Identification of Boundary Conditions Using Natural Frequencies

The present investigation concerns a disc of varying thickness of whose flexural stiffness $D$ varies with the radius $r$ according to the law $D=D_0 r^m$, where $D_0$ and $m$ are constants. The problem of finding boundary conditions for fastening this disc, which are inaccessible to direct observation, from the natural frequencies of its axisymmetric flexural oscillations is considered. The problem in question belongs to the class of inverse problems and is a completely natural problem of identification of boundary conditions. The search for the unknown conditions for fastening the disc is equivalent to finding the span of the vectors of unknown conditions coefficients. It is shown that this inverse problem is well posed. Two theorems on the uniqueness and a theorem on stability of the solution of this problem are proved, and a method for establishing the unknown conditions for fastening the disc to the walls is indicated. An approximate formula for determining the unknown conditions is obtained using first three natural frequencies. The method of approximate calculation of unknown boundary conditions is explained with the help of three examples of different cases for the fastening the disc (rigid clamping, free support, elastic fixing). Keywords: Boundary conditions, a disc of varying thickness,inverse problem, Plucker condition.Comment: 19 page

Semuloparin for prevention of venous thromboembolism after major orthopedic surgery: Results from three randomized clinical trials, SAVE-HIP1, SAVE-HIP2 and SAVE-KNEE

Background: Semuloparin is a novel ultra-low-molecular-weight heparin under development for venous thromboembolism (VTE) prevention in patients at increased risk, such as surgical and cancer patients. Objectives: Three Phase III studies compared semuloparin and enoxaparin after major orthopedic surgery: elective knee replacement (SAVE-KNEE), elective hip replacement (SAVE-HIP1) and hip fracture surgery (SAVE-HIP2). Patients/Methods: All studies were multinational, randomized and double-blind. Semuloparin and enoxaparin were administered for 7-10days after surgery. Mandatory bilateral venography was to be performed between days 7 and 11. The primary efficacy endpoint was a composite of any deep vein thrombosis, non-fatal pulmonary embolism or all-cause death. Safety outcomes included major bleeding, clinically relevant non-major (CRNM) bleeding, and any clinically relevant bleeding (major bleeding plus CRNM). Results: In total, 1150, 2326 and 1003 patients were randomized in SAVE-KNEE, SAVE-HIP1 and SAVE-HIP2, respectively. In all studies, the incidences of the primary efficacy endpoint were numerically lower in the semuloparin group vs. the enoxaparin group, but the difference was statistically significant only in SAVE-HIP1. In SAVE-HIP1, clinically relevant bleeding and major bleeding were significantly lower in the semuloparin vs. the enoxaparin group. In SAVE-KNEE and SAVE-HIP2, clinically relevant bleeding tended to be higher in the semuloparin group, but rates of major bleeding were similar in the two groups. Other safety parameters were generally similar between treatment groups. Conclusions: Semuloparin was superior to enoxaparin for VTE prevention after hip replacement surgery, but failed to demonstrate superiority after knee replacement surgery and hip fracture surgery. Semuloparin and enoxaparin exhibited generally similar safety profiles. \ua9 2012 International Society on Thrombosis and Haemostasis