This thesis considers two isoperimetric inequalities for the eigenvalues of the Laplacian on a family of spherically symmetric Riemannian manifolds. The Payne-Pólya-Weinberger Conjecture (PPW) states that for a bounded domain Ω in Euclidean space Rn, the ratio λ1(Ω)/λ0(Ω) of the first two eigenvalues of the Dirichlet Laplacian is bounded by the corresponding eigenvalue ratio for the Dirichlet Laplacian on the ball BΩof equal volume. The Szegö-Weinberger inequality states that for a bounded domain Ω in Euclidean space Rn, the first nonzero eigenvalue of the Neumann Laplacian μ1(Ω) is maximized on the ball BΩ of the same volume. In the first three chapters we will look at the known work for the manifolds Rn and Hn. Then we will take a family a spherically symmetric manifolds given by Rn with a spherically symmetric metric determined by a radially symmetric function f. We will then give a PPW-type upper bound for the eigenvalue gap, λ1(Ω) − λ0(Ω), and the ratio λ1(Ω)/λ0(Ω) on a family of symmetric bounded domains in this space. Finally, we prove the Szegö-Weinberger inequality for this same class of domains.

<p>This dissertation addresses one of the most vexing issues in American foreign policy: Under what circumstances should the United States use military force in pursuit of national interests? Despite not having a policy upon entering office or articulating one throughout its first term, the Reagan administration used military force numerous times. Two-weeks following Reagan's landslide reelection victory, Secretary of Defense Caspar W. Weinberger articulated six tests for when and how to use military force, which surprisingly seemed to call for restraint. Through the examination of three case studies, the Reagan administration's decisions are found to have been influenced by the assimilation of lessons from Vietnam, the reading of public pulse, the desire to placate Congress, and the need to protect the nation's strategic interests. All these factors, ultimately codified by Weinberger, were considered by the leaders in the Reagan administration as they tried to expand the military's ability to help the U.S. meet an increasingly wider range of threats. Thus this dissertation will show that, contrary to what one finds in contemporary scholarship, the Weinberger doctrine was intended as a policy to legitimize the use of military force as a tool of statecraft, rather than an endorsement to reserve force as a last resort after other instruments of power have failed.</p> / Dissertation

Thesis (M.A. in National Security Affairs)--Naval Postgraduate School, June 2006. / Thesis Advisor(s): Donald Abenheim. "June 2006." AD-A451 305. Includes bibliographical references (p. 89-100).

Thesis (Master of Military Studies)-Marine Corps Command and Staff College, 2008. / Title from title page of PDF document (viewed on: Feb 8, 2010). Includes bibliographical references.

Thesis (Master of Military Studies)-Marine Corps Command and Staff College, 2008. / Title from title page of PDF document (viewed on: Feb 2, 2010). Includes bibliographical references.

This paper examines the different share valuation methods and principles likely to be used by a court in determining the fair value of dissenting shareholders’ shares in appraisal proceedings in terms of section 164(14) of the Companies Act 2008. It is submitted that the valuation principles and methods used by the courts will affect the operation of the triggering actions contemplated in subsections 164(2)(a) - (b). It is proposed that section 164 court appraisals are likely to be guided by the valuation methods and principles developed in section 252 and section 440K court appraisals under the Companies Act 1973, as well as by the decisions of the courts in the state of Delaware relating to share valuations under the appraisal remedy. It is further proposed that the purpose ascribed to the appraisal remedy will influence the application of these valuation methods and principles. / Mercantile Law / LL.M. (Corporate law)

This paper examines the different share valuation methods and principles likely to be used by a court in determining the fair value of dissenting shareholders’ shares in appraisal proceedings in terms of section 164(14) of the Companies Act 2008. It is submitted that the valuation principles and methods used by the courts will affect the operation of the triggering actions contemplated in subsections 164(2)(a) - (b). It is proposed that section 164 court appraisals are likely to be guided by the valuation methods and principles developed in section 252 and section 440K court appraisals under the Companies Act 1973, as well as by the decisions of the courts in the state of Delaware relating to share valuations under the appraisal remedy. It is further proposed that the purpose ascribed to the appraisal remedy will influence the application of these valuation methods and principles. / Mercantile Law / LL. M. (Corporate law)