Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown...

injury, I opened the joint, under spray, by a semilunar-shaped incision, extending from side to side across the front of the joint, its convexity passing over the lower part of the patella. By reflecting upwards the flap thus formed, the patella was completely exposed, and was found broken into five pieces. A horizontal fracture divided the bone into two nearly equal portions which were widely ...

This study was designed to evaluate the results of treatment of joint contractures (6 patients) and dislocations (2 cases) with an Ilizarov device. Six patients with restricting joint contractures were successfully treated and after gradual scar expansion they achieved a significant improvement in their range of motion. One patient with elbow instability after closed dislocation achieved 5 degr...

For gambles—non-numerical consequences attached to uncertain chance events—analogues are proposed for the sum of independent random variables and their convolution. Joint receipt of gambles is the analogue of the sum of random variables. Because it has no unique expansion as a first-order gamble analogous to convolution, a definition of qualitative convolution is proposed. Assuming ranked, weig...

In this note, I briefly revisit the possibility of a physical 12-dimensional F-theory, in view of a recent joint investigation with H. Sati [1, 2, 3] on expansion from type II string theory to F-theory. In particular, I shall discuss Lagrangians and signatures, in particular a new possible phenomenological scenario of compactificaton from dimension (9, 3) to (3, 1).

Cash crop expansion has been a major land use change in tropical and subtropical regions worldwide. Quantifying the determinants of cash crop expansion should provide deeper spatial insights into the dynamics and ecological consequences of cash crop expansion. This paper investigated the process of cash crop expansion in Hangzhou region (China) from 1985 to 2009 using remotely sensed data. The ...

In this companion paper to “Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon”, we give an accuracy proof for the finite time optimal investment and consumption problem under fast mean-reverting stochastic volatility of a joint asymptotic expansion in a time scale parameter and the small transaction cost. AMS subject classification 91G80, 60H30. JEL su...