We introduce the arctic matrix method for automatically proving termination of term rewriting. We use vectors and matrices over the arctic semi-ring: natural numbers extended with −∞, with the operations “max” and “plus”. This extends the matrix method for term rewriting and the arctic matrix method for string rewriting. In combination with the Dependency Pairs transformation, this allows for s...

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2 Director, Prosthetics Research Study, Seattle, Wash. AHE elective amputation must be considered plastic and reconstructive in nature. The need to create a dynamic and sensory motor end-organ should be foremost in the surgeon's mind in planning an amputation, and is emphasized here once more. The below-knee stump no longer hangs suspended in an open-end socket. The variable degrees of pressure...

In recent decades amputee management has advanced significantly. With the ad­ vent of blood flow studies and new surgical procedures, more knee joints are being saved. Physical therapists, using ad­ vanced facilitation techniques such as pro­ prioceptive neuromuscular facilitation (PNF), are better able to restore limb strength, range of motion, and coordina­ tion. Advances in the field of pros...

Proof. Let us assume that G is planar but not free planar. Then there exists an edge xy not belonging to the graph whom adding to the graph it becomes non-planar. Then in G for an arbitrary cycle C through x, y there exists a pair of screening bridges Bx and By x from y with respect to C, i. e. either Bx and By are not placeable on one side against C or they are connected [i.e. not placeable to...

In the paper the “way-below” relation, in symbols x y, is introduced. Some authors prefer the term “relatively compact” or “way inside”, since in the poset of open sets of a topology it is natural to read U V as “U is relatively compact in V ”. A compact element of a poset (or an element isolated from below) is defined to be way below itself. So, the compactness in the poset of open sets of a t...

It was 3:15 A.M. on a cold night in Urbana, Illinois about 25 years ago. I had been on my feet since the previous morning, preparing the experiment. Professor Enrico Gratton had instructed me to machine a brass piece to replace a window in the cryostat. I finished the piece on a lathe, drilled a hole in the center, soldered a 1/4-in. copper tube and sealed the end outside the cryostat with a co...

We apply the inductive counting technique to nondetermin-istic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. As a con...

Throughout the history of lower-extremity amputation surgery, the relative emphasis placed on various parts of the procedure has undergone many changes as new techniques have become available and as new goals have been appreciated. At present, the amount and direction of available knowledge demand the surgeon's concern with fundamental principles. Since some of these problems must be considered...