We extend the classical Ambarzumyan's theorem for the Sturm-Liouville equation, which is concerned only with the Neumann boundary conditions, to the general boundary conditions, by imposing an additional condition on the potential function. Our result supplements Poschel-Trubowitz's inverse spectral theory. We also have parallel results for the vectorial Sturm-Liouville system.

In this work, we investigate c-optimal design for polynomial regression model without intercept. Huang and Chen (1996) showed that the c-optimal design for the dth degree polynomial with intercept is still the optimal design for the no-intercept model for estimating certain individual coe cients over [−1, 1]. We found the c-optimal designs explicitly for estimating other individual coe cients over [−1, 1], which have not been obtained earlier. For the no-intercept model, it is shown that the support points are scale invariant over [−b, b]. Finally some special cases are discussed for estimating the coe cients of the 2nd degree polynomial without intercept by Elfving theorem over nonsymmetric interval [a, b].

A mixture experiment is an experiments in which the q-ingredients are nonnegative and subject to the simplex restriction on the (q-1)-dimentional probability simplex. In this work , we investigate the robust A-optimal designs for mixture experiments with uncertainty on the linear, quadratic models considered by Scheffe' (1958). In Chan (2000), a review on the optimal designs including A-optimal designs are presented for each of the Scheffe's linear and quadratic models. We will use these results to find the robust A-optimal design for the linear and quadratic models under some robust A-criteria. It is shown with the two types of robust A-criteria defined here, there exists a convex combination of the individual A-optimal designs for linear and quadratic models respectively to be robust A-optimal. In the end, we compare efficiencies of these optimal designs with respect to different A-criteria.

If the market of military procurement conforms to the double auction (Chatterjee and Samuelson, 1983), the government and the manufacturer can try to reach a binding agreement and maximize the monopoly profit. When they both comply with the agreement, the game constitutes a cooperative game. The government and the firm can extend the periods of the game from one to two through signing the research and development contract. When they carry out the research and development contract in the second phase, the trading probability in the first phase that is double auction model will rise. However the R&D contract causes an increase of transaction probability, the market offers an opportunity let the ineligible manufacturer participate in the defense procurement. We can find the trade-off relationship between the advancement of trading probability and the appearances of unqualified firm. The result is consistent with Inefficiency theorem that an incentive-compatible mechanism which is ex post efficient will not be individual theorem.

In this paper we discuss the electoral behavior of the 7th Legislator Election in single-member districts. The system impacted the election essentially. According to Median Voter Theorem by Anthony Downs, the candidates become imperious to look for support from the median voters rather than the partisans. And the candidates manipulate the elections with moderate campaign strategies. Base on Downs¡¦ theory, in this paper we extended the analysis by considering conditions such as the properties of electoral districts and candidates¡¦ status to clarify the electoral behavior in the election.

Die vorliegende Arbeit kombiniert Aspekte der nichtlinearen Dynamik mit denen der Unordnungsphysik. Die bekannte Standardabbildung wird mit einem räumlich ungeordneten aber periodischen Potential modifiziert. Transportexponenten sowohl für den Impuls als auch die kanonisch konjugierte Koordinate für das Standard- und das Zufallsmodell werden gegenübergestellt. Für das Zufallspotential ergibt sich verstärkter Transport. Gemittelte Transportexponenten des Zufallspotentials werden präsentiert und für verschiedene Systemausdehnungen verglichen. / The thesis at hand combines aspects of nonlinear dynamics with the physics of disorder. The standard map potential is replaced by a spatially quenched random periodic potential. Transport exponents for the standard and the random model are determined for the momentum as well as the canonically conjugate coordinate. Transport for the disordered potential is increased in comparison to the standard map. For the random case, quenched average transport exponents are presented. Finite-size effects are examined.

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 195-204). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 107-111).

Thesis (Ph. D.)--Oregon State University, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 43-46). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 1226-131).