths using verbal autopsy (VA) and its socio-demographic characteristics. 2) To study the feasibility of use of the lay interviewer to ascertain causes of adult death using verbal autopsy and a simple algorithm. Methods: The present study was done in Wardha district, Maharashtra, India. Taking into account feasibility, out of 23 villages of Primary Health Centre, Anji, 15 villages were chosen having total population of 14,590. Out of 273 estimated adult deaths during the study period, 209 (77%) could be traced by house to house visit and a lay interviewer, interviewed the close caretakers of the deceased. Both lay interviewer and a physician individually derived their diagnosis using verbal autopsy report and a simplified algorithm. The data was entered and analyzed by using Epi_info 6.04. The inter-observer reliability between the lay interviewer and a physician for each possible diagnosis was assessed by using the Kappa statistics. Considering the diagnosis made by a physician as a gold standard, the diagnostic and predictive accuracy for each diagnosis made by the lay interviewer was calculated. Results: The communicable diseases accounted for 52 percent of the adult deaths while non-communicable for 32 percent and injuries for nine percent deaths. The overall agreement between the lay interviewer and a physician for communicable diseases was found to be good (k = 0.65 + 0.06) and for non-communicable diseases it was found to be excellent (k = 0.80 + 0.06). The lay interviewer using VA performed adequately for individual conditions of public health importance like acute febrile illness, diarrheal diseases, tuberculosis and injuries. Interpretation & conclusions: The present study has been successful to demonstrate feasibility of use of the lay interviewer to provide useful information on population-level estimation of broad causes of adult deaths and its socio-demographic characteristics that are reasonably reliable. The study suggests the possible utility of the method for rural India, where the majority of deaths occur at home. Further research work on development of sensitive and specific yet simple algorithms for lay interviewers to ascertain causes of adult deaths is required

Bending of an Isotropic Compressible Rectangular Block into a Parabolic Shell

The problem of bending of an isotropic compressible rectangular block into a parabolic shell has been solved. It is shown the deformation can be maintained by applying forces and couples to the edges of the shell only