The rate of convergence is a useful measure of the performance of an algorithm. Knowledge of the rate can help determine which algorithm is best suited for a given problem. This research is a study of the rate of convergence of a few algorithms used for nonlinear programming problems. The Newton-Raphson procedure and a higher order procedure used for the solution of nonlinear equations is studied. Both the convergence and the rate of convergence for the multivariate Newton-Raphson procedure is presented in the simple format of the Newton-Raphson procedure for scalar functions. A higher order procedure, which results directly from Taylor series expansion is presented. Its convergence is established and a measure for the rate of convergence is obtained. A multivariate generalization of this higher order procedure is seen to have little practical value. In analyzing the simplex algorithm, it was not possible to obtain an expression for its rate of convergence, however, an expression for the improvement in the objective function between successive iterations is obtained. This expression is entirely in terms of the original problem rather than intermediate computations. The bound, due to Kantorovich, for the rate of convergence of the optimal gradient method used in solution for a system of linear equations is shown to hold for the general unconstrained quadratic programming problem. The result is then extended for the general directional procedure. Rosen presented a bound for the rate of convergence of his algorithm. The bound was obtained under very strict assumptions of the computational procedure. It is seen that under the same assumptions, tighter bounds are available for Rosen's method and that these bounds are also applicable under less stringent assumptions about the computational procedure. / Ph. D.

Introduction: Numerous past reports have mentioned or have been totally concerned with the significance of spermatozoan agglutination following treatment with blood sera, female genital fluids and other biological and synthetic media. Since semen is a colloid (undissolved particles suspended in a suitable medium such as gas, liquid, solid), spermatozoan agglutination should be at least partially definable by physical chemical measurements and should thereby be predicted and controlled... / Ph. D.

The false lock characteristics of a sampled-data phase lock loop containing a phase detector with a sawtooth characteristic are investigated. The ideal processor of data operated on by such a phase detector nonlinearity is derived in open-loop form. A second system is proposed which is shown to approximate the operation of the ideal system with increasing accuracy for decreasing noise variance. The operation of the approximate system is interpreted in geometric terms. This geometric interpretation is used to place a lower bound on the probability of false lock of the ideal system. A suboptimal system which uses feedback and a time-varying linear filter is analyzed. It was necessary to use a computer to perform the integration leading to the probability distribution of the error of this system. The bound on the probability of false lock for the ideal system is compared with the probability of a similar error for the suboptimal system. It is concluded that this bound is a conservative one. / Ph. D.

Three different definitions for the determinant of a matrix over arbitrary lattices have been developed to determine which properties and relations were reminiscent of the determinant or permanent of elementary algebra. In each determinant there are properties concerning: the elements of the matrix in the expansion of its determinant; the determinant of a matrix and its transpose; a principle of duality for rows and columns; the interchange of rows and columns; the determinant of a matrix formed from another by a row or column meet of certain elements; and evaluations of certain special matrices. An expansion by row or column is given for one determinant and a lemma on inverses is proven in light of another. A preliminary section on Lattice Theory is also included. / Master of Science

The purpose of this research is to improve area Automatic Generation Control (AGC) by using the Multi-Pass Dynamic Programming developed in this research. The AGC of power systems coordinates the Load Frequency Control problem and the Economic Dispatch problem together to form a dynamic optimal control problem. A power system was partitioned into the Electric Power Network subsystem and the Mechanical Power Control subsystem. Earlier work has solved the Electric Network subsystem control problem, used analytical methods to find optimal trajectories and controls for the Mechanical Power Control subsystem, but only for the limited case of two generators. This research develops the multi-pass dynamic programming, checks convergence, derives the conditions for singular solutions and provides optimal control sequences and optimal trajectories for cases involving several generators. Parameter sensitivity is also studied here. Finally, some consideration is given to the comparison of multi-pass dynamic programming and conventional dynamic programming. / Master of Science

The objective of this thesis is to study the fluid oscillation modes in compact stars, understand their properties and infer stellar structures from their frequencies. The first part of the thesis focuses on the Newtonian theory of stellar pulsation and the Cowling approximation (CA), which neglects the change in gravitational potential. We modify the conventional CA, devise a more accurate version of the CA and calculate the first-order correction to the conventional CA. In the second part, we apply the variational approximation method proposed by Chandrasekhar [Astrophys. J. 139,664 (1963)] and δ-perturbation expansion proposed by Bender et. al. [J. Maths. Phys. 30, 1447 (1989)] to explain the universality in the relationships between the fundamental mode frequency and the moment of inertia of neutron stars, which was discovered by Lau et. al. [Astrophys. J. 714, 1234 (2010)]. We reveal that stiff equations of state are the conditions for the observed universality. In the third part, we consider the relativistic pulsation formulation and relativistic CAs for compact stars. We unify several known CAs with a single second-order differential equation. We also extend the modified CA derived from the formalism established by Allen et. al. [Phys. Rev. D 58, 124012 (1998)] to include the effect of buoyancy. Finally, we find the first-order and the second-order post-Newtonian expansions for the nonradial pulsations in quark stars. We derive an analytic formula expressing the fundamental mode frequency in terms of the compactness of quark stars. As a result, we are able to verify the universality mentioned above for quark stars. / 這論文是對在牛頓力學以及相對論框架下緻密星流體振盪的研究結果。論文第一部分集中討論牛頓力學下流體振盪以及近似方法。這近似方法忽略重力勢的擾動，令系統由四階微分方程減少為二階微分方程。我們修正了已往的近似方法和提出一個更精準的近似方法。第二部分包括變分近似方法。我們利用該方法和δ微擾理論解釋基本模式頻率的普通性。第三部分包括相對論框架下緻密星流體振盪和近似方法。我們以一條二階微分方程總結之前出現的近似方法並且在近似方法中加入浮力。最後，我們執行一階和二階的後牛頓展開，以分析夸克星的基本模式。我們驗證了展開的準確度和發現了基本模式頻率的方程。 / Chan, Tsang Keung = 有關在緻密星中流體振盪的研究 / 陳增強. / Thesis M.Phil. Chinese University of Hong Kong 2013. / Abstracts also in Chinese. / Title from PDF title page (viewed on 07, October, 2016). / Chan, Tsang Keung = You guan zai zhi mi xing zhong liu ti zhen dang de yan jiu / Chen Zengqiang. / Detailed summary in vernacular field only.

Thesis (S.M. in Biology)--Joint Program in Biological Oceanography (Massachusetts Institute of Technology, Dept. of Biology; and the Woods Hole Oceanographic Institution), 1999. / Includes bibliographical references (leaves 23-30). / Phytoplankton mortality (herbivory) and bacterivory were examined experimentally in West Neck Bay and Coecles Harbor, Long Island, NY from April through September, 1998. Small algae (<5 [tm diameter) dominated phytoplankton communities in both ecosystems throughout the summer, and zooplankton were also small (mostly <40 tm). Generally, plankton abundances were indicative of eutrophic ecosystems. Oscillations in standing stocks and mortality of prey indicated tight coupling of growth and grazing mortality in both bays. Phytoplankton mortality rates accounted for the removal of 14% to 65% of total phytoplankton standing stocks daily, while bacterivory accounted for the removal of 14% to 88% of total bacterial standing stocks daily. Estimates of carbon consumption revealed high energy flux through the nano- and microzooplankton assemblages of these estuarine environments. / by Katie Rose Boissonneault Cellineri. / S.M.in Biology

We propose a Markov chain model for credit rating changes. We do not use any distributional assumptions on the asset values of the rated companies but directly model the rating transitions process. The parameters of the model are estimated by a maximum likelihood approach using historical rating transitions and heuristic global optimization techniques. We benchmark the model against a GLMM model in the context of bond portfolio risk management. The proposed model yields stronger dependencies and higher risks than the GLMM model. As a result, the risk optimal portfolios are more conservative than the decisions resulting from the benchmark model.