OPERATIONS ON THE SPINAL COLUMN

Column-to-row Operations on Partitions: the Envelopes

Conjugation and the Bulgarian solitaire move are considered as extreme cases of several column-to-row operations on integer partitions. Each operation generates a state diagram on the partitions of n, which leads to the questions: How many Garden of Eden states are there? How many cycle states? How many connected components? All of these questions are answered for partitions of n when at least ...

The Fifth Column: On Using Operations Research to Fund Operations Research (Economically)

The Preparation for Battle Many, many years ago in a nameless western state there existed a small but feisty operations research program (OR) of the hands-on variety. This program was renowned for requiring students to do real projects in which real costs were reduced and real profits were made. It was not long before this program attracted the attention of one of the educational arms of one of...

Some Properties of Line and Column Operations on Matrices

The articles [8], [13], [17], [11], [1], [18], [5], [6], [2], [7], [15], [16], [9], [10], [20], [4], [3], [21], [12], [14], and [19] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: j, k, l, n, m, i are natural numbers, K is a field, a is an element of K, M , M1 are matrices over K of dimension n × m, and A is a matrix over K of dimension n...

Movements of the lumbar spinal column.

Observations on the management of failed spinal operations.

A system is presented for the analysis of failure after spinal operations: 1) outright failure; 2) temporary relief; 3) failure in spondylolisthesis; and 4) infections. With this system it is possible to trace the causes of failure and to correct some of them. When they are used as a guide before operation, the recommendations made should help to prevent many failures.