In recent work, Schweber [7] introduces a framework for reverse mathematics in a third order setting and investigates several natural principles of transfinite recursion. The main result of that paper is a proof, using the method of forcing, that in the context of two-person perfect information games with moves in R, open determinacy (Σ1 -DET) is not implied by clopen determinacy (∆ R 1 -DET). ...

SUMMARY For a variable and parameter of the same dimension, the tangent exponential model (Fraser, 1988) approximates an asymptotic model to third order in a rst derivative neighbourhood of the data point and to second order otherwise. For the more usual case of a variable of larger dimension than the parameter, we obtain a unique expression for the third order ancillary distribution as project...

In this study, we define third order bronze Fibonacci quaternions. We obtain the generating functions, Binet's formula and some properties of these give d'Ocagne's-like Cassini's-like identity use q-determinants for quaternionic matrices to Cassini's