Inaug.-dis.--Zürich. / "Litteraturnachweis für die citate": p. [69].

Inaug.-dis.--Zürich. / "Litteraturnachweis für die citate": p. [69].

Thesis--University of Göteborg, 1972. / Includes bibliographical references.

Inaug-diss.--Tübingen.

Inaug-diss.--Tübingen.

There is a need for outcome measurement tools which are able to provide accurate and reliable information regarding the efficiency and efficacy of therapeutic intervention of soft tissue injury e.g. ligament tear. Electrical activity within the body tissues has been shown to be influenced by the tissue state, and following injury, bioelectric changes have been demonstrated for example in bone healing and nerve regeneration. This project considers the relationship between the electrical potentials recorded from the skin surface and clinical recovery following a soft tissue lesion. The measurement of the skin potential is not new but the application and approach used is novel in that a non invasive differential skin surface potential is used instead of the traditional and invasive transcutaneous potential. The differential potential was initially investigated in non injured subjects in order to gain an understanding of its character and behaviour. Simultaneous monitoring of environmental, physiological and psychological factors enabled evaluation of their influence on the generation mechanisms. In order to carry out the work, specialist instrumentation was designed and computer software developed. Injured subjects were recruited during two test series and the results compared with those obtained from the non-injured subjects. Differences in potential profiles were marked on occasions. However a significant percentage of injured subjects presented a profile which was very similar to the non injured subject potentials. The failure to demonstrate consistent differences between potentials from the groups may reflect the lability of tissue potentials or that their behaviour is not purely related to local tissue state. Psychological factors were shown to exert influences on the potentials and differences in environmental and physiological conditions may also be responsible for the variations seen. The refinement of the test apparatus and protocol which is discussed may facilitate more discriminative data collection.

This dissertation analyzes the Wigner-Poisson system in the presence of an external Coulomb potential. In the first part, the Weyl transform is defined and used to derive an exact quantum mechanical equation for the Weyl transform of the density function ρw (the Wigner function) known as the Wigner equation. This equation holds for any Hamiltonian which is a function of the position and momentum operators. The Wigner-Poisson system is then formally derived by imposing various assumptions on the structure of the Hamiltonian. This system describes the behaviour of an effective one-particle distribution in the presence of a large ensemble of particles. Furthermore, it allows the particles to either attract or repel each other as well as attract or repel as a whole from a fixed Coulomb source located at the origin. The second part details the question of existence and uniqueness for the Wigner-Poisson system. It is shown that provided the initial Wigner function is sufficiently regular [special characters omitted] and is a valid Wigner distribution, then the Wigner-Poisson system has a unique global mild solution [special characters omitted]. This result is independent of both the nature of the external Coulomb potential as well as the interparticle interaction.The proof of this result is accomplished by first transforming the Wigner-Poisson system into a countably infinite set of Schrödinger equations which results in what is referred to as the Schrödinger Poisson system. Using standard semigroup theory arguments, existence and uniqueness of the Schrödinger-Poisson system is established. The properties of the Wigner-Poisson system are then obtained by reversing the transformation step. Regularity results for both the Schrödinger-Poisson and the Wigner-Poisson systems are compared to the case with no external Coulomb potential. In addition, the known regularity results are extended when there is no external field. The results illustrate that the introduction of an external Coulomb potential slightly reduces the regularity of the solution. This confirms a conjecture of Brezzi and Markowich. The third part analyzes the asymptotic behaviour of the Wigner-Poisson system. If the configurational energy Εₐ,ᵦ(t) is positive for all times then by considering the Schrödinger-Poisson system, solutions will decay in the sense of Lᵖ for 2 < p < 6. This generalizes a result of Illner, Lange and Zweifel. Moreover, If the total energy is negative then the solutions will not decay in the sense of Lᵖ for any 2 < p ≤ ∞. This generalizes a result of Chadam and Glassey. Decay estimates for both the Schrödinger-Poisson and the Wigner-Poisson systems are compared to the case with no external Coulomb field. As with the regularity results, the introduction of an external Coulomb field degrades the reported decay rates of the solution. / Graduate

When a slit opening is made in a plane electrode forming the boundary between two unequal electric fields, a distortion of the fields occurs. This paper studies the influence of the slit opening on the electrical potential distribution on both sides of the slit. A theory is developed for calculating the potential at any point, and from it two methods are derived for finding curves of equal potential disturbance. Several computed curves are presented for each method. The curves suggest a simple graphical construction for approximating the potential disturbance at points not too near the slit. Because the potential disturbance is the same at image points on either side of the slit, it is found that all the important formulas can be expressed in terms of distances, without regard to sign. To facilitate the reproduction or extension of this work, a computer program in the widely used Fortran language is given for the simpler of the two methods. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A number of potentials have been suggested as approximations to the 'true' potential function for the nuclei of a diatomic molecule. The relative merits of these potentials are discussed. Whenever possible the eigenfunctions and eigenvalues corresponding to these potentials are given. For the Morse potential the calculations of the eigenfunctions and eigenvalues are reproduced in detail. These eigenfunctions are used to derive general formulae for the radial parts of the dipole and quadrupole matrix elements. The expression for the dipole matrix element is [formula omitted] and for the quadrupole matrix element [formula omitted] The symbols are defined in sections 20, 21, and 22, The expression for M[subscript D] is in agreement with the one derived by Infeld and Hull while the expression for M[subscript Q] is a result which, so far as the author is aware, has not been published in the literature. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis Investigates the Green's functions for the operator T defined by [ Equation omitted ] Here H ¹₀ (E) is a standard Sobolev space, Δ is the Laplacian, and E is a domain in which is taken to be "quasi-bounded". In particular we assume that E lies in the half-space x₁ > 0 and is bounded by the surface obtained by rotating φ(x₁) about the x₁-axis, where φ is continuous, φ(x₁) > 0 and φᵏ∈ L₁(0,+∞) for some k > 0. The Green's function G(x,y,λ) for the operator T + λ is obtained as the limit of the Green's functions for the well known problem on the truncated domain Eₓ=E ∩ [X₁ < X]. Most of the expected properties of the function are developed including the iii equality [ Equation omitted ] where K is the fundamental singularity for the domain. The eigenvalues and eigenfunctions are constructed, and it is shown that [ Equation omitted ] where λₓ,n and λn are the eigenvalues for the problem on Eₓ and E respectively. Furthermore, it is shown that the eigenvalues {λn} are positive with no finite limit point, and the corresponding eigenfurictions are complete. A detailed calculation involving the inequality displayed above shows that some iterate (Gᵏ ̊) of G(x,y,λ) is a Hilbert-Schmidt kernel. From this property of Gᵏ ̊ it follows that the series ∑λn ˉ²ᵏ ̊ is convergent. From the convergence of this series three results are derived. The first one is an expansion formula in terms of the complete set of eigenfunctions, and the second is that some iterate of the Green's function tends to zero on the boundary. The last one Is the construction of the solution H(x,λ,f), for the boundary value problem ΔH + λH = f [ Equation omitted ] for a sufficiently regular f on E. The final property of the Green's function, namely, that G(x,y,λ) tends to zero on the boundary, is proved using the fact that Gᵏ ̊is zero on the boundary, and certain inequaiitites estimating the iterates G(x,y, λ) is also shown to be unique. The asymptotic formula [ Equation omitted ] a generalization of the usual asymptotic formula of Weyl for the eigenvalues, first given by C. Clark, is derived for these quasi-bounded domains. Finally, the usual asymptotic formula due to Carleman for the eigenfunctions is shown to remain valid. / Science, Faculty of / Mathematics, Department of / Graduate