The effect of a weighted-vest strength and balance training program on obstructed walking in postmenopausal women

SUMMARY Background: Age related declines in lower extremity strength have been associated with impaired mobility and changes in gait patterns, which increase the likelihood of falls. Since community dwelling adults encounter a wide range of locomotor challenges including uneven and obstmcted walking surfaces, we examined the effect of a strength 11 and balance exercise program on obstructed walking in postmenopausal women. Objectives: This study examined the effect of a weighted-vest strength and balance exercise program on adaptations of the stance leg during obstacle walking in postmenopausal women. Methods: Eighteen women aged 44-62 years who had not engaged in regular resistance training for the past year were recruited from the St. Catharines community to participate in this study. Eleven women volunteered for an aerobic (walking), strength, and balance training program 3 times per week for 12 weeks while 7 women volunteered as controls. Measurements included: force platform dynamic balance measure of the center of pressure (COP) and ground reaction forces (GRFs) in the stance leg while going over obstacles of different heights (0,5, 10,25 and 30 cm); and isokinetic strength measures of knee and ankle extension and flexion. Results: Of the 18 women, who began the trial, 16 completed it. The EX group showed a significant increase of 40% in ankle plantar flexion strength (P < 0.05). However, no improvements in measures of COP or GRFs were observed for either group. Failure to detect any changes in measures of dynamic balance may be due to small sample size. Conclusions: Postmenopausal women experience significant improvements in ankle strength with 12 weeks of a weighted-vest balance and strength training program, however, these changes do not seem to be associated with any improvement in measures of dynamic balance.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].