This paper presents a direct proof of the recursive formulae for the generalized LMinverse of a matrix augmented by a column vector. The recursive relations are proved by direct verification of the four conditions of the generalized LM-inverse. Several auxiliary results pertaining to generalized inverses are also provided. 2006 Elsevier Inc. All rights reserved.

Basic relations between the distributions of hitting, occupation, and inverse local times of a one-dimensional di usion process X , rst discussed by Itô-McKean, are reviewed from the perspectives of martingale 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 ...

Some recursive matrix relations for the geometric analysis, kinematics and dynamics of a 3-RRR symmetric spherical Agile Wrist parallel mechanism 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...

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, Functions and Countability 2 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 5 1.3 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Equivalence Relations . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Functions . . . . . . . . . . . . . . . . . . . . . . . . ...

Let Θ be an arbitrary variety of algebras and H an algebra in Θ. Along with algebraic geometry in Θ over the distinguished algebra H, a logical geometry in Θ over H is considered. This insight leads to a system of notions and stimulates a number of new problems. Some logical invariants of algebras H ∈ Θ are introduced and logical relations between different H1 and H2 in Θ are analyzed. The pape...

The two main types of law are legislation and precedents. Both types have a corresponding reasoning pattern determining legal consequences: legislation can be applied and precedents followed. The separate modelling of these two reasoning patterns using logical techniques has recently seen considerable progress. About the logical links between the two less is known, although progress has already...

Physician assistants (PAs) have been used for decades in the Canadian military. Now, PAs are being introduced in various clinical settings to provide patient care for the general population. This article reviews major developments in the PA profession across Canada over the last decade. Nearly 541 PAs are employed in Canada or work for a Canadian agency. Growing evidence demonstrates the positi...

A paper previously published in Law and Human Behavior by D. Davis and W. C. Follette (2002) argued that certain "profiling" characteristics commonly admitted into court have little or no probative value. They argued that this is especially likely to be true when the characteristic used as evidence (e.g., having an extramarital affair) is rather common in the population whereas the act in quest...

The word problem for inverse monoids generated by a set Γ subject to relations of the form e = f , where e and f are both idempotents in the free inverse monoid generated by Γ , is investigated. It is shown that for every fixed monoid of this form the word problem can be solved in polynomial time which solves an open problem of Margolis and Meakin. For the uniform word problem, where the presen...