Functional central limit theorems on Lie groups: A survey

The general solution of the functional central limit problems for triangular arrays of random variables with values in a Lie group is described. The role of processes of finite variation is clarified. The special case of processes with independent increments having Markov generator is treated. Connections with Hille–Yosida theory for two–parameter evolution families of operators and with the martingale problem are explained

A chewing robot based on parallel mechanism-- analysis and design : a thesis presented in partial fulfilment of the requirements for the degree of Master of Engineering in Mechatronics at Massey University

Masticatory efficiency, dependent on number and condition of the teeth, length of time spent in chewing a bolus and the force exerted when chewing, influences an individual with the selection of food and therefore nutritionally diet. A characterisation of the masticatory efficiency could be possible with a chewing robot that simulates human chewing behaviours in a mechanically controllable way (Pap et al. 2005; Xu et al. 2005). This thesis describes such a chewing robot, developed from a biological basis in terms of jaw structure and muscles of mastication according to published articles. A six degrees of freedom parallel mechanism is proposed with the mandible as a moving platform, the skull as a fixed platform, and six actuators representing the main masticatory muscle groups, temporalis, masseter, and lateral pterygoid on the left and right side. Extensive simulations of inverse kinematics (i.e., generating muscular actuations with implementing recorded human trajectories) were conducted in SolidWorks and COSMOS/Motion to validate two mathematical models of the robot and to analyse kinematic properties. The research showed that selection of appropriate actuation systems, to achieve mandible movement space, velocity, acceleration, and chewing force, was the key challenge in successfully developing a chewing robot. Two custom designed actuation systems, for the six actuators, were developed and built. In the first approach, the muscle groups were presented as linear actuators, positioned so as to reproduce the resultant lines of action of the human muscles. However, with this design concept the spatial requirements specified from the human masticatory system made the physical building of the model impossible. The second approach used a crank mechanism based actuator. This concept did not allow a perfectly linear actuator movement that copied the muscle line of action. However, it was possible to fulfil the spatial requirements set by the human system and to allow reproduction of human chewing behaviours in relation to kinematic requirements and chewing force. The design, manufacture and testing of the entire chewing robot with crank actuators was then carried out. This included the implementation of realistic denture morphology, a mechanical jaw and the framework design for the whole system. In conclusion, this thesis research has developed successfully a mathematical and a physical robotic model. Future work on the control and sensing of the robot and design of a food retention system are required in order to fully functionalise the device

Decision Making by Hybrid Probabilistic - Possibilistic Utility Theory

It is presented an approach to decision theory based upon nonprobabilistic uncertainty. There is an axiomatization of the hybrid probabilisticpossibilistic mixtures based on a pair of triangular conorm and triangular norm satisfying restricted distributivity law, and the corresponding non-additive Smeasure. This is characterized by the families of operations involved in generalized mixtures, based upon a previous result on the characterization of the pair of continuous t-norm and t-conorm such that the former is restrictedly distributive over the latter. The obtained family of mixtures combines probabilistic and idempotent (possibilistic) mixtures via a threshold.Decision making, Utility theory, Possibilistic mixture, Hybrid probabilistic- possibilistic mixture, Triangular norm, Triangular conorm, Pseudoadditive measure.

Fourier transform of a Gaussian measure on the Heisenberg group

An explicit formula is derived for the Fourier transform of a Gaussian measure on the Heisenberg group at the Schrodinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two Gaussian measures to be a Gaussian measure.Comment: 38 pages, completed versio