Some iterative matrix relations for the kinematics and dynamics of a spherical Agile Wrist parallel robot are established. The manipulator prototype is a three-degree-offreedom mechanical system with three parallel legs. Controlled by concurrent torques, which are generated by some electric motors, three active elements of the robot have three independent rotations. Supposing that the position ...

2 Sets and Functions 1 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.6 Congr...

2 Sets and Functions 10 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 10 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 14 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6...

1 Sets and Functions 1 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Unions, Intersections and Complements of Sets . . . . . . . . . 1 1.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 3 1.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 5 1.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.6 Congr...

2 Sets and Functions 10 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 10 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 14 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6...

In this paper the principal-agent models between the investor and the manager of the open-ended fund are made from the new view about the liquidity risk management, and the optimal contracts and optimal policies are obtained in closed form by solving these modes. By the analysis of the optimal contract, we find that the fixed compensation of manager is the positive relationship with redemption ...

Basic relations between the distributions of hitting, occupation, and inverse local times of a one-dimensional diiusion process X, rst discussed by It^ o-McKean, are reviewed from the perspectives of mar-tingale calculus and excursion theory. These relations, and the technique of conditioning on L y T , the local time of X at level y before a suitable random time T, yield formulae for the joint...

2 Sets and Functions 10 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 10 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 14 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6...

We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of non-binary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. This translation suggests that we will tend to achieve more pruning in the dual than in the hidden va...

We point out a simple but hitherto ignored link between the theory of updates and counterfactuals and classical modal logic: update is a classical existential modality, counterfactual is a classical universal modality, and the link between the two (called the Ramsey rule) is simply the link between two inverse accessibility relations of a classical Kripke model.