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A three-dimensional method of stress analysis using finite element techniques is presented for determining the stress distribution in centrifugal impellers. It can treat all of the three types of loading possible in an inpeller, viz centrifugal, thermal and fluid. The method has no known limitations with regards to the geometric factors such as asymnetry of disk, blade curvature, presence of a cover disk or shroud, single or double sided impeller etc. A comparison of results with available experimental photoelastic results is presented with good agreement. The problem of the inter-blade bending effect, on the stress characteristics of an impeller, with relevance to the number of blades is studied in some depth. An insight into the effect of blade curvature on the stress characteristics of an impeller is also achieved. As an extension of the above work, a method is proposed for the analysis of the dynamic, behaviour of impe1lers, achieving a reasonable degree of success, particularly considering the limited period of time that was available for such an exercise.

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The theory of 2-convex norms is applied to Banach space valued random vectors. Use is made of a norm on random vectors, introduced by Pisier, equal to the 2-absolutely summing norm on an associated space of operators. For Q the variance of some centred Gaussian random vector in a separable Banach space it is shown that, necessarily, Q factors through l2 as a product of 2-summing operators. This factorisation condition is sufficient when the Banach space is of Gaussian type 2. The stochastic integral of a family of operators with respect to a cylindrical Q-Wiener process is shown to exist under a Hölder continuity condition involving the 2-summing norm. A Langevin equation dZt + ΛZtdt = dBt with values in a separable Banach space is studied. The operator Λ is closed and densely defined. A weak solution (Zt ; Bt), where Zt is centred, Gaussian and stationary while Bt is a Q-Wiener process, is given when iΛ and iΛ* generate C0 groups and the resolvent of Λ is uniformly bounded on the imaginary axis. Both Zt and Bt are stochastic integrals with respect to a spectral Q-Wiener process. The convolution of two arcsine probability densities is shown to be an elliptic integral. Ensembles (Xn)n≥1 of random Hermitian matrices are considered. Each Xn is n by n with distribution invariant under unitary conjugation and induced by a positive weight function on R. New proofs are given of results, due to Boutet de Monvel, Pastur, Shcherbina and Sodin, on the behaviour of the empirical distribution of the eigenvalues of Xn as n tends to infinity. Results in analytic function theory are proved. An H∞ interpolating sequence in the disc D whose Horowitz product does not lie in the Bergman space L2a(D) is exhibited. A condition satisfied by Banach spaces of non-trivial analytic Lusin cotype is obtained.

Pick's theorem states that there exists a function in H1, which is bounded by 1 and takes given values at given points, if and only if a certain matrix is positive. H1 is the space of multipliers of H2 and this theorem has a natural generalisation when H1 is replaced by the space of multipliers of a general reproducing kernel Hilbert space H(K) (where K is the reproducing kernel). J. Agler showed that this generalised theorem is true when H(K) is a certain Sobolev space or the Dirichlet space. This thesis widens Agler's approach to cover reproducing kernel Hilbert spaces in general and derives sucient (and usable) conditions on the kernel K, for the generalised Pick's theorem to be true for H(K). These conditions are then used to prove Pick's theorem for certain weighted Hardy and Sobolev spaces and for a functional Hilbert space introduced by Saitoh. The reproducing kernel approach is then used to derived results for several related problems. These include the uniqueness of the optimal interpolating multiplier, the case of operator-valued functions and a proof of the Adamyan-Arov-Kren theorem.

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No description available.